Use of Ganna Ray Attenuation; Acoustic Velocity; and Electrical Resistivity in the Extracation of Sediment Physical Properties

Sediment physical properties, such as porosity, shear strength, shear modulus, and grain size, from six different geographical marine environments (Central Arctic Ocean, Central Scotian Shelf, Gulf of Mexico, Caribbean Sea, North-Eastern Pacific, Western Equatorial Pacific and Mid-Atlantic Ridge) were analyzed and correlated with non-destructive measurements of compressional wave velocity, bulk density and electrical resistivity'. In coarse grained sediments (median grain diameter >4 μm) with a sand fraction greater than 15%, larger grain size is associated with higher velocity. In fine grained sediments (median grain diameter < 4 μm) velocity does not correlate with median grain size. However, a pronounced linear relationship exits between compressional wave velocity and percent clay fraction (grain diameter < 2 μm) regardless of sediment grain size. The use of electrical resistivity is limited for predicting porosity in unconsolidated sediments. In general, the trend of decreasing sedimentary porosity with increasing electrical resistivity, is consistent with previous observations (e.g., Archie, 1942). However, the trends are sediment-type dependent and therefore resistivity measurements cannot be used as sole predictor of porosity. Compressional wave velocity and bulk density, expressed as the elastic parameter b ( v: * p8 ) correlate well with miniature vane shear data. These non-destructive measurements can be used to predict undrained shear strength.

In coarse grained sediments (median grain diameter >4 µm) with a sand fraction greater than 15%, larger grain size is associated with higher velocity. In fine grained sediments (median grain diameter < 4 µm) velocity does not correlate with median grain size. However, a pronounced linear relationship exits between compressional wave velocity and percent clay fraction (grain diameter < 2 µm) regardless of sediment grain size.
The use of electrical resistivity is limited for predicting porosity in unconsolidated sediments. In general, the trend of decreasing sedimentary porosity with increasing electrical resistivity, is consistent with previous observations (e.g., .
However, the trends are sediment-type dependent and therefore resistivity measurements cannot be used as sole predictor of porosity.
Compressional wave velocity and bulk density, expressed as the elastic parameter b ( v: * p 8 ) correlate well with miniature vane shear data. These non-destructive measurements can be used to predict undrained shear strength.

PREFACE
This thesis was prepared and submitted in the manuscript style and includes three manuscripts and one appendix. The manuscripts are formatted for publication in a scholarly journal. Each manuscript describes the evaluation of physical properties by non-destructive measurements such as gamma-ray attenuation, compressional wave velocity, and electrical resistivity. These non-destructive measurements are compared to direct measurements of porosity, grain size and shear strength. Relationships were found between sediment properties and non-destructive measurements from a wide range of marine environments to increase the boarder applicability of the findings.
Manuscript I focuses on the correlation of compressional wave velocity and bulk density with grain size. The prediction of porosity by means of electrical resistivity, compressional wave velocity and bulk density comprises Manuscript II. The last manuscript describes the prediction of shear parameters such as shear strength and shear modulus using compressional wave velocity and bulk density.

LIST OF TABLES
Grain size also depends on with compressional wave velocity, although to a lesser extent. These parameters are of great interest for the geotechnical engineer.
Developing fully automated systems such as Multi-Sensor-Tracks (MST) to measure compressional wave velocity and other parameters (e.g., gamma-ray attenuation, electrical resistivity, and magnetic susceptibility), which also can be related to physical properties, enabled us to correlate between non-destructive measurements and physical properties. Many studies concern the relationships between compressional wave velocity and physical properties such as bulk density, porosity, and grain size . Impedance, the product of compressional wave velocity and bulk density has also been used as an acoustic property, to determine physical properties .
The purpose of this paper is to determine the empirical correlation between compressional wave velocity and grain size. The aim is to present a relationship that is significant enough to allow for prediction of grain size. This prediction can be made in terms of median grain diameter or in terms of fractional contents of different particle sizes (Sand, Silt, Clay).
The empirical correlation was performed by using laboratory determined grain size values and non-destructive evaluated compressional wave velocity. Furthermore the incorporation of non-destructive derived bulk density (GRAPE density) is used as a factor to improve the correlation results.
For this study, sediment physical properties of five cores from three different geographic marine environments were analyzed and correlated: (1) three cores from the Central Arctic Ocean (Lomonosov Ridge); one core from the Central Scotian Shelf (Emerald Basin); and one core from the Western Equatorial Pacific (Ontong Java Plateau). The core analyses were performed for each respective scientific project and not by the author, however, a sufficient description of the testing conditions and physical properties is provided.

Background
In general, the velocity of a compressional wave is an expression of the elastic properties of the medium, through which it penetrates. The basic equation for the velocity of a compressional wave is: (1) where VP is the compressional wave velocity (mis), B is the bulk modulus (KN/m 2 ), G is the shear modulus (KN/m 2 ), and PB is the bulk density (Mg/m 3 ) .
Other physical properties such as porosity and grain size affect the compressional wave velocity through its effects on the elasticity of the sediments (bulk modulus and shear modulus) and on the bulk density. A general trend is observed in the relationship between velocity and grain size: an increase in grain size is associated with an increase in velocity Morgan, 1969;.
The grain size affects the velocity predominately by its influence on porosity. The porosity, in tum, highly influences the bulk density and the bulk modulus of the sediments and thus indirectly influences the velocity. The influence of porosity on the bulk modulus is straight forward. Marine sediments can be considered as two-phase mixtures and consequently the porosity is an expression of the water content since typically no gaseous phase is present (100% saturated). The relationship between porosity and bulk modulus is given by Equation (2): (2) where BF is the pore fluid bulk modulus (KN/m 2 ), Bs is the bulk modulus of the mineral constituent (KN/m 2 ), and ~ is the fractional porosity ( -)  ).
This equation is only valid for sediments that lack rigidity. However, to emphasize the influence of porosity on bulk modulus, this equation is appropriate. From Equation (2) it can be deduced that a decrease in porosity decreases the denominator and thus decreases the influence of the water bulk modulus on the overall bulk modulus.
Although within the same order of magnitude, the bulk modulus of water is lower than the bulk modulus of the mineral solids. Therefore, a decrease in water increases the bulk modulus. An increase in bulk modulus is associated with an increase in compressional wave velocity (Equation (1 )).
In comparison to the porosity-bulk modulus relationship, the influence of grain size on porosity is very complex. Numerous factors affect this relationship. The most important interrelated factors, in terms of the mineral grains and influence on porosity, are grain size, uniformity of grain size (sorting), grain shape, packing of grains, and mineralogy. In general, an increase in porosity is interdependent with a decrease in grain size . Some general observations of the influences of mineral grain characteristics on porosity are: (1) well-sorted sediments (high uniformity) have higher porosities; (2) fine grained platy sediments have a more porous structure than coarser spherical sediments due to interparticle forces that cause the fine particles to stick together and do not allow a reorientation of the particles to form a more dense packing;

and
(3) well rounded (spherical) grains are less porous than angular grains.
Also, grain size influences the sediment shear modulus and, therefore, influences velocity . Given the same velocity, less solid grain-to-grain contact occur in fine grained sediments with oriented, platy grains than in coarser sediments with more spherical grains. This grain-to-grain contact (packing) influences the shear modulus in terms of an increasing shear modulus with increase in grain-tograin contacts. This, however, contributes, to a lesser extent, to the velocity-grain size relationship.
The grain size also affects bulk density. The relationship between bulk density and porosity was investigated in earlier studies . As expected, a decrease in porosity is linearly related to an increase in bulk density. A decrease in porosity increases the bulk modulus and thus increases the velocity. Since bulk density is in the denominator of Equation (1 ), an increase is linked to a decrease in velocity when other parameters remain constant. However, the influence of porosity (in terms of grain size) on bulk density and hence on velocity, when compared with its influence on the bulk modulus is negligible. This becomes evident when absolute values are compared.
A decrease in porosity as a consequence of a variation in grain size changes bulk density by less than 10-1 ' whereas the bulk modulus changes under the same conditions by at least 10 3 .

Methods
Compressional Wave Velocity. Compressional wave velocity was determined using a P-wave logger (PWL) on the Multi Sensor Track (GEOTEK). An ultrasonic pulse with a dominant frequency of 500 kHz was transmitted across the unopened core sample and the travel time was measured. The velocity was then calculated by dividing the core diameter by the pulse travel time. Corrections for transducer and core liner time delays as well as for core diameter deviations were applied (APPENDIX A, .
Bulk Density. Bulk density measurements were performed using a gamma-ray attenuation porosity evaluator (GRAPE) . The measurement of sediment bulk density using gamma-rays is based on the principles of Compton scattering and attenuation. A parallel, monoenergetic beam of gamma-rays {1 37 Cs) penetrates the core sample and is detected on the opposite side by a scintillation counter. When passing through the sample some of the gamma-rays are absorbed or scattered and lose energy and direction, respectively. The scintillation counter detects the gamma-rays that pass through the absorber without any loss of energy. The energy loss and the attenuation respectively are directly related to bulk density. A discrete value for bulk density is then derived by calibrating the attenuation of gamma-rays through the unopened core sample with the attenuation through standards of aluminum and water (APPENDIX A, . Porosity. The porosity ~ was determined from the bulk density using an estimated specific gravity of 2.75 with Eq. (17): where Ps is the specific gravity (Mg/m 3 ), PB is the bulk density (Mg/m 3 ), and PF is the pore fluid density (Mg/m 3 ) (density of sea water, Psw = 1.025 Mg/m 3 ).
Grain Size Analysis: Grain size analyses were performed using two different methods. Sediments from the Central Arctic Ocean (Lomonosov Ridge) were analyzed using X-ray attenuation (SediGraph gram size analyzer) and the coulter counter method (Coulter Counter) was used to determine the grain size of sediments from the Central Scotian Shelf (Emerald Basin) and the Western Equatorial Pacific (Ontong Java Plateau).
The Sedigraph grain size analyzer measures the attenuation of X-rays by particles that are suspended in a solution . The SediGraph determines the concentration of particles remaining at decreasing depth within a suspension as a function of time. The principle of Stoke's Law of Settling is used to convert vertical profiles of suspension density to weight percentages of grain size.
The coulter counter method is based on a principle where particles suspended in an electrolyte pass through a small aperture with electrodes on both sides. The passing particles displace their own volume of electrolyte, whereby the resistance in the current is changed in proportion of the volumetric size of the particles. The number of changes per time reflects the number of particles per volume in suspension.
Before analysis, the sediments were chemically pretreated to remove orgamc matter and to disaggregate the particles. The suspension was washed on a 63 µm sieve to separate the sand-sized grains from silt and clay. The retained portion was oven dried and then dry sieved, following ASTM D~2 l/422. The clay and silt fraction ( <63 µm) was analyzed in the Coulter Counter and in the Sedigraph, respectively.
Finally, the results of both tests were combined and a cumulative semi-logarithmic frequency curve for each analyzed sample was developed. The median grain diameter which is the value that corresponds to the 50% mark (d 50 ) on the cumulative frequency curve was then determined.

Site Description and Sediment Properties
Five cores from three different sites were selected for this study. The maJor geographic environments are: (1) the Central Arctic Ocean (Lomonosov Ridge), (2) the Scotian Shelf (Emerald Basin), and (3) the Western Equatorial Pacific (Ontong Java Plateau). A summary of the cores used in this study and a detailed description of the locations are shown in Table 1.
Central Arctic Ocean (Lomonosov Ridge). The Lomonosov Ridge is located in the Central Arctic Ocean between the longitude 130° to 155° East and the latitude 85° to 90° North ( Figure 1 ). The Lomonosov Ridge separates the Markarov Basin and the Amundsen Basin. The ridge crest is at its highest less than 1000 m below sea level and drops down on both sides into the adjacent basins with depths of more than 3000 meters below sea level. The sediments of the Lomonosov Ridge are predominantly hemipelagic with minor ice rafting components.
The sediments of the retrieved cores from the Lomonosov Ridge (96/09-1 pc, 96/12-lpc, and 96/13-lpc) are described as clays ~nd silty clays and the lithology was divided into three geotechnical·units . Unit I consists of a thin layer of dark brown clay at the surface and is underlain by a layer of yellowish brown to dark gray silty clay. The second Unit II is composed of olive gray clay and silty clay and unit III is an indurated dark olive gray silty clay ( Figure 2 to Figure 4 )  Basin is filled with glacial till that is overlain by Quaternary fine grained glaciomarine and marine sediments and underlain by firm bedrock. In general the sediment stratigraphy can be divided into three major geotechnical units ( Figure 6). However, the sediments retrieved with core 87003-02 are only composed of the upper two units.
Unit I consists predominantly of marine silty ~lay and clayey silt, olive gray in color.
Unit II is mainly dark gray glacio-marine silty clay . Bulk density increases uniformly with depth and no distinct variation in bulk density due to the differences in composition between Unit I and II are observed. Density ranges from 1.40 Mg/m 3 at the top of the core to 1.6 Mg/m 3 at a depth of 16.5 meters. The compressional wave velocity is relative constant with depth and has an average value of 1446 mis.
Median grain size is constant with depth and is narrowed to a very small range with an average size of 2 µm. A peak median grain size Of 20 µm appears to be anomalous at the unit break.
Western Equatorial Pacific (Ontong Java Plateau). The Ontong Java Plateau, with an area of 1.5 million km 2 , is the largest plateau found in the world oceans. It is located in the western equatorial Pacific north of the Solomon Islands ( Figure 7). The Ocean Drilling Program Site 807 A is located at the northern rim of the plateau in a water depth of 2804 meters. In general the sediments are divided into three major geotechnical units. However, grain size analyses were performed on the sediments of Unit I only and therefore this unit is emphasized in this discussion ( Figure 8).
Unit I consists primarily of silts that range from sandy silts to clayey silts.
Noticeably, the sediments are predominately composed of foraminifers and nannofossils. The nannofossil content in the sediments averages about 75% and the foraminifer abundance averages approximately 23%. The remaining fraction is composed of trace amounts of quartz and clay minerals.
Foraminifers and nannofossils are skeletal remains of pelagic orgamsms and predominantly composed of carbonate. The si~e of these particles range between 10 and 40 µm. Foraminifer and nannofossils are characterized by a hollow structure consisting of one or more affiliated chambers with wall thicknesses between 1.0 to 1.5 micrometers ( Figure 9).  Figure 10 and Figure 11 show plots of median grain size versus compressional wave velocity and impedance for all sediments. Two main data populations are observed. The hemipelagic sediments from the Central Arctic Ocean and the Central Scotian Shelf seem to form a different population than the calcareous sediments from the W estem Equatorial Pacific. The grouping of the sediments is more pronounced in the correlation of median grain size and impedance ( Figure 11 ). On this account the hemipelagic and calcareous sediments are separately investigated in the following.
Hemipelagic Silts and Clays: Plots of median grain size versus compressional wave velocity and impedance (V p x p 8 ) are shown in Figure 12 and Figure 13. The empirical relationships betwee:Q these parameters published by  and  are also presented. Two different trends are observed. Grain sizes between 1 µm and 4 µm seem to have no influence on compressional wave velocity.
The observed trend of these fine grained sediments is parallel to the velocity axis and covers nearly the whole range of velocities used in this study (1420 mis to 1600 mis).
At a median of 4 µm, the influence of the grain size on the velocity becomes more pronounced. An increase in median grain size is associated with an increase in velocity. A logarithmic regression line, fit to all data, results in a low interdependency, demonstrated by low correlation (R 2 = 0.297). An analysis of the standard error of estimate yields a value of 27 .88, i.e., the error in estimating the velocity from grain size, using the regression equation, results in an average velocity error of 27.88 mis.
The empirical relationships, proposed by  and , and the obtained logarithmic regression line are similar with Hamilton's approximation showing a lower limit and Bachman's an upper limit.
The relationship of impedance and median grain size is similar to that of velocity and median grain size ( Figure 13). Between 1 µm and 4 µm the trend is parallel to the impedance axis, indicating no distinct interdependency. Above a median grain size of 4 µm, a trend of increasing impedance with increasing median grain size is observed.
The correlation coefficient (R 2 = 0.290) suggests considerable scatter around the logarithmic regression line. The analysis of the standard error of estimate results in 105.23 Mg/m 2 s. The empirical relationship provided by  falls below the logarithmic regression line. Figure 14 shows the plot of compressional wave velocity versus the percentage of sand, silt, and clay constituents. The difference between fractions is adopted from the Udden-Wentworth size classification system for sediment grains. Therefore, the boundary between sand and silt is at 63 µm and all particles smaller than 2 µm are classified as clay. The boundary between clay versus silt may be physically better presented at 4 µm. However, data used here define less than the 2 µm size as the clay size. Linear regression lines fit to the populations of sand, silt, and clay, only show correlation with the clay fraction (R 2 = 0.598). The sand fraction shows small interdependency (R 2 = 0.432) while the silt fraction shows no correlation (R 2 = 0.122).
The relationship is the same as the velocity correlations when described in terms of impedance versus the percentage of sand, clay, and silt ( Figure 15).
In Figure 16 and Figure 17, the sand and clay fraction are extracted from the data in Figure 14 and are plotted versus compressional wave velocity. In the plot of percentage clay fraction the earlier-derived empirical relationship  is included. The slope of Hamilton's proposed relationship is lower than the slope of the regression line for the sediments used in this study. Noteworthy is the intersection of curves at 50% clay fraction. Also shown in Figure 16 are the prediction intervals (confidence 95% ). The regression analysis for the data falling into this interval results in an improved regression coefficient of 0.881.
A closer look at the relationship between percent sand fraction and compressional wave velocity shows two trends ( Figure 17). A sand fraction of approximately 15% appears to be the limit for the influence of the grain size on velocity. At lower sand contents, the data is scattered and shows no correlation with velocity. Above a sand fraction of 15% the velocity increases linear with the amount of sand in the sediment (solid line). However, the low correlation coefficient (R 2 = 0.294) suggest wide scatter around the linear regression. The regression coefficient is slightly improved where the data falls in the 95% confidence prediction interval.
Porosity is correlated with median grain size in Figure 18. In the fine-grained sediments (median grain size < 4 µm), porosity ranges between 0.4 and 0.8 and no distinct relationship is apparent. Above 4 µm, an increase in median grain size is correlated with a decrease in porosity.
Calcareous Sediments: Plots of compressional wave velocity and impedance versus median grain size of the calcareous sediments from the Western Equatorial Pacific (Ontong Java Plateau) are shown in Figure 19 and Figure 20. No distinct trend can be seen. The scatter around the regression line is too wide to predict any correlation. Contrary to the common trend of increasing velocity with increasing grain size, calcareous sediments seem to behave differently. The velocity is almost constant over the range of median grain sizes and a small decrease in velocity with increasing median grain size is indicated by the regression line. This trend is even more pronounced when comparing impedance instead of velocity with grain size.

Discussion
As the correlations show, the observed relationships between compressional wave velocity and grain size generally follow trends and prediction lines published by other authors . The discrepancy between the published regression lines  and those fit to the data ( Figure 12, Figure 13) can be attributed to the difference in the parameter that describes the grain size characteristics, to the fact that the proposed relationships may not be applicable for a wide range of sediment types, or to measurement errors.
In this study, the grain size characteristic is -expressed in terms of the median grain diameter which is defined as the 50% mark on the cumulative frequency curve (divides the normal frequency curve into to equal parts). The linear relationship, proposed by Hamilton and the polynomial relationship of Bachman, are based on the mean grain diameter after , which is defined as the mean of the average grain size of the coarsest fraction of the sediment, the finest fraction and the medium fraction and is expressed in ~-units. The difference in mean and median is only of influence when the grain size distribution is strongly skewed or of bimodal character. However, since the evaluated regression curve lies between the proposed relationships it is assumed that the difference between mean and median grain size can be neglected.
Early efforts to determine the compressional wave velocity of sediments used small chunk samples. Methods such as the resonant chamber method  suffered from the problem that the velocity could not be determined from undisturbed samples. Later, compressional wave velocity measurements were taken on chunk samples with an apparatus known as a Hamilton Frame . These samples were visually undisturbed (e.g. undistorted bedding), but likely suffered from stressrelief and sample disturbance. Compressional wave velocity measurements on wholecore samples encased in the original sample liner are considered as relatively undisturbed.
Therefore, the offset of the three relationships may be attributed to a lack of general applicability or to differences in the measurement methods of velocity due to sample disturbance.
Comparing the porosity-grain size relationship ( Figure 18) and the velocity-grain size relationship (Figure 12), interdependency is observed. In the fine-grained sediments (median grain size < 4 µm), the porosity and the grain size show no correlation. When exceeding a median grain size of 4 µm the porosity seems to be directly related to the grain size. The relationship between grain size and velocity shows the same behavior. In the fine-grained section, grain size changes have no influence on the velocity. Above 4 µm, grain size shows a more distinct trend. Since compressional wave velocity and porosity show similar trends when compared with grain size, it is apparent that grain size influences the velocity in terms of porosity.
Porosity, in tum affects the bulk modulus and thus the velocity.
This behavior can probably be attributed to the mineral-grain structure of these sediments. Fine grained sediments (silt and clay) are apt to adhere together when deposited because of physico-chemical bonds . The structure formed is controlled by interparticle forces. In marine environments, the particles are in edge to face contact and form a three-dimensional porous structure ( Figure 2 ld and f).
When subjected to overburden pressure, the weak interparticle force can not retain this porous configuration. Therefore, the porosity change is predominantly caused by pressure and particle rearrangement. This behavior is also seen by an increase in bulk density with depth, linearly related to a decrease in porosity with depth ( Figure 2 to When the median gram size mcreases, the structure formed by the particles changes. Spaces are filled with larger grains (silt,. sand) and mineral-grain structures such as in Figure 21 c and e ·are formed. Since the grains have no grain-to-grain contact, the porosity is still dominated by pressure, but the influence of particle size slightly increases. Not until the particles have grain-to grain contact ( Figure 21 a and b ), does the porosity form a strong dependency with grain size. An increase m pressure forces the particles to rearrange and the rearrangement or packing 1s dependent on the size of the grains. The amount of larger particles (sand) needed to influence the grain-to-grain structure, seems to be approximately 15% sand ( Figure   17). At this percentage and above, an increasing velocity with percent sand is observed. The correlation, observed in Figure 16 between velocity and percentage clay fraction affirms these findings. A decrease in the clay fraction is correlated with an increase in velocity.
The regression equations for the more distinct relationships between grain size and compressional velocity for the hemipelagic sediments are as follows: The lack of a relationship between median grain size and compressional wave velocity of the calcareous sediments from the Ontong Java Plateau may be explained by the nature of the calcareous particles. These particles have no physico-chemical bonds. The chamber-like structure of the foraminifers and the rigid frame of nannofossils ( Figure 9), results in a very high porosity (50% -70%). The high porosity results in low bulk moduli since water has a much lower bulk modulus (higher compressibility) than the mineral phase. The decrease in porosity due to an increase in the size of the grains that is shown to be an important factor for hemipelagic sediments seems to be of less influence when calcareous particles are abundant. The variations in porosity due to changes in grain size are limited and results in limited variations of velocity ( Figure 19).

Conclusion and Recommendations
The observations made in this study on the relationships between compressional wave velocity and grain size generally follow findings of other investigators . The results are summarized as follows: (1) Grain size affects compressional wave velocity indirectly. Grain size is one of the controls of porosity. Porosity controls bulk modulus and thus compressional wave velocity.
(2) In coarse-grained sediments, an increase in median gram size 1s directly associated with an increase in velocity. In fine-grained sediments, however, grain-size changes have little influence on the velocity. A median grain size of 4 µm and a sand content of 15% appear to be the limiting factors in the distinction between fine-grained behavior and coarse grained behavior.
(3) The use of the percent clay (grain size < 2 µm) is a much better parameter for correlation with compressional wave velocity than the median diameter parameter.
(4) When calcareous particles (nannofossils, foraminifers) are abundant in sediments, there is no relationship between velocity and grain size. The influence of the hollow structure of the particles on porosity and thus on bulk modulus and compressional wave velocity dominates. Therefore, the influence of grain size on the porosity, bulk modulus and velocity is too small to detect with standard methods.
In general, the influence of grain size on physical properties is highly complex.
The graduations and classifications developed to characterize sediments in terms of the mineral grains (size, distribution) may not be adequate to be described by compressional wave velocity. On this account considerations should be made in further studies, to employ different characteristics or limits of grain size in the correlation with velocity (e.g. the fraction of particles smaller than 3 µm might be better approximated by velocity than the fraction of 2 µm particles).

Resistivity-Porosity Relationships in Unconsolidated Marine Sediments
Electrical resistivity measurements as a predictor of porosity are used extensively by the hydrocarbon exploration industry. Porosity is of fundamental interest in the exploration of hydrocarbon resources, since it affects the quality of both the source rock and the reservoir rock. In geotechnical engineering, the porosity is of primary interest in the prediction of soil and sediment behavior.
Archie ( Commonly, electrical resistivity is measured in situ by means of down-hole logging tools. With the development and introduction of smaller resistivity probes (Wenner spread, galvanic method) and the extension of investigation of the sea floor, marine scientists adopted the resistivity method to evaluate porosity of unconsolidated marine sediments .
However, large scatter is observed in the relationship of porosity and electrical resistivity of unconsolidated marine sediments. This suggests that Archie's Law, applied on unconsolidated marine sediments, may not be an effective predictor of porosity.
The purpose of this work is to investigate the accuracy of using electrical resistivity to predict the porosity of unconsolidated marine sediments. Therefore, resistivity measurements of cores from three different geological marine environments were analyzed. Porosity was plotted versus resistivity to evaluate the coefficients used in Archie's Law. To improve predictions, other non-destructive measurements were incorporated: compressional wave velocity and bulk density. The results are compared with published relationships.
The core analyses were performed for each respective scientific project and not by the author, however, a description of the testing conditions and physical properties is provided.

Background
Electrical resistivity (reciprocal of electrical conductivity) is defined as the resistance between opposite faces of a sample of a given material to the flow of an electrical current. The resistance is a function of the material's resistivity and shape (length and cross-section). In porous media such as marine sediments the bulk resistivity is composed of the resistivity of the interstitial pore fluid and the resistivity of the mineral grains. In general, the mineral grains are assumed to be infinitely resistive. Since the resistance is also a function of the path of electrical flow around soil particles , the bulk resistivity of sediment samples yields information of the pore space occupied by the pore fluid.
Electrical resistivity measurements as a predictor for physical properties of sediments and rocks was first applied by . Archie introduced the formation resistivity factor FF which is defined as the bulk resistivity R ( ohm-m) divided by the resistivity of the interstitial pore fluid Rw (ohm-m) (Eq. (6)). Atkins and  showed that systems of cohesionless particles obey Archie's Law, and that the magnitude of m depends on the shape of the individual particles, increasing as they become less spherical. They also demonstrated theoretically that a combination of different particles (different shapes) leads to a relation in the form of Equation (8).
Even though Archie's Law and its derivations   Rw =interstitial water resistivity.
Since some of these variables are sometimes omitted, the complexity of Equation (9) can be reduced. For example, when sand is used, Equation (9) can be simplified to (10) which is the general expression of Archie's Law.

Methods
Electrical Resistivity: Electrical resistivity was measured usmg a linear fourelectrode-array (Wenner spread). The probes were pushed 2 mm into the split-core surface and an alternating current was applied to the two outer electrodes. The potential drop across the two inner probes was measured and converted to resistance by dividing by the instrument current. The resistivity was then obtained by multiplying the resistance by the instrument cell constant. The cell constant is defined as the crosssectional area of the sediment divided by the distance of the two voltage electrodes and was determined by measuring the resistance of sea water (known resistivity) at a controlled temperature . The formation factor was calculated using Equation ( 6), with a pore fluid resistivity of 0.209 ohm-m .
Compressional Wave Velocity. Compressional wave velocity was determined using a P-wave logger (PWL) on the Multi Sensor Track (GEOTEK). An ultrasonic pulse with a dominant frequency of 500 kHz was transmitted across the unopened core sample and the travel time was measured. The velocity was then calculated by dividing the core diameter by the pulse travel time. Corrections for transducer and core liner time delays as well as for core diameter deviations were applied (APPENDIX A, .
Bulk Density. Bulk density measurements were performed using a gamma-ray attenuation porosity evaluator (GRAPE) . The measurement of sediment bulk density using gamma-rays is based on the principles of Compton scattering and attenuation. A parallel, monoenergetic beam of gamma-rays ( 137 Cs) penetrates the core sample and is detected on the opposite side by a scintillation counter. When passing through the sample some of the gamma-rays are absorbed or scattered and lose energy and direction, respectively. The scintillation counter detects the gamma-rays that pass through the absorber without any loss of energy. The energy loss and the attenuation respectively are directly related to bulk density. A discrete value for bulk density is then derived by calibrating the attenuation of gamma-rays through the unopened core sample with the attenuation through standards of aluminum and water (APPENDIX A, .
Porosity: Porosity was determined from measurements of wet and dry sediment mass and wet sediment volume. Samples of approximately 10 cm 3 were taken from the sediment cores. Wet sediment mass was determined using an electronic balance. Wet sediment volume was calculated by means of a helium-displacement pycnometer. The dry sediment mass was obtained after oven-drying at 105° to 110°C for 12h to 24h and weighing on an electrical balance.
These measurements were used to calculate water content and bulk density following the methods of the ASTM D 2216. All measurements were corrected for salt assuming a pore water salinity of 35%0. Porosity was calculated from bulk density and water content using the following equation: where PB is bulk density (Mg/m 3 ), Pw is the density of pore fluid (Mg/m 3 ), and w is water content ( -).
In cases where no discrete measurements of physical properties were performed, the porosity was calculated from GRAPE bulk density using an assumed specific gravity of 2.75: where PG is the specific gravity (Mg/m 3 ), PB is the bulk density (Mg/m 3 ), and Pw is the pore fluid density (sea water Pw = 1.024 Mg/m 3 ).

Site Descriptions and Sediment Properties
14 cores from three different sites were selected for this study. The maJor geographic environments are (1) the North Atlantic (Ceara Rise), (2) the Northeastern Pacific (Cascadia Margin) and (3) Caribbean Sea (Barbados Ridge). A summary of the cores used in this study and a detailed description of the location are given in Table 2.
North Atlantic (Ceara Rise): The Ceara Rise is located in the eastern equatorial North Atlantic between the longitude 42° to 45° West and the latitude 3 ° to 7° North ( Figure 22). The Ceara Rise is a bathymetric high and reaches a minimum water depth of about 2600 m. The rise consists of a series of platform-shaped shoals oriented in a northwest-southeast direction. It is bounded on the north-east and east by the Ceara Abyssal Plain and on the north, west, and southwest by the Amazon Fan with water depth of about 4500 m .   .
The sediments of Cascadia Margin can be described as terrigenous and hemipelagic clays and silts. Three geotechnical units are used to distinguish the sediments. The recovered sediments of Unit I are predominately dark gray to dark olive gray silty clays and clayey silts with alternating thin layers of fine sand. Unit II is composed of firm clayey silts of dark gray to dark olive gray color. The sediments contain varying amounts of biogenic components (up to 10%). Unit II differs from Unit I in that Unit II has a lower abundance of sand and thus is more fine-grained than Unit I. Unit II and Unit III are identical in structure and composition. The difference in both is based on significant increases in glauconite in Unit III ( Figure 28, Figure 29).
Electrical resistivity increases with depth and the observed values range from 0.5 Om to 2.4 Om. The increase in resistivity is associated with a decrease in porosity.

Results
Plots of the formation factor versus measured values of porosity at each site are shown in Figure 30 to Figure 36. The empirical relationship between formation factor and porosity published by  and Winsauer et al. (1952, Humble Formula) are also shown in the plots. Power law regression lines, following the form of Equation (8) (solid line), are fit to the data to obtain coefficients a (lithology) and m ( cementation, tortuosity).
In general, the sediments of all sites follow the relationship of decreasing porosity with increasing resistivity .  measurements versus a calculated formation factor using bulk density and compressional velocity ratio as a and m coefficients in Equation (8), and the measured porosity for sediments of the North Atlantic (Ceara Rise). Due to lack in data quality and quantity of compressional wave velocity and bulk density, sediments from the Caribbean Sea (Barbados Ridge) and Northeastern Pacific (Cascadia Margin) were excluded. The compressional wave velocity ratio is the ratio between the sediment and pore fluid (sea water) velocity. For this study a sea water velocity of 1522 mis is assumed, which corresponds to a temperature of 20°C and a salinity of 35%0 .
In Figure 38, the coefficient a is approximated by bulk density and the coefficient m by the velocity ratio. A linear regression line, fit to the data, indicates a very low correlation (R 2 = 0.079).

Discussion
The general trend observed in the resistivity-porosity relationship of unconsolidated marine sediments is similar to published relationships. The a and m coefficients range between 0.30 to 6.22 and -0.135 to 2.48, respectively (Table 3).
With the exception of the negative m value obtained from the sediments at Site 926, and a very high a value from Site 891 the values are generally in agreement with published data that range between 0.6 and 1.30 for a and 1.2 to 3.0 for m .
The wide scatter around the regression lines indicates high variations m a (lithology) and m (tortuosity, cementation). Even in sediments of adjacent sites ( Figure  3 o to Figure 32) and with identical lithologies, major differences in these coefficients are apparent. In sands and sandstones where electrical resistivity is usually used to extract porosity, no such extensive scatter is observed .
Reasons for the extensive scatter and the high variation in the coefficients a and m in unconsolidated marine sediments may be due to the textural properties of the sediments. When fine particles (clay, silt) are deposited on the sea floor, they adhere to each other by means of physico-chemical bonds . The mineral-grain structure that is formed is thereby highly random and irregular (high tortuosity, Figure   39d, e, f), even in intervals of similar sediment content. Electrical current is constrained to follow complex meandering paths whose lengths increase with tortuosity and whose cross-sectional areas (and hence resistance) vary erratically between the pores and fine interconnecting capillaries. Furthermore, clay particles can not be considered as infinitely resistive due to the negative charges on the particle surfaces. The path of the electrical current is therefore not only dependent on tortuosity, but also dependent on the conductivity of the particles.
Privious investigators show significant relationships between dielectric constant and porosity (Arulanandan, 1991;Smith and Arulanandan, 1981). However, these studies predominantly use uniform soils that are not representative of natural deposits.
When coarser particles are deposited, the mineral-grain structure is controlled by gravity and the structure is more regular than in fine grained sediments (Figure 39a, b, c ). The tortuosity is therefore more dependent on the arrangement of the particles.
Tortuosity variations within similar sediments are less for sands. Since coarser grains are predominantly composed of quartz, they can be considered non-conductive and therefore, variations in resistivity due to the conductivity of particles are negligible.
Comparing the results of this study (e.g. a and m values) wi, th published relationships, the porosity is not predicted well. The closest relationship is obtained between the equation published by   Yet, the approach seems to be reasonable if one considers the characteristics of a and m. The coefficient a reflects the lithology and · a change in lithology is usually associate with a change in bulk density. The coefficient m incorporates cementation and tortuosity (increase in cementation and tortuosity, increases the factor m). These two parameters also influence the compressional wave velocity. An increase in cementation increases the bulk modulus and the shear modulus of sediments. Since these two parameters interdependent with velocity, the velocity would also increase.
However, the relationship in Figure 38 indicates no interdependency between a, m, bulk density and velocity ratio.

conclusion
The applicability of electrical resistivity to extract porosity of clean sands, sandstones, and limestones is well demonstrated . It is also common practice in the hydrocarbon exploration industry to use published charts of formation factor to predict porosity of source and reservoir rocks ( Figure 40). However, the results of this study indicate that the resistivity-porosity relationship in unconsolidated fine-grained sediments is much more complex. It may not be possible to develop similar chart-type relationships to predict porosity for these sediment types. The wide scatter of data around regression lines results in poor approximations of porosity, even when the a and m coefficients are known (i.e. evaluated by means of discrete porosity measurements). However, as a starting point, the high porosity fine-grained data presented in this study are presented in chart form ( Figure 41 ).
Compressional wave velocity and bulk density show no relationship with either coefficient a or m. However, changes in velocity and density may be used to identify changes in lithology, cementati~n · and tortuosity. This could be used to group data of similar texture and lithology to apply appropriate a or m values and to refine charts that can be used to predict porosity.   --Resistivity (Om) --Resistivity (Om) --Resistivity (nm) · · · · · · · · Porosity ( -) · · · · · · · · Porosity ( -) · · · · · · · · Porosity ( -) · · · · · · · · Porosity ( -) · · · · · · · · Porosity ( -)      The proper evaluation of these properties in ·the laboratory is labor and cost intensive. The quantity of information obtained is limited because of the effort required to acquire data information on how shear strength and shear modulus vary with depth and sediment type. For regional studies this limited amount of information makes it necessary to interpolate or extrapolate between data points to get an area wide profile that can be used to make assumptions for design. This extrapolation of infonnation can lead to extensive errors and misinterpretations, since soils and sediments are inhomogeneous, non-linear, and non-uniform. In geotechnical engineering, uncertainties and errors caused by lack of information and extrapolation are compensated by the use of the factor of safety approach and consequently, an underestimation of the capacity of a structure. Methods to improve the quantity and quality of such data would reduce uncertainty and risk. Thus, this study's focus is the investigation of non-destructive methods for assessment of shear strength properties, to improve data quantity and quality at a relative low cost. The ability to extract sediment shear characteristics, such as the shear strength and the shear modulus nondestructively, by measurements of compressional wave (P-wave) velocity and bulk density would lead to high resolution profiles and ultimately to a better estimation of design parameters.
Compressional wave velocity and bulk density can readily be measured by means of a P-wave logger (PWL) and gamma-ray attenuation porosity evaluator (GRAPE),

respectively. Both sensors are incorporated into the Multi-Sensor-Track (MST) and
are part of a standard instrument configuration (APPENDIX A). This state-of-the-art device is fully automated and able to measure these parameters at high resolutions (less than 1 cm intervals) along a sediment core. Providing a relationship between nondestructive measurements such as these and ·shear strength could potentially improve the design and the safety of structures. Furthermore, the influence of sample disturbance on the parameters is reduced, since the MST measures relatively undisturbed whole-core samples encased in the original sample liner.
The main objective of this study is to develop empirical relationships between nondestructive measurements of P-wave velocity, bulk density and discrete measurements of undrained shear strength or shear modulus evaluated by miniature vane shear tests.
Although the provided relationship is completely based on statistical and empirical approaches, a discussion of the theoretical significance of the results is also included. Despite these results , an evaluation of shear strength or shear modulus from miniature vane shear tests (MV) and non-destructively derived compressional wave velocity and bulk density was conducted by following a different approach. The basis of this study differs from former studies, in that the velocity is not directly compared with shear strength parameters (peak shear strength and shear modulus) but rather with velocity m conjunction with bulk density because both parameters are related to moduli. In addition, these earlier studies were not non-destructive; probes were used or samples taken to measure velocity and density.
Theoretically the relationships among shear strength, compressional wave velocity and bulk density are based on the basic equation for the velocity of an acoustic compressional wave: where VP is the compressional wave velocity (mis), B is the bulk modulus (KN/m 2 ), G is the shear modulus (KN/m 2 ), and PB is the bulk density (Mg/m 3 ). Since shear strength depends on shear modulus, these are directly related.  developed a relationship to estimate the shear modulus, G, from the initial slope of a miniature vane stress versus strain (rotation) data plot as follows: (14) where to is the shear stress (KN/m 2 ) and 80 is the angle of vane rotation ( 0 ). Since Equations (13) and (14) are functions of the shear modulus, it is reasonable to assume a relation between the two. The shear modulus derived from Eq. (13) is a dynamic shear modulus at very small strains (< 0.001 %) whereas the shear modulus using Eq.
(14) is large strain caused by the rotation of a four bladed vane in an assumed linear elastic medium. The assumptions used to evaluate the shear modulus from Eq. (14) are: (1) the failure surface is fully mobilized and in the same shape and size as the cylinder formed by the vane rotation; (2) the disturbance of the stress distribution due to insertion of the vane is negligible; (3) drainage and progressive failure do not occur in significant magnitude during the test; ( 4) the material is isotropic and infinite in all directions; and ( 5) Hooke's law is valid.
Although, the vane shear test is a "destructive" one, resulting in a measure of large strain behavior, it is assumed that there is a relationship between small strain and large strain behavior. The initial slope of the vane shear stress -rotation curve expresses the shear properties of the sediment in terms of large strain (static) with a different absolute value than the small strain (dynamic) shear modulus that is obtained using , for example, resonant column  or shear wave velocity measurements . Therefore, the relationship between dynamic shear modulus in tenns of the factor v: * p 8 (Eq.(13)) and the vane derived shear properties was investigated. For convenience, the v: * p 8 , an elastic parameter, is defined here as B, as an expression for the elastic behavior of sediments in terms of bulk modulus and shear modulus. To verify the assumption that B can be used to express G, B is correlated with an empirically derived dynamic shear modulus (Jamiolkowski et al., 1991).

Methods
Compressional Wave Velocity. Compressional wave velocity was determined using a P-wave logger (PWL) on the Multi Sensor Track (GEOTEK). An ultrasonic pulse with a dominant frequency of 500 kHz was transmitted across the unopened core sample and the travel time was measured. The velocity was then calculated by dividing the core diameter by the pulse travel time. Corrections for transducer and core liner time delays as well as for core di~meter deviations were applied (APPENDIX A, .
Bulk Density. Bulk density measurements were performed using a gamma-ray attenuation porosity evaluator (GRAPE) . The measurement of sediment bulk density using gamma-rays is based on the principles of Compton scattering and tt . 137 a enuat10n. A parallel, monoenergetic beam of gamma-rays ( Cs) penetrates the core sample and is detected on the opposite side by a scintillation counter. When passing through the sample some of the gamma-rays are absorbed or scattered and lose energy and direction, respectively. The scintillation counter detects the gamma-rays that pass through the absorber without any loss of energy. The energy loss and the attenuation respectively are directly related to bulk density. A discrete value for bulk density is then derived by calibrating the attenuation of gamma-rays through the unopened core sample with the attenuation through standards of aluminum and water (APPENDIX A, . Undrained Shear Strength. The undrained shear strength of the sediments was determined at selected intervals using a motorized miniature vane shear device (MV) .
The vane blade torque was measured either using an electronic torque transducer or linear springs. A four bladed vane with a geometry ratio of 1 (the height is equal to the diameter) was used and the measurements were performed in accordance with ASTM D 4648-94.

Undrained Shear Modulus (GMv). The maximum undrained shear modulus GMv
was evaluated using the initial slope of the shear stress -rotation plot derived from miniature vane shear measurements. The maximum shear modulus occurs at strains lower than 0.001 % and decreases after exceeding this limit .
Conversion from angle of vane rotation was calculated following Equation (14) where GMAX is the maximum shear modulus (initial slope of the shear stress -strain curve, MN/m 2 ), e is the void ratio ( -), OCR is the over-consolidation ratio ( -),-k is the over-consolidation exponent as a function of plasticity index (Hardin and Drnevich, 1972), and p' is the mean effective pressure (MN/m 2 ). The void ratio e was determined from the bulk density using an estimated specific gravity of 2.75 with Eq.
where ~ is the porosity ( -), Ps is the grain density (Mg/m 3 ), p 8 is the bulk density (Mg/m 3 ), and PF is the pore fluid density (Mg/m 3 ) (density of sea water, Psw = 1.025 Mg/m 3 ). The over-consolidation ratio was assumed to be 1.0 for normally consolidated sediments. For over-consolidated sediments the normalized vane shear strength was used in conjunction with published charts that approximate the over-consolidation ratio . The plasticity index was derived from normalized vane shear strength  where the major principle stress (overburden) was derived from the bulk density.  Table 4.

Central Arctic Ocean (Lomonosov Ridge). The Lomonosov Ridge is located in the
Central Arctic Ocean between the longitude 130° to 155° East and the latitude 85° to 90° North ( Figure 43). The Lomonosov Ridge separates the Markarov Basin and the Amundsen Basin. The ridge crest is at its highest less than 1000 m below sea level and drops down on both sides into the adjacent basins with depth of more than 3000 meters below sea level. The sediments of the Lomonosov Ridge are predominantly hemipelagic with minor ice rafting components.
The sediments of Core 96/09-1 pc are described as clays and silty clays and the lithology was divided into three geotechnical units . Unit I consists of a thin layer of dark brown clay at the surface and is underlain by a layer of yellowish brown to dark gray silty clay. The second Unit II is composed of olive gray clay and silty clay and unit III is an indurated dark olive gray silty clay (Figure 44 ).  The Basin is filled with glacial till that is overlain by Quaternary fine grained glaciomarine and marine sediments and underlain by firm bedrock. In general the sediment stratigraphy can be divided into three major geotechnical units ( Figure 46). However, the sediments retrieved with core 87003-02 are only composed of the upper two units.
Unit I consists predominantly of marine silty clay and clayey silt, olive gray in color.
Unit II is mainly dark gray glacio-marine silty clay . The marine silty clay and clayey silts have relatively low shear strength and a high plasticity index. Shear strength increases with depth except for several anomalous peaks that are probably measurement errors. Bulk density is uniformly increasing with depth and no distinct variation in density due to the differences in composition between Unit I and II can be observed. Density ranges from 1.40 Mg/m 3 at the top of the core to 1.6 Mg/m3 at a depth of 16.5 meters. The compressional wave velocity is relative constant with depth and has an average value of 1446 mis.

Gulf of Mexico (Texas-Louisiana Slope and Rise). The Texas-Louisiana slope and
rise encompasses approximately 120,000 km 2 (Figure 4 7). In general the sediments can be divided into four major geotechnical units. Core JPC 32 contains sediments of all four units whereas Unit IV in core JPC 41 is missing (Figure 48). Unit I consist of brown to light brownish gray silty clays with some minor amounts of carbonate sands.
Unit II is composed of olive gray, grayish brown and dark gray silty clays. Unit III is brownish gray and light olive gray silty clays with significant amounts of foraminifera and unit IV is a stratified deposit consisting of thick layers of reddish silty clays and dark gray silty clays

Large Strain and Small Strain Shear Modulus. The large strain shear modulus GMv
derived from the initial slope of the shear stress -rotation plot is compared with the small strain shear modulus GMAx, calculated using Equation (16) and the elastic parameter 3 (Figure 50 and Figure 51 ). Both plots show scatter in the observed values.
Scatter in the large strain shear modulus is wider for the elastic parameter 3 than for the small strain shear modulus GMAX· However, the difference in both plots is, if expressed in terms of the correlation coefficient, very small (R 2 = 0.461 and 0.338). In general, the vane derived small strain shear modulus (GMv) is much smaller than the calculated small strain shear modulus ( GMAx), by two orders of magnitude. Values in the higher shear modulus range seem to be more scattered than in the lower range. Apparently, the over-consolidated sediments from the Arctic behave differently from the nonnally consolidated sediments or the offset can be ascribed to measurement derived errors. Since the over-consolidated values of Core JPC 41 (Gulf of Mexico) are within the limits of the general trend, it is more likely an artifact of errors in data acquisition. This is also confirmed by the unusual high ratio of undrained shear strength over the effective overburden pressure that exceeds absolute values of 5 .0. This is much higher than values published for similar sediments . On this account, values exceeding shear strengths of 50 kPa are considered carefully and additional correlations are provided that excludes these values. Figure Figure   55). However, the correlation in terms of coefficient R 2 is not as pronounced. In Figure 56 the over-consolidated sediments of the Arctic are removed. The scatter around the regression line is much wider than in previous correlation with the shear modulus. Two data populations are noticeable. Above the regression line the overconsolidated data from Core JPC 41 and below the regression curve on the right side the normally consolidated sediment from the Arctic seem to follow different trends. Figure 57 shows the plot of the elastic parameter Sand the calculated small strain shear modulus GMAX · Since Sis an expression of the elastic properties of the sediments, in terms of bulk modulus and shear modulus, a good correlation between these parameters is obvious. Sediments of the different cores are all following a linear relationship (with slightly varying slopes and intercepts) with increased shear modulus associated with an increase in the elastic parameter S . Noteworthy is that the regression lines of Core JPC 41 and 96/09-1 pc follow the same trend, even though they are slightly offset. Core JPC 32 and 87003-02 also follow this trend, but offset from the other.

Discussion
The correlation between the large strain shear modulus GMv and the small strain shear modulus GMAX and the elastic parameter S, respectively, yield a low coefficient correlation relationship, but show a trend of interdependence. Scatter is too wide to be able to use the regressions equation as predictors of large strain shear behavior.
Reasons for the data scatter could range from variable stress history to small scale sedimentological differences to measurement errors.
The most probable factor is the low measurement resolution of the shear stressrotation (strain) plots. A resolution of 1° vane rotation is too large for evaluation of the initial slope (shear modulus) of the curve. To obtain a value for the shear modulus, the initial part of the shear stress rotation curve was approximated by a best fit nonlinear regression line. This procedure is based on a subjective extraction of points on the curve, used to fit the regression line into the shear stress -rotation plot. Small changes to the input parameter slightly causes an overall change of the regression line and thus a change in the initial slope of the curve. Additionally, minor problems with the vane shear device during data acquisition, such as slipping of the driving belt, resulted in a non-uniform curve and complicated tlw ap!)roximation of shear modulus (Figure 42).
In general, the vane-derived shear modulus is much lower than the small strain shear modulus. In addition to the low resolution shear stress -rotation plots, reasons for this difference could be attributed to the vane shear procedure. Assumptions made with regard to the absence of sediment disturbance (see assumption (2) in the background chapter), to evaluate the shear modulus and shear strength from vane shear tests , are not met with the first insertion of the vane into the sediment. The vane insertion forces the soil to displace, and the strains caused by the insertion exceed 0.001 %. This error affects the shear modulus to a much higher degree than the shear strength, since the shear modulus is a measure at very small strains ( < 0. 001 % ) whereas the strength is measured at high strain.
In spite of the scatter and associated errors, general trends exist. The general trend of increasing large strain shear modulus GMv with increasing small strain shear modulus is observed,, despite the data quality. Another indication of a relationship between large strain and small strain shear modulus or the elastic parameter is seen in  .
The influence of over-consolidation is demonstrated by the wide scatter around the regression line that can be observed for the over-consolidated sediments of Core JPC 41 ( Figure 54). The over-consolidation ratio of normally consolidated sediment is one and, therefore, the plasticity index that is represented in the over-consolidation ratio exponent, does not influence the equation. This is seen in the small data scatter of normally consolidated sediments at moderate shear strength(< 25 KPa). The error that is made in the empirical determination of the over-consolidation ratio for overconsolidated sediments and in the determination of the plasticity index and overconsolidation ratio exponent k is expressed by the shift in the data for the over-  Figure 57. Since, the elastic parameter 8 is an expression of the bulk modulus K and the shear modulus G, the parallel shifts of the regression lines can be attributed to differences in bulk modulus. These differences are reflected in Figure 56 in terms of the scatter of the data populations. The over-consolidated sediments from core JPC 41 have a higher bulk modulus, as do some of the deeper test from the Arctic sediments.

Conclusion and Recommendations
Correlations between parameters derived from miniature vane shear tests, including large strain shear modulus and undrained shear strength, and non-destructive measurements of compressional wave velocity and bulk density are presented. An empirically derived small strain shear modulus was compared with undrained shear strength and shear modulus acquired from miniature vane shear tests. Data from three different geographical environments were used to establish an empirical relationship that allows for a prediction of shear parameters from non-destructive measurements.
The study has shown that small strain and large strain shear characteristics are interdependent. This is shown by a strong linear relationship between the undrained shear strength and small strain shear modulus (R 2 = 0.733, crest= 4.27 KPa).
The existing relationship between compressional wave velocity, bulk density and small strain shear modulus (Eq .( 13)) can be used to approximate undrained shear strength. However, numerous other factors complicate the prediction and have to be taken into account when deriving an empirical equation. Furthermore, the relationship between Su and B is not as strong as Su and GMAX because B is representative of the bulk modulus and shear modulus. Variability in bulk modulus among sites ( Figure 57) introduces more scatter into the Su versus B plot ( Figure 56) because GMAX appears to be a more sensitive indicator of Su, since it does not rely on the determination and incorporation of bulk modulus.
A definitive relationship between the large strain shear modulus of the initial slope of the vane shear -rotation plot and small strain shear modulus or B can not be made.
The resolution of the vane shear stress -rotation plot ( 1 ° vane rotation) is not high enough to evaluate a sufficient shear modulus. Improving the resolution of the vane shear stress -rotations plots, holds promise for developing such a correlation.
This study suggests that a general equation can be developed to predict shear strength or shear modulus from non-destructive measurements for normally consolidated fine grained sediments. More experimental research is needed to refine the relationships presented here. The promising results of this study provide a basis on which further studies can be built.          .c         The multi sensor core logging system is a versatile instrument because of its modular design. This design allows the user to adapt the system to individual testing requirements. The adaptability affects not only the different sensor configurations but also the adaptability to samples. MSCL devices are able to process whole cores and split cores encased in plastic liners as well as .exposed hard rock samples. The basis of the system configuration is formed by a horizontal motorized core conveyer system that moves the cores past the different stationary sensors using a core pusher ( Figure A   1 ). The conveyer is driven by a stepper motor, which controls forward motion to intervals as low as 0.5 mm. The sensors, or measurement devices, are either placed within or around the conveyer system on a center stand. The range of sensors available is multifaceted and currently consists of measurement devices for core diameter and temperature, compressional wave velocity (P-Wave ), gamma-ray attenuation, magnetic susceptibility, core imaging, natural gamma ray and electrical resistivity. All integral sensors are connected to a central electronic rack that controls the sensor settings and provides the interface between the sensors and a computer. Customized software enables full automated core logging and recording of the data. The whole MSCL unit is at least 4 meters long (depending on the configuration) and is capable of logging core units with a length of up to 1.50 meters ..
The following chapters focus ·on the gamma-ray attenuation porosity evaluator, the compressional wave velocity device and on the electrical resistivity device. The individual components, their configuration and the theory that underpins each are described in detail. Methods for calibration and data processing are also presented.
The different MSCL devices shown in the figures are fabricated by GEOTEK Ltd.
and only depict examples of the different sensors available. However, since the described mechanisms and principles are standards, they are applicable to all other devices available and are not only limited to GEOTEK systems.

Displacement Transducers
The measurement of the sediment thickness and outside core diameter, is essential for almost all sensors mounted on the MSCL. The thickness is a fundamental value for calibrating the instrument response when calculating bulk density, compressional wave velocity, magnetic susceptibility and electrical resistivity.
Apparatus. MSCL systems are equipped with an integral thickness measuring device. In most instances, the determination of the core or sediment thickness results from a displacement measurement. A common approach is to couple rectilinear displacement transducers to the P-Wave transducers (Figure A 2).
Due to the fact that the P-Wave transducers must have close contact to the sample they must be able to compensate for core thickness discontinuities during measurement. This is achieved by imbedding the transducers into a plastic housing using a spring mechanism and horizontal or vertical housing slides perpendicular to the core sample. The coupling of the P-Wave transducer with the displacement transducer results in a simultaneo.us movement during the logging process. Since this layout yields only a displacement deviation of the core being logged, the displacement transducers have to be adjusted to a reference thickness.
Calibration. A cylindrical reference sample with a known thickness (diameter) is placed between the P-Wave transducer faces. The transducer housing is then adjusted to the reference sample in such a way that the displacement of the spring is approximately midway, (ie. the transducer is able to move in and out of the housing by the same distance). The position of the displacement transducers is then set at zero.
The reference sample does not necessarily need to be of the same size as the core being logged, however the thickness should be equivalent because once the vertical slides of the transducer housings are fixed and the zero position is set, the core sample has to fit between the P-Wave transducers in the same manner as the reference sample.
The sediment thickness ds can be derived from the core thickness deviation measured by the displacement transducers and follows the relationship: In this equation the dref is the reference sample core or diameter (in m), dw is the total wall thickness of the liner of the core sample being logged (in m) and CTD is the core thickness deviation (in mm) provided by the transducers.

Gamma-Ray Attenuation
The Gamma-Ray Attenuation Porosity Evaluator (GRAPE) provides continuous, non-destructive determination of sediment and rock bulk density. These data can also be used to calculate porosity and.water content.
Apparatus. A single GRAPE apparatus consists of a gamma-ray source, a scintillation detector and a caliper (Figure A 3). The gamma-ray source and the scintillation counter (detector) can be aligned vertically or horizontally to measure across split or whole cores, respectively. The design of the gamma-ray source is simple. The radio active element is housed in a capsule which, in tum, is inside a lead filled steel container (Figure A 4).
The size of the lead container in comparison with the source capsule is very large to provide for user radiation protection. Using a 10 mC 137 Cs source, the maximum radiation at the surface of the steel container is less than 7.5 µSv/h (GEOTEK), subject to the dimensions for enclosure given in Figure (Table A 1 ).
Slits placed in front of the gamma-ray source collimation facilitate nearly parallel beams and can also be used to alter the beam diameter. For general applications, collimator slit diameters of 5 mm are adequate. Collimator slits with a diameter less than 5 mm (e.g. 2.5 mm) are utilized only to obtain measuring data of very high resolution.
The gamma-ray detector looks similar to the source from its external appearance, but internally is configured differently (Figure A 5). The detector is also encased in steel and lead housing. The detection element, a Nal crystal with a photo-multiplier tube, is located in the center of the housing.
Principle. The measurement of sediment and rock bulk density using gamma-rays is based on the principles of Compton scattering and attenuation ( Figure A 6). A parallel, mono energetic beam of gamma-rays penetrates a sample (also referred to as absorber). When passing through the absorber some of the gamma-rays are absorbed or scattered and loose energy and direction, respectively. The scintillation counter only detects the gamma-rays that pass·through the absorber without any loss of energy. The energy loss and the attenuation are directly related to bulk density.
Three main mechanisms affect the attenuation or alteration of the gamma-rays: Photoelectric absorption, pair production and Compton scattering. The influence that the energy level of the bombarding photons has on the attenuation coefficient was studied and results show that the coefficient does not vary much for common materials at particular gamma-ray energies ). This energy range is between 0.2 and 3.0 MeV. For example the attenuation coefficient of quartz, using 137 Cs (0.662 MeV), has aµ of 7.4 m 2 /Mg, and, the value of µis 10.0 m 2 /Mg, using 133 Ba (0.30 to 0.36 MeV) as the radiation source (Table A 2).
Similarly, for common minerals found in sediments and rock, the influence ratio of the atomic number Z to the atomic weight of the absorber A is almost constant. Both, the energy level and the ratio Z/ A results in a constant attenuation coefficient for compounds of C, 0, Na, Al, Mg, Ca and Si.
The mass attenuation coefficient can vary for other reasons. Problems occur when the coefficient µ diverges from the mean value. That is, the Equation (A 3) is only accurate for sediments and rocks composed of minerals which have similar coefficients. For example, the ratio of Z/ A of hydrogen is not the same as many common materials. Water for instance has a 10 % higher µ value then the most common minerals (µwater= 8 .56 m 2 /Mg and µsi=7.4 m 2 /Mg by using 137 Cs as radiation material). Therefore, the attenuation coefficient changes when sediments have a large percentage of hydrogen (e.g. water) in their pore space.
Calibration. The most common core samples the Multi-Sensor Core Logger operates on are sediments contained in plastic liner or rocks. If the coefficient µ is known with sufficient accuracy, it is possible to calculate the bulk density directly by using Equation (A 3).
Sediments and rocks, for example, are naturally composed of different minerals and therefore the specific mass attenuation coefficient of the sample is dependant on the composition. Furthermore, sediment samples are mostly saturated with water, therefore the determination of the mass attenuation coefficient is difficult due to the attenuation coefficient being 10 percent higher. Finally, attenuation through the liner wall as well as the spreading of the emitted gamma-ray beam results in imprecise data.
Considering this, the computed bulk density from Equation (A 3) under an assumed or estimated average coefficient would not lead to valid results.
It is more practical and accurate to evaluate the bulk density by using an empirical approach. The basic principle of this approach is based on a comparison of the measured gamma-ray counts of a sample with a standard curve, evaluated by means of measuring bulk density standards. The core sample is looked upon as a two phase system, wherein phase one is minerals and phase two is the pore or interstitial water.
This system can be replicated by means of density standard. As the bulk density standard for the mineral phase, aluminum is used due to its similar mass attenuation coefficient to the most frequently occurring minerals (e.g. quartz). The liquid phase is replaced by distilled water. The assumption is now that the attenuation of the standard, consisting of aluminum and distilled water, is equivalent to the attenuation of the core sample, consisting of minerals and water, at the same density level. Therefore, only the attenuation has to be determined to evaluate the bulk density of the core.
In practice the calibration curve is derived by using predefined standards. Actual devices are illustrated Figure  This approach is based on the same principle as previously described ( Figure A 9).
The advantage of this method is that for each measurement the specific liner of the core sample can be used for calibration, that is, the liner attenuation is taken into account. However, the difficult handling of this method (the plates must be aligned perpendicular to the gamma-ray beam) is a disadvantage which eventually resulted in the development and application of the prefabricated aluminum rod standards.
The average density of a standard can easily be calculated because the densities of aluminum and water are known as well as the geometry. The density at each section (each different diameter of the rod) is then: where The sediment thickness used in Equation (A 6) 1s determined from the core thickness deviation measurement (Eq.(A 1)).
In the densiometry method, described above, the attenuation coefficient is assumed to be constant for the mineral phase, that is, the minerals have nearly the same µ as the aluminum standard. Yet, if mineralogical analysis indicates significant differences in coefficients, corrections for the bulk density must be applied. Prior to the introduction of the calibration method, described above, calibration of the GRAPE device was performed with two aluminum cylinders of different thickness. In this procedure, different attenuation behavior of water was not taken into account and therefore the calculated density was about 10 % too high. However, the over estimated density data can be corrected by using Equation (A 9), which was developed by Boyce ( 197 6) and accounts for the lower Compton mass attenuation coefficient of water. In Equation (A 9), PBc as well as PFc are known and calculated, respectively. The values for true grain density, grain density calculated from gamma counts, and true fluid density must be estimated. To simplify Equation (A 9), Po is equated with p 0 c.
Values for grain density of different geologic minerals and fluid densities are given in Table A 3.
Today, the use of fluid correction is not necessary because the new calibration procedure accounts for the influence of fluids (water). However, the procedure is still needed to readjust older log data in which the influence of fluids is disregarded.
Porosity and Water Content. In porous materials bulk density is related to the matrix density and grain density? respectively, as well as to the fluid density and can be described by the following expression: where Ps = Ps * ( 1-<f>) + PF * <f> The unknown values in (A 11) are the grain density PG and the density of the interstitial fluid PF· For common geologic minerals, estimation of these values can be made with sufficient accuracy. Table A 3 displays grain densities of common minerals as well as densities for frequently occurring interstitial fluids.

Compressional Wave Velocity
The compressional (P) wave velocity system can be used to differentiate and quantify physical properties such as elastic modulus, density, porosity, homogeneity and grain structure of solids and liquids.
Apparatus. The compressional (P) wave velocity unit is mounted on the center stand of the MSCL device. The assembly consists· of a pair of P-Wave transducers (PWT) and the rectilinear displacement transducers (DT) that are located diametrically across the core sample ( Figure A 11 ).
Two different types of PWT's are available in present devices; a) stainless steel piston transducers (old style) and b) oil filled acoustic rolling contact (ARC) transducers (new style). The heart of the stainless steel piston transducer is a piezoelectric element that is embedded in epoxy resin and encased in a stainless steel container. A piezo-electric element is a crystal plate of natural or synthetic material that is able to deform mechanically by means of an applied electric field and thereby generates ultrasonic vibrations. The performance of the piezo-electric element is invertible, that is the element also produces an electrical pulse while deforming. Thus, the transducers can either operate as a transmitter or as a receiver. The epoxy resin attenuates and scatters the back-transmission and thus shields back of the source. The front face of the piston consists of a thin plastic window that allows for the forward energy transmission (Figure A 12).
The oil filled acoustic rolling contact (ARC) transducer has a similar design as the piston transducer. The active element is a piezo-electric crystal embedded in a shielding epoxy resin. However, the crystal is mounted stationary on a center spindle and is surrounded by a rotating, soft and deformable diaphragm. The space between the active element and the diaphragm is filled with castor-oil ( Figure A 13).
For whole core logging the alignment of the transducers is horizontal. To ensure proper coupling between the sample and the transducers, the active element is springloaded and mounted within a plastic housing. By using piston transducers, the ultrasonic coupling can vastly be improved if the liner surface or the face of the transducer is moistened with water or other lubricants. Since, the ARC transducer already has an excellent ultrasonic coupling due to the soft oil-filled diaphragm it becomes redundant to moisten the surfaces during the logging process.
While logging split cores, the transducers are vertically orientated. The receiver is usually an ARC transducer and is mounted stationary within the conveyer track. The receiver has permanent contact to the sample whereas the upper PWT (piston type) is mounted on a vertical slide and can be raised or lowered during measurement intervals by means of a stepper motor. To protect the upper PWT from contamination and to improve coupling the exposed core surface has to be covered with a thin plastic wrap and moistened.
Principle. The velocity of the P-Wave, traveling through a medium (sample), is controlled by the physical properties of the medium and the ambient temperature. The elasticity and density are the basic physical properties that govern the velocity of the wave propagation. The compressional (P) wave is a longitudinal wave in which the displacement of the particles through which the wave travels is parallel to the propagation of the wave. The displacement is expressed as an elastic back and forth oscillation about an equilibrium position, rather than as an absolute change of position.
The ignition of a P-Wave is a vibration (caused by the active element) that sets the adjacent medium in motion ( Figure A 14) The particles in front of the wave are forced together creating a zone of higher density (compression) and behind the wave an area of lower density (rarefaction). The propagation of the P-Wave through the medium can be described as a chain reaction. The first particles that are set into an oscillating motion transfer the energy to the adjacent particles which in tum begin to oscillate and transmit the energy to the next particles and so on. The velocity with which the energy transmission occurs strongly depends on the inertia of the medium. Denser mediums possess a higher inertia and the time needed to set the particles in oscillating motion increases. Consequently the transmission of the P-Wave (energy transfer from particle to particle) is slowed down and results in a decreasing velocity. The elasticity (restoring forces) affects the P-Wave velocity in the opposite way. The higher the elasticity of the medium, the better is the ability of the particles to oscillate, and transfer energy to the adjacent particles.
The basic equation for the relationship between density, elasticity and velocity is given by: where The bulk density is determined by discrete measurements (destructive) or by the gamma-ray attenuation porosity evaluator (nondestructive) and the shear (rigidity) modulus can be estimated from charts or empirical correlations.
The most essential processes to evaluate accurate P-Wave velocity data are accurate pulse travel times, and the setting of the pulse timing circuitry. An ultrasonic pulse transmitter produces a 500 kHz pulse (corresponding to a wave period T of 2 µs; T=l/f) with a voltage spike of 120 Vanda repetition rate of 1 kHz. The pulse is sent to the transmitter transducer and excites the piezo-electric element that in tum launches the P-Wave at approximately 500 kHz. The frequency of the emitted pulse or the P-Wave can vary between a few Hz and a GHz because the pulse travel time through a medium is not affected by the frequency. However, shorter wavelengths are more responsive to changes in the medium through which they pass. For geotechnical applications it turned out that a frequency between 250 kHz and 500 kHz is sufficient.
The P-Wave then propagates through the sample, detected on the other side by the receiver transducer and is amplified by an automatic gain control (AGC This detection procedure is insensitive to amplitude variations and noise, and is therefore reliable for weak signals. A short time after the ultrasonic pulse transducer has generated the transmit pulse ( 500 kHz, 120V), a delay pulse is triggered. The time set of the delay pulse is just a few microseconds less than the transmit pulse needed to propagate through the sample. The end of the delay time pulse is a signal for the oscilloscope to start recording the P-Wave and to set the gate time pulse that in tum describes the duration of the oscilloscope recording. The delay time pulse works like a shield for the receiver in a way that it insulates the receiver from background noise before the objective wave arrives. This ensures that there is no interference or pre-stimulation that could alter the pulse time measurement. At the end of the gate pulse, which is normally set to at least three frequencies, the gate pulse terminates the oscilloscope recording. While the oscilloscope is recording the incoming pulse a threshold detector, integrated in the oscilloscope, detects all negative deflections of the received pulse that are crossing a preset threshold level. The magnitude of the threshold level depends on the intensity of the incoming signal amplitude and consequently on the sample characteristics and is set to approximately 10 to 20 % of the maximum signal amplitude voltage. Parallel to the threshold detection a zerocrossing detector (also integrated into the oscilloscope) monitors all crossings of the pulse signal with the abscissa. The count time pulse that is triggered at the same time as the ultrasonic pulse is then terminated and recorded after the first zero-crossing following the first threshold level detection ( Figure A 15).
When the pulse travel time is determined the velocity is derived using: where VP =the P-Wave velocity in the sediment (in mis), <ls =the sediment thickness (in m; see Eq.(3.1)), ts =the measured travel time through the sample (ins).
Besides an accurate pulse time measurement, environmental and non-physical influences have to be taken into account for sufficient velocity data acquisition. The P-Wave velocity is very sensitive to temperature. This property mainly affects the interstitial fluid. A temperature difference of one degree can cause velocity variation higher than between different sediment strata. Increasing temperature results in decreasing density and this in turn results in increasing P-Wave velocity ( Figure A   16).
Core quality is regarded as a non-physical influence which can influence the P-Wave velocity to a great extent. Insufficient coupling between the core liner and the sample due to sampling effects as well as embedded gas voids and bubbles in the sample may result in variations of the velocity. This is mainly attributed to the different P-Wave velocities of gases. The velocity of gases is about four times less than that of solid or liquids and due to the fact that the size of the voids is not known sufficiently the correction of the velocity is impractical. Table A 4 displays compressional (P) wave velocities of common sediment types, elements and fluids.
Calibration. The measured total pulse travel time (count pulse, see Figure A 15) has to be calibrated before calculating the P-Wave velocity. Four time delays have to be taken into account for the purpose of evaluating the absolute pulse travel time through the core sample; (1) pulse delay, (2) transducer delay, (3) circuitry delay, and ( 4) core liner delay.
The pulse delay is an error in time measurement due to the first arrival detection method (zero crossing). The pulse delay is a time constant and depends on the wave length and the system wiring. Figure A 17 illustrates the dependency of the wiring on the pulse delay. If the first peak is positive, the pulse delay is one times the wave length because the threshold detection is only triggered for incoming negative signal peaks. In case of an inverse wiring the first signal peak is negative and therefore the pulse delay is one and a half times the wave length. Since the pulse delay is a constant it is already integrated into the edit routine of the PWL system and usually requires no adjustment while logging. However, if hardware is replaced or samples with a different geometry are measured the pulse delay has to be adjusted.
The calibration for circuitry delay (time needed by the emitted pulse of the pulse transmitter to reach the active element and vice versa from the receiver to the oscilloscope as well as electrical delays), transducer delay (time needed by the P-Wave to propagate the distance between the active elements and the transducer faces) and liner delay (time needed by the P-W ave to travel trough the liner walls) is performed simultaneously . by means of a calibration standard. A small segment of liner filled with distilled water is placed between the transducer faces. The most suitable calibration liner is a liner segment of the same type and size as the core being logged. After placing the standard in the core track, an ultrasonic pulse is triggered (same pulse as if logging a normal core) and the total pulse travel time is recorded, including all delays described above. The absolute travel time through the sediment (distilled water) can be calculated due to the fact that the P-Wave velocity of distilled water at a particular temperature is known (Figure A 18). The equation to calculate the absolute travel time is given by: where ts is the pulse travel time in sediment (distilled water), de is the distance between the transducer faces, dw is the total wall thickness of the liner of the calibration standard, ds is the sediment thickness obtained from the displacement measurement (see 3.1) and Vp,w is the P-Wave velocity of distilled water.
The total delay time of the pulse {tctetay) due to circuitry delay {tcirc), transducer delay (ttrans), liner delay (tw) and pulse delay {tpulse) results in: where ttot is the recorded travel time of the measurement.
The total delay time is a constant of the measurement device in conjunction with the calibration standard liner (liner of the core being logged) and therefore has only to be inserted into the PWL system once before logging.
To obtain the P-Wave velocity through the sediment inside the core liner (corrected velocity) Equation (A 18) is used: Data Processing. Post-processing of the logged P-Wave velocity is inevitable to provide universal and comparable data sets that can be used for investigation and research. The major corrections .of the measured laboratory P-Wave velocity are for temperature (laboratory and in situ correction), salinity (in situ correction) and pressure (in situ correction).
The temperature of the interstitial fluid effect on the P-Wave velocity is described previously. However, differences in temperature between different logging environments (sites) have to be addressed to obtain compatible data sets. The standard or set temperature for velocity data is 20°C. An equation for the approximation of the ambient or environmental temperature to the standard temperature is provided by: (A 19) In this equation Vp,T (in mis) is the corrected P-Wave velocity at temperature T ( 0 C), Vp the logged P-Wave velocity (in mis) Vp,T,w is the velocity of the pore water at desired temperature (mis) and V p,T,L is the temperature of the pore water at the moment of logging.
In some cases it is desirable to compare the laboratory measurement with in situ down-hole measurements. However, the environment in respect of temperature, salinity and pressure (depth) is obviously very different to provide sufficient statements. To account for these differences a polynomial function  together with the ratio method  can be used; where Yp,z is the in situ P-Wave :velocity (in mis), Vµ , 20 is the logged P-Wave velocity at 20°C (in mis), z is the depth (in m), Tis the temperature (in °C), Sis the salinity (in %0) and Vp,sw is P-Wave velocity of sea water at 20° C.

Electrical Resistivity
The electrical resistivity has been used as a fundamental tool for physical property evaluation for over 60 years. Commonly it is measured in situ by means of down hole probes. Recently, non-contacting electrical resistivity (NCR) measurements were performed with core logging devices using a methodology called the eddy current technique. The most important property that can be derived by resistivity is porosity.
Apparatus. The NCR device is integrated at the end of the sensor track. It is placed below the conveyer track and just between the set of rails (Figure A 19). The distance between the sensor and the moving core sample is limited to a minimum, due to physical restrictions of the methodology of the resistivity measurement. The external appearance of the sensor is box shaped and about 10 by 15 cm. The internal configuration of the sensor and the electrical units as well as the specifications remains unknown for the user due to the fact that most of these devices are legally patent protected. However, the main components are briefly described and are similar for a wide range of devices.
The NCR device uses eddy current techniques that consist of two sets of coils. The first set of coils (measuring coils) is located in the upper part of the sensor box and is aligned vertically and perpendicular to the core sample axis. One of these coils acts as the transmitter coil and is connected to an alternating current source at the electronic rack. The other one acts as the receiver coil and is connected to an impedance analyzer ( eddyscope) at the electronic rack. The second set of coils is identical but located in the lower part of the sensor and is insulated from the sphere of influence of the measuring coils. The connections to the electronic rack are similar to the first set.
Principle. The main principle, on which the non-contact resistivity (NCR) is based, is the eddy current technique. The eddy current technique takes advantage of the ability of conductive materials to generate a magnetic field while under the influence of an electric current that can be measured and converted into resistivity. The transmitter coil is connected to an alternating current (AC). If the current is passed through the coil, an alternating magnetic field is generated in and around the coil. If the coil is placed close to the sample the alternating magnetic field of the coil penetrates into the sample. The penetration depth of the magnetic field depends on the frequency of the excitation current, the design of the coil (number of loops), and the conductivity and magnetic permeability of the sample. The depth increases with decreasing frequency, increasing number of loops (larger magnetic field) and increasing conductivity and magnetic permeability ( Figure A 20).
Due to the conductivity and the magnetic permeability of the sample, the applied magnetic field initiates current flow within the sediment sample by means of induction. The direction of movement is orbital and perpendicular to the magnetic flux. This induced current is called the eddy current because of its similar appearance to swirling water currents. The eddy currents in the sediment sample, in tum, generate their own magnetic field which can be detected and converted into a voltage by the receiver coil (re-induction).
The magnetic field generated by the eddy currents is very small. To be able to measure this small magnetic field with as much accuracy as possible, a reference set of coils operating in air is used. This methodology minimizes the effect and influence of natural or artificial (electronic devices) magnetic fields in the immediate vicinity.
The measured voltage, as result of the eddy current magnetic field, is a function of the conductivity of the sample and, consequently, its resistivity which is the reciprocal of the conductivity.
Calibration. As described previously, the non-contact resistivity (NCR) device measures only the voltage of the receiver coil, induced by the eddy currents. Placing the saline solution contained in a core liner over the electrical resistivity sensor and measuring the sensor response (voltage) for each case, a plot of resistivity over sensor response and voltage, is evaluated. The core liner used for the calibration should have the same liner specifications as the liner of the core being logged (size, shape and material) because the resistivity sensor is very sensitive to different measurement geometries.
Once the sensor is calibrated (i.e. Table A  The resistivity of materials is very sensitive to variations m temperature. The resistivity decreases as temperature increases. To be able to provide comparable resistivity data it is essential to apply a temperature correction for the logging environment. This can be done by using the charts given in the literature or by using an approximation :

R =R *[T 1 +21.5]
T,2 T,1 T2 + ~1.5 In Equation (A 23), RT,2, is the electrical resistivity corrected for temperature (ohmm), RT,l is the measured electrical resistivity, T 1 is the temperature at which the sample was measured ( 0 C) and T 2 is the desired temperature ( 0 C). It should be mentioned that Equation (A 23) is an approximation.
Data Processing. For the relationship between the electrical resistivity and the porosity no universal model covers the wide range of sediment types and mixtures.
Several empirical and theoretical models that yield sufficient results for the porosity evaluation are described in the literature. The resistivity of a sample is influenced by several factors such as type of sediment (sand, silt, clay, etc), size, shape, structure, distribution and cementation of particles, and tortuosity that have to be taken into account by selecting an appropriate model.
In 1942, Archie was the first who linked the electrical resistivity of fluid saturated sandstone to the porosity and to the resistivity of the interstitial pore fluid. He introduced the formation factor FF which is the ratio of formation resistivity (resistivity of the whole sample) and the resistivity of the interstitial pore fluid and is unique for each soil or sediment composition: where FF =the formation factor (non-dimensional), R = electrical resistivity of the sample ( ohm-m), and Rw = electrical resistivity of the interstitial pore fluid ( ohm-m).
The evaluation of the electrical resistivity of the sample is described above. The resistivity of the interstitial pore fluid can be calculated using Equation (A 21 ).
Furthermore, Archie provided an empirical relationship between the formation factor and the porosity that he developed from investigations of sandstones: In this equation m is a dimensionless constant and allows for tortuosity of the pore sediments. Archie's equation (also referred to as Archie's Law) is based on the assumption that the conductivity of a fluid saturated sediment sample is due to the connectivity of conductive fluid-filled pores. The solid phase (i.e. particles) is considered to have infinitive resistance ( R ~ oo ). However this assumption is only valid for sands with little or no clay-mineral content. If the samples contain clay particles, the conductivity of the sample is not only due to the conductivity of the interstitial pore-fluid but also due to the conductivity of the clay particles. Clay particles are charged particles and therefore are able to conduct currents.