CA1216681A

CA1216681A - Formation density logging while drilling

Info

Publication number: CA1216681A
Application number: CA000440854A
Authority: CA
Inventors: Daniel F. Coope
Original assignee: NL Industries Inc
Current assignee: Halliburton Energy Services Inc; NL Industries Inc
Priority date: 1983-03-11
Filing date: 1983-11-09
Publication date: 1987-01-13
Also published as: AU561685B2; FR2542455A1; GB2136562A; GB8331582D0; BR8306189A; GB2136562B; AU1850183A

Abstract

ABSTRACT
A gamma ray density sub and method useful for measurement-while-drilling applications utilizing a gamma ray source and detector located on the rotating sub and computation of the product of the counting rates obtained from at least three locations in the formation sample, the locations being located in an azimuthally symmetric pattern about the sub therefore indicating the average density location in the formation sample surrounding a borehole traversing an earth formation. Alterna-tively, a gamma ray density sub utilizing three pairs of gamma ray sources and detectors located symmetrically about the axis of the sub and computation of the product of the counting rates obtained from the three detectors to indicate the average density of a formation sample surrounding a borehole traversing an earth formation. The sub is able to measure the density of the sample, independent of the location of the sub within the borehole and the chemical composition of the interfering mater-ials lying between the formation sample and the detectors.

Description

~Z166~i Coope FORMA~ION DENSITY LOGGING WHILE DRILLING

Background of the Invention 1. Field of the Invention The present invention relates to logging of subterranean formations for determination of density using gamma rays.
Particularly, this invention relates to determination of forma-tion density while drilling a borehole traversing the earth formation. More particularly, this invention relates to deter-mination of formation density without positioning the logging probe against the wall of the borehole traversing the earth formation.

2. Setting of the Invention Wireline gamma ray density probes are devices incorporating gamma ray source and a gamma ray detector, shielded from each other to prevent counting of radiation emitted directly from the source. During operation of the probe, gamma rays (or photons) emitted from the source enter the formation to be studied, and interact with the atomic electrons of the material of the forma-tion by photoelectric absorption, by Compton Scattering, or by ;681 pair production. In photoelectric absorption and pair production phenomena, the particular photons involved in the interacting are removed from the gamma ray beam~
In the Compton Scattering process, the involved photon only loses some of its energy while changing its original direction of - travel, the loss being a function of the scattering angle. Some of the photons emitted from the source into the sample are accordingly scattered toward the detector. Many scattered rays do not reach the detector, since their direction is changed by a second Compton scattering, or they are absorbed by the photoelec-tric absorption process of the pair production process. The scattered photons that reach the detector and interact with it, are counted by the electronic equipment associated with the detector.
The major difficulties encountered in conventional gamma ray density measurements include definition of the sample size, limited effective depth and sampling, disturbing effects of undesired, interfering materials located between the density probe and the sample and the requirement that the probe is positioned against the borehole wall. The chemical composition of the sample also affects the reading of conventional gamma ray density probes. This is complicated further when the density measurement tool is made part of a drilling string and operated during drilling operations. There are no known density probes useful in measurement while drilling apparatus.

~21~

One prior art wireline density probe disclosed in U.S. Pat.
No. 3,202,822 incorporates two gamma ray detectors, one colli-mated gamma ray source and ratio building electronic circuits, and is useful as long as the interfering materials, located between the detectors of the probe ana the formation sample, are identical in thickness and chemical composition along the tra~ec-tories of emitted and received gamma ray. Non-uniformities in the wall of the borehole will interfere with the proper operation of the probe. Such non-uniformities can be caused by croo~ed holes, by cave-ins, and by varying thicknesses of the mudcake on the wall of the hole.
The prior art also includes U.S. Pat. No. 3,846,631 which discloses a wireline density probe that functions regardless of the thickness and the chemical composition of materials that ar`e located between the density probe and the sample. The method comprises passing of two gamma ray beams from two intermittently operated gamma ray sources into the sample, receiving the radia-tion back-scattered from each of the two sources by two separate detectors, and building ratios of products of the four separate counting rates in such a manner that the numerical result is an indication of the density of the sample.
The critical dimension of the two-detector probe is the spacing between the detectors. If the interfering materials are non-uniform over distances comparable to the spacing of the two detectors, the measured density will be erroneous.

~2i668~ --Neither of the wireline probes described above is disclosed as being useful for measurement when clrilling and incorporation into a rotating drill string.

SUMMARY OF THE INVENTION
It is a primary object of this invention to provide a method and apparatus for measuring the density of a subterranean forma-tion while drilling a borehole traversing the formation.

Another object of this invention is an apparatus of the invention for logging the density of a formation surrounding a borehole traversing the formation, the apparatus adapted for use in a drill string including; a means for emitting gamma rays into the formation; a means for counting emitted gamma rays scattered from a sample in the formation back to the apparatus, the count-ing means producing I number of separate counts, each count being determined over a preselected period of time the periods being equal and commencing each 360/I angle of rotation, wherein I is an integer equal to at least three; and a means for determining a product of the I number of counts, wherein the product is indica-tive of the average density of the formation sample.
The object of this invention is realized further by the method of determining the average density of a formation sample of earth formation surrounding a borehole traversing the forma~
tion comprising rotating the device; emitting gamma rays into the formation determining I number counts of the emitted gamma rays scattered from a first formation sample back to the device, each count being determined over a preselected period of time and commencing each 360/I angle of rotation, wherein I is an integer equal to at least three and determining a product of at least three counts, wherein the product is indicative of the average density of the first formation sample.
Another object of this invention is realized in the appara-tus of the invention which includes a device for use in a bore-hole traversing an earth formation including a gamma ra~ emitting 1~ means, the means emitting collimated gamma ray beams along at least three trajectories, the trajectories projecting in an azimuthally symmetric pattern about the axis of the device, intersecting at a first point on the axis of the device, and intersecting a first circle located in a sample of the formation to be measured, a first gamma ray detecting means oriented to receive emitted gamma rays scattered from at least three loca-tions within the formation sample along a first at least three trajectories, the trajectories projecting in an azimuthally symmetric pattern about the axis of the device, intersecting a second point on the axis of the device, intersecting a second point on the axis of the device and intersecting the first circle, and a means for determining the product of the counting rate of gamma rays received by the detecting means from each of the at least three trajectories as scattered from the at least three locations within the formation sample, wherein, the product is indicative of the average density of the formation sample.

~31,66~.

The object of this invention is realized still further by the method of determining the average densi.y of a sample of earth formation surrounding a borehole including the steps of lowering a device into the borehole to a location adjacent to the sample; emitting gamma rays into the formation from the device along at least three trajectories projecting in an azimuthally symmetric pattern about the axis of the device, intersecting at a first point on the axis of the device and interesecting a first circle located in the formation sample, counting the emitted g~mma rays scattered from the formation sample back to the device along a first set of at least three trajectories project-ing in an azimuthally symmetric pattern about the axis of the device, interesecting at a second point on the axis of the device and interesecting the first circle, and determining the product of the at least three count measurements, wherein the product is indicative of the average density of the formation sample.

BRIEF DESC~IPTION OF THE DRAWING
-Other features and intended advantages of the invention will be more readily apparaent by reference to the following detailed description in connection with the accompanying drawings.
Fig. 1 is cross-sectional representation of a device in accordance with the present invention for logging densities in a formation having three sources and three detectors.
Fig. 2 is a cross-sectional representation of a device in accordance with the present invention for logging densities in a ~Z1668~

formation traversed by a rotating drill string, in which the device may be which the device may be located, the device having one source and one detector.
While the invention will be described in connection with presently preferred embodiments, it will be understood that it is not intended to limit the invention to the embodiment. On the contrary, it is intended to cover all alternatives, modifications and equivalents as may be included within the spirit of the inventor as defined in the appended claims.

PREFE~RED EMBODIMENTS OF THE INVENTION
The gamma density sub 10 of this invention is shown in the drawing as interconnected between the upper drill string 12 and the lower drill string 14 rotates causing the drill bit 16 to form borehole 18 traversing earth formation 20.
The sub 10 includes a gamma ray source 22 and a first gamma ray detector 24. The first detector 24 is preferably situated on the sub 10 in azimuthal alignment with the source 22. The first detector 24 is collimated to receive gamma rays scattered from the formation along a trajectory 26 which intersects the trajec-~ tory 28 of the gamma rays emitted from the source 22.
The sub 10 may include a second gamma ray detector 30. This second detector 30 is preferably situated on the sub 10 in azimuthal alignment with the source 22, and the first detector 24~ The second detector 24 will receive gamma rays along a ~Z~

trajectory 32 which interesects the trajectory 28 of the gamma rays emitted from the source. The trajectory 32 of the rays received by the second detector should parallel the trajectory 24 of the received rays of the first detector.
The first and second detectors are shielded from the source ~ to prevent the emitted gamma ~ays from reaching the detectors directly.
A first circle 34 is formed by the point of intersection of the trajectory 28 of ~he rays emitted from the source and the trajectory 26 of the rays received from the first detector as the sub 10 is rotated about its axis. A second circle 36 is formed by the point of intersection of the trajectory 28 of the rays emitted from the source and the trajectory 32 of the rays re-ceived from the second detector as the sub is rotated. The first circle 34 lies in a first formation sample 38 which is to be measured for density, and the second circle 36 lies in the second formation sample 40 which is to be measured for a compensated average.
In the method of this invention the sub 10 rotates about its axis 42 as gamma rays 28 are emitted into the sample by the source 22. The emitted collimated beams of gamma rays form a first cone-shaped region of formation which is radiated.
In the formation 20, gamma rays 28 of the emitted gamma rays 28 are scattered by the sample formation 38 at location 44 toward the first detector 24 and counted during a first collection ~216681 time, T1. Gamma rays 46 and 48 are scattered at locations 50 and 52 in formation sample 38 towards and received by the first detector 24 during second and third collecting times, T~ and T3 respectively.
Since there is only one collimated source 22, there is only one right conical region radiated during the sub's rotation. The collimated detector 24 receives scattered gamma rays 26, 46 and 48 from the formation sample 38 along trajectories forming a second cone, inverted with respect to the first cone and inter-secting at the first circle 34.
The cone's thicknesses are determined by the diameter of the collimator for the source and first and second detectors. The first circle 34 formed by the intersection of the cones has as its center axis 42 of sub 10. In one rotation of the drill string, gamma rays from three small sectors 54, 56 and 58 of the formation sample 38, each 120 from the others, will be received by the detector 24 and sampled during the collecting times T1, T~, and T3.
Even though T1 = T2 = T3, (the collecting times are equal) 2~ the count measurements during T1, T2 and T3 ~ay vary in magni-tude due to the location of the sub and the intermediary material The individual counts from the first and second detectors for a respective collecting time may vary with time due to the sub's location within the borehole as caused by rotation of the drill string off of the axis of the borehole.

6~ ~

Counting of received gamma rays commences when the sub has rotated an incremented 360/I degrees from a starting point and continues for a preselected period of time. Each measurement of counts for the preselected period of time is maintained sepa-rately. The I number of measurements for a given rotation are multiplied to form a product, the product being indicative of the average density of the formation sample. The time periods are determined by the sensitivity of the receiver and the rate of emission of the source, such that the number of counts is repre-sentative of the rays scattered back from the formation.
The angle of rotation may be determined by conventional means. Additionally, it is contemplated to be within this invention, the angle of rotation may be eliminated where the angular rotation rate is relatively constant. In such a case, the counting period would commence at time intervals spaced by the time of rotation divided by the I integer.
In the method of this invention, the at least three instan-taneous counts from the first detector made during one rotation are multiplied thereby resulting in a constant value thus indi-cating elimination of variables with time between one rotationand subsequent rotations such as the thickness of mud through which the emitted gamma rays must pass to be received at the detectors and the movement of the sub in relation to the borehole wall.
The sub in an off axis position will receive gamma rays 26, 46 and 48 that have scattered from the formation sample 38 at ~21~681 detector 24 that have traveled through a different amount of mud and formation. However, the sum of the path lengths through mud, and the sum of the path lengths through the formation are constant provided that the diameter of the sub 10 is substanti-ally similar to the diameter of borehole 18.
Alternatively, the sub 110 includes a first gamma ray source 122, a second gamma ray source 124, and a third gamma ray source 126. The three sources are situated about the sub in an azimuth-ally symmetric pattern. More sources may be utilized provided that total number are in azimuthally symmetrically orientation about the sub 110. The sources are collimated to form trajec-tories which are also azimuthally sym~etrical. The trajectories are oriented to pass through a first point 128 located on the axis 129 of the sub 110. The term trajectory as used herein indicates not only the actual path of travel of the gamma ray but also a line of extension behind the source as well as beyond the detector.
The plurality of sources may be a single primary source from which the emitted gamma rays are collimated to form the at least three symmetrical gamma ray beams.
The sub 110 further includes a first set of detectors including a first gamma ray detector 130, a second gamma ray detector 132, and a third gamma ray detector 134. The detectors are situated about the sub 110 in an azimuthally symmetrical pattern which is in radial alignment with the first, second and 12166~1 `

third sources 122, 124 and 126. If more sources are utilized, an equivalent number of detectors will also be used. The detectors are collimated to receive gamma rays scattered from the formation along trajectories which are also azimuthally symmetrical. The trajectories are oriented to intersect the axis 129 of the sub 110 at a second point 136.
The trajectories from the sources will intersect the first set of detector trajectories at a first circle 138 about the sub 110. The first circle fall~ in a plane which is perpendicular to the axis of the sub 110, the plan intersecting the axis 129 at a third point 139. The second point is positioned an axial dis-tance away from the first point and the first and second points are preferably on opposite sides of the third point 139.
The sub 110 includes a second set of detectors including a fourth gamma ray detector 140, a fifth gamma ray detector 142 and a sixth gamma ray detector 144. This second set of detectors is situated about the sub 110 in an azimuthally symmetrical pattern which is also an azimuthal alignment with the first, second and third sources~ 122, 124 and 126 and the first set of detectors 20 130, 132 and 134.

The second set of detectors will receive gamma rays along a third set of at least three trajectories which are azimuthally symmetric about the sub 110 and are oriented to intersect the axis 129 at a fourth point 145 and to intersect a second circle 172~ Preferably, the fourth point 145 and the first point are on ~21~;68~l opposite sides of the third point 139. Each trajectory of the third set should parallel to a corresponding trajectory of the second set.
The first and second set of detectors are shielded from the sources to prevent the emitted gamma rays from reaching the detectors directly.
The first circle 138 and the second circle 172 formed in the formation 120 will be the center of the formation samples 146 and 147 respectively which are to be measured for density.
In the method of this invention the sub 10 rotates about its axis 129 as gamma rays 14B are emitted into the sample by the first source 122, gamma rays 150 by the second source 124 and gamma rays 152 by the third source 126. The emitted collimated beams of gamma rays form a cone-shaped region of formation which is radiated.
In the formation 120, some of gamma rays 148, 150 and 152 are scattered by the sample formation 146 toward the first set of detectors. Gamma rays 154 are scattered at location 156 in formation sample 146 toward and received by the first detector 30. Gamma rays 158 and 160 are scattered at locations 162 and 164 in formation sample 146 towards and received by the second and third detectors 132 and 134 respectively. Since the three collimated sources 122, 124 and 126 are symmetrically located, there is only one right conical region radiated during the sub's rotation. The three collimated detectors 130, 132 and 134 ~2~

receive emitted gamma rays scattered from the formation sample 146 back to the sub 110 alon~ trajectories forming a second cone, inverted with respect to the first cone.
The received gamma rays 154, 158 and 160 will react with the first set of detectors 130, 132 and 134 and cause electrical - pulses. The pulse amplitudes are proportional to the energy of the received gamma rays. If it is desîred to provide countin~
rates indicative of only those rays which have been scattered only once in the sample 134, these pulses would be amplified by l~ preamp~ifiers and amplifiers, and fed to discriminators not shown, which are set to pass only those pulses having energy levels of gamma rays that were scattered at the location 156, towards the detector 130, at location 162 towards the detector l32 and at location 164 towards the detector 134. Gamma rays that underwent multiple scattering prior to entering the detec-tors 130, 132 and 134 will be rejected by the discriminators.
The output of the detectors and, if used, the discriminators leads to the gates, not shown, which provide individual counting rates of received gamma rays from the three detectors 130, 132 and 134.
The individual counts from the first and second set of detectors may vary with time due to the sub's location within the borehole as caused by rotation of th drill string off of the axis of the borehole.

3~6681. --In the alternative method of this invention, the threeinstantaneous counts from the first set of detectors are multi-plied thereby resulting in a constant value thus indicating elimination of variables with time such as the thickness of mud and casing which the emitted gamma rays must pass to be received at the detectors and the movement of the sub in relation to the borehole wall.
A density log for measurement while drilling applications should be accurate to within about O.l g/cm3. since formation density is typically 2.5 g/cm3, an accuracy of better than 4%
is required. If vertical resolution required for the log is 0.5 foot, a required counting rate may be estimated as follows:
< 0.01 NlN2N3 where:
is the statistical variation of the product N1N2N3, Nl is the counting rate at detector 30, N2 is the counting rate at detector 32, and N3 is the counting rate at detector 34.

Assuming N1 = N2 = N3 = N

then 2 = 3N5 and = c 3 < 0 01 _ Solving for N

N > 3.0 x 104 counts ~2~;68~ --Each density log measurement should detect an average of 30,000 counts per measurement and there should be at least one measurement every 1/2 foot. At 60 feet per hour drilling rate, each measurement will therefore be completed in 10 seconds, or less, since it must be completed in no more than 1/3 of a rota-tion.
Therefore, the first detector and the second detector if utilized for compensation purposes should have sufficient sensi-tivity such that about 1000 counts per second per detector are registered. Alternatively, the source may be adjusted to emit at a rate such that the detectors receive at the required rate of 1000 counts per second per detector.
Since the sub is rotating, each count measurement may be less than that required for a statistically accurate measurement of the formation density. One method of achieving accuracy, is to sum the products of each rotation until sufficient counts are obtained~ The summation of products or ratios of products in the case of a compensated density does not result in an absolute density but is indicative of the density when correlated with prior measurements.
To compensate the average density for the formation sample 38, the method of this invention may include use of the counts from the second detector 30 during the at least three counting periods of one rotation of the drill string. The product of these at leat three counts would be used to form a ratio between ~2~

the product of the first detector and the product of the second detector. Alternatively, the product of the three ratios of the first detector to the second detector may be used to determine the average compensated density.
A similar arrangement for the second detector 30 may be included in the sub 10 for receiving, discriminating, counting, storing and using the gamma rays received by the second detector.
The type of the gamma ray source is not an object of the invention, since different types are preferred for different applications. Capsule type sources containing the radioactive isotopes such as cobalt 60 and cesium 137, are the gamma ray sources most frequently used in gamma ray density probes.
The diameters of the borehole and the sub 10 should be substantially equivalent. This can be accomplished by use of stabilizers on the exterior of the sub 10 which are then part of the relative diameter determination.
Various other alterations in the details of construction and the sequence of computations can be made without departing from the scope of the invention, which is indicated in the appended claims.

Claims

WHAT IS CLAIMED

1. A rotating device for use in a borehole traversing an earth formation comprising a gamma ray emitting means, said means emitting a collimated gamma ray beam along a first trajectory, intersecting a first circle located in a sample of said formation to be measured, a first gamma ray detecting means oriented to receive emitted gamma rays scattered from locations within said first circle, a means for counting said received gamma rays during I preselected periods of time, each period being equal and commencing each 360°/I of rotation, wherein I is a integer which is at least three, and a means for determining the product of said I counting rates of gamma rays received by said first detecting means wherein said first product is indicative of the average density of said formation sample.

2. The device of Claim 1 wherein said device is operate irrespective of the location of said device within said borehole.

3. The device of Claim 1 wherein the diameter of said device is substantially equivalent to but smaller than the diameter of said borehole.

4. The device of Claim 1 comprising additionally a second detecting means oriented to receive emitted gamma rays scattered from locations within a second circle which is intersected by the trajectory of said emitted gamma ray and a means for determining a second product of the counting rates of gamma rays received by said second detecting means during said I preselected periods of time, wherein said first product is divided by said second product to determine a ratio which is indicative of an average compensated density of said formation sample.

5. The device of Claim 4 wherein for the trajectory of the gamma rays received by said second detecting means is parallel to said trajectory of the gamma rays receivec by said first detector means.

6. A method of determining the average density of a formation sample surrounding a borehole traversing and formation comprising rotating said device; emitting gamma rays into said formation determining I number counts of said emitted gamma rays scattered from a first formation sample back to said device, each said count being determined over a preselected period of time and commencing each 360°/I angle of rotation, wherein I is an integer equal to at least three and determining a first paroduct of said at least three counts, wherein said first product is indicative of the average density of said first formation sample.

7. The method of Claim 6 comprising additionally determin-ing at least three separate counts of said emitted gamma rays scattered from a second formation sample back to said device, each said count being determined during said time period corres-ponding to said at least three counts of said first formation sample, determining a second product of said at least three counts and determing the ratio between said first and said secont product, wherein said ratio is indicative of an average compen-sated density of said formation sample.

8. The method of Claim 6 wherein said method is accom-plished without positioning said device within said borehole.

9. The method of Claim 7 wherein the trajectories of rays scattered back from said first formation sample are parallel to the trajectories of rays scattered back from said second forma-tion sample.

10. The method of Claim 6 comprises additionally collimat-ing said rays emitted from said device to form a beam which has a trajectory which intersects said first and second formation sample.

11. The method of Claim 6 comprises additionally collimat-ing said device to receive only gamma rays scattered from said first sample.

12. The method of Claim 7 comprises additionally collimat-ing said device to receive only gamma rays scattered from said second sample.

13. Apparatus for logging the density of a formation surrounding a borehole traversing said formation, said apparatus adaptaed for use in a drill styring comprising; a means for emit-ting gamma rays into said formation; a means for counting emitted gamma rays scattered from a sample in said formation back to said apparatus, said counting means producing I number of separate counts, each count being determined over a preselected period of time each said period being equal and commencing each 360°/I
angle of rotation, wherein I is an integer equal to at least three; and a means for determining a first product of said I
number of counts, wherein said first product is indicative of the average density of said formation sample.

14. The apparatus of Claim 13 wherein said counting means is oriented to detect scattered gamma rays along a trajectory intersecting said formation sample.

15. The apparatus of Claim 13 wherein I is 3.

16. A device for use in a borehole traversing an earth formation comprising a gamma ray emitting means said means emitting collimated gamma ray beams along a first set of at least three trajectories, said trajectories projecting in a azimuthally symmetric pattern about said axis of said device, and intersect-ing a first circle located in a sample of said formation to be measured, a first gamma ray detecting means oriented to receive emitted gamma rays scattered from at least three locations within said formation sample along a second set of at least three trajectories, said trajectories projecting in an azimuthally symmetric pattern about said axis of said device intersecting a second point on the axis of said device and intersecting said first circle, and a means for determining the product of the counting rates of gamma rays received by said first detecting means from each of said at least three trajectories as scattered from each of said at least three locations within siad formation sample, wherein said first product is indicative of the average density of said formation sample.

17. The device of Claim 16 wherein said first circle lies in a first plane which is perpendicular to the axis of said device and intersects said axis at a third point.

18. The device of Claim 16 wherein said device is adaptable for use in a drill string.

19. The device of Claim 16 wherein said gamma ray emitting means comprises gamma sources, each source collimated to emit gamma rays along one of each of said first set of at least three trajectories.

20. The device of Claim 19 wherein said sources are posi-tioned in an azimuthally symmetric pattern about said device and lie in a second plane which is perpendicular to tahe axis of said device.

21. The device of Claim 16 wherein said first detecting means comprises at least three detectors, each said detector collimated to receive gamma rays along one of said second set of at least three trajectories.

22. The device of Claim 16 wherein said device is operate irrespective of the location of said device within said borehole.

23. The device of Claim 16 wherein the diameter of said device is substantially equivalent to but somewhat smaller than the diameter of said borehole.

24. The device of Claim 16 comprising additionally a second detecting means oriented to receive emitted gamma rays scattered from said at least three locations within said formation sample along a third set of at least three trajectories, said trajec-tories intersecting at a fourth point on the axis of said device and intersecting a second circle about said axis, said circle intersected by said first set of at least three trajectories and a means for determining a second product of the counting rates of gamma rays received by said second detecting means from each of said at least three trajectories as scattered from each of said at least three locations within said formation sample, wherein said frist product is divided by said second product to determine a ratio which is indicative of an average compensated density of said formation sample.

25. The device of Claim 16 wherein said first point is spaced apart from said second point.

26. The device of Claim 24 wherein said first point and said second point are spaced apart from said fourth point.

27. The device of Claim 26 wherein said first point is on one side of said third point and said second point is on the opposed side of said third point.

28. The device of Claim 24 wherein said first point is on one side of said third point and said fourth point is on the opposed side of said third point.

29. A method of determining the average density of a formation sample surrounding a borehole comprising lowering a device into said borehole to a location adjacent to said sample;
emitting gamma rays into said formation from the device along a first set of at least three trajectories projecting in an azi-muthally symmetric pattern about the axis of said device, inter-secting at a first point on the axis of said device and inter-secting a circle located in said formation sample, counting said emitted gamma rays scattered from said formation sample back to said device along a second set of at least three trajectories projecting in an azimuthally symmetric pattern about the axis of said device, intersecting at a second point on the axis of said device and intersecting said circle, and determining a first product of said at least three counts, wherein said first product is indicative of the average density of said formation sample.

30. The method of Claim 29 wherein said method is accom-plished without positioning said device within said borehole.

31. The method of Claim 29 comprising additionally counting said emitted gamma rays scattered from said formation sample back to sdaid device along a third set of at least three trajectories projecting in an azimuthally symmetric pattern about the axis of siad device, intersecting at a third point spaced apart from said second point on said axis of said device, and intersecting a second circle about said axis, said circle being intersected by said first set of at least three trajectories; determining a second product of said at least three counts, and determining the ratio between said first and said second product, wherein said ratio is indicative of an average compensated density of said formation sample.