16
Suggested Methods for Geophysical Logging 69 Suggested Methods for Geophysical Logging of Boreholes PART 1. TECHNICAL INTRODUCTION 1. Geophysical borehole logging may be used to measure a number of physical properties of the geologi- cal formations intersected by boreholes. The informa- tion gained may then be employed to determine, inter alia, the geometry of major subsurface structural dis- continuities and to estimate the mechanical properties of the formations surrounding the borehole. 2. Owing to the high cost of the specialized equip- ment and experience in interpretation required for geo- physical borehole logging, these are usually provided as a service by specialist organizations. However, some relatively simple borehole logging systems are also mar- keted for use in small-diameter boreholes (< 80 ram) to depths of less then 1000 m. WIRELINE EQUIPMENT 1. 3, Wireline equipment is generally used to perform geophysical borehole logging. While all wireline equip- ment is similar in its essential elements, it differs in detail among the specialist logging organizations. 4. A geophysical borehole logging system is com- prised essentially of the following elements: (a) A downhole probe (or sonde) containing the appropriate sensing systems. A probe may contain a number of sensing devices, so that several physical measurements can be made simultaneously. (b) An armoured, multi-conductor electric cable (the wireline), to which the probe is attached, and through which signals from the probe are transmitted from within the borehole to the surface. (c) A winch and mast, or tripod, for lowering and raising the probe in the borehole. (d) A calibrated sheave on the mast or tripod for measuring the length of cable in the borehole. (e) A surface power unit. (f) An electronic system for recording the signals received from the probe. The resulting signals are recorded as a function of depth, and constitute the geo- physical borehole log. 5. These elements are assembled as a unit best suited for the site at which the borehole logging is to be per- formed. Trucks are employed where the site is access- ible, but the equipment may be disassembled into several skid-mounted components for helicopter trans- port to remote sites or transport underground. * Numbers refer to Notes at the end of Part 1. GEOPHYSICAL BOREHOLE LOGGING MEASUREMENTS 6. The different types of logging probes fall into four major classes: (a) Electric logs, including the electrical resistivity (normal, microlog and focussed devices), spontaneous potential (SP) and induction logs. (b) Radiation logs. including the natural gamma ray, neutron and gamma-gamma density logs. (c) Sonic logs, including the borehole televiewer. (d) Miscellaneous logs, including the caliper and tem- perature logs, the directional survey, dipmeter and TV logs. ELECTRIC LOGS 7. Electric log probes are used to measure the electri- cal resistivity of the formations surrounding the bore- hole, and the spontaneous potentials existing within the borehole itself. With the exception of rocks containing electrically-conductive minerals, the electrical resistivity of formations is governed by the presence and salinity of interstitial water and by the size and continuity of the interstices. Spontaneous potentials in boreholes are caused chiefly by the differences in salinity existing between the fluid filling the borehole and that saturat- ing the adjacent formation. The response of electric logs is therefore strongly affected by the nature of the water contained in the interstices of the adjacent formation, and by the nature of the interstices themselves. 8. The conventional resistivity logs include the single- point resistance, and the normal and lateral resistivity devices. These probes are responsive to the electrical resistivity of the formations surrounding the borehole. The normal devices are often used for stratigraphic control purposes, and under certain conditions may provide an estimate of the porosity of porous, per- meable zones. 9. The spontaneous potential (SP) log responds to differences in electrical potential occurring opposite boundaries between different formations down the borehole. These potentials are of electrochemical ori- gin; their presence requires a contrast in resistivity between the fluid filling the borehole and the naturally- occurring fluid in the formation. The SP log is employed with the resistivity devices for correlation purposes and for defining the boundaries between for- mations. The magnitude of the SP can, under certain circumstances, be used to determine the resistivity, and hence the salinity, of the naturally-occurring formation water.

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Page 1: Suggested Methods for Geophysical Logging of Boreholes · The SP log is employed with the resistivity devices for correlation purposes and for defining the boundaries between for-

Suggested Methods for Geophysical Logging 69

Suggested Methods for Geophysical Logging of Boreholes

PART 1. T E C H N I C A L I N T R O D U C T I O N

1. Geophysical borehole logging may be used to measure a number of physical properties of the geologi- cal formations intersected by boreholes. The informa- tion gained may then be employed to determine, inter alia, the geometry of major subsurface structural dis- continuities and to estimate the mechanical properties of the formations surrounding the borehole.

2. Owing to the high cost of the specialized equip- ment and experience in interpretation required for geo- physical borehole logging, these are usually provided as a service by specialist organizations. However, some relatively simple borehole logging systems are also mar- keted for use in small-diameter boreholes (< 80 ram) to depths of less then 1000 m.

WIRELINE EQUIPMENT 1.

3, Wireline equipment is generally used to perform geophysical borehole logging. While all wireline equip- ment is similar in its essential elements, it differs in detail among the specialist logging organizations.

4. A geophysical borehole logging system is com- prised essentially of the following elements:

(a) A downhole probe (or sonde) containing the appropriate sensing systems. A probe may contain a number of sensing devices, so that several physical measurements can be made simultaneously.

(b) An armoured, multi-conductor electric cable (the wireline), to which the probe is attached, and through which signals from the probe are transmitted from within the borehole to the surface.

(c) A winch and mast, or tripod, for lowering and raising the probe in the borehole.

(d) A calibrated sheave on the mast or tripod for measuring the length of cable in the borehole.

(e) A surface power unit. (f) An electronic system for recording the signals

received from the probe. The resulting signals are recorded as a function of depth, and constitute the geo- physical borehole log.

5. These elements are assembled as a unit best suited for the site at which the borehole logging is to be per- formed. Trucks are employed where the site is access- ible, but the equipment may be disassembled into several skid-mounted components for helicopter trans- port to remote sites or transport underground.

* N u m b e r s refer to N o t e s at the end of Pa r t 1.

GEOPHYSICAL BOREHOLE LOGGING MEASUREMENTS

6. The different types of logging probes fall into four major classes:

(a) Electric logs, including the electrical resistivity (normal, microlog and focussed devices), spontaneous potential (SP) and induction logs.

(b) Radiation logs. including the natural gamma ray, neutron and gamma-gamma density logs.

(c) Sonic logs, including the borehole televiewer. (d) Miscellaneous logs, including the caliper and tem-

perature logs, the directional survey, dipmeter and TV logs.

ELECTRIC LOGS

7. Electric log probes are used to measure the electri- cal resistivity of the formations surrounding the bore- hole, and the spontaneous potentials existing within the borehole itself. With the exception of rocks containing electrically-conductive minerals, the electrical resistivity of formations is governed by the presence and salinity of interstitial water and by the size and continuity of the interstices. Spontaneous potentials in boreholes are caused chiefly by the differences in salinity existing between the fluid filling the borehole and that saturat- ing the adjacent formation. The response of electric logs is therefore strongly affected by the nature of the water contained in the interstices of the adjacent formation, and by the nature of the interstices themselves.

8. The conventional resistivity logs include the single- point resistance, and the normal and lateral resistivity devices. These probes are responsive to the electrical resistivity of the formations surrounding the borehole. The normal devices are often used for stratigraphic control purposes, and under certain conditions may provide an estimate of the porosity of porous, per- meable zones.

9. The spontaneous potential (SP) log responds to differences in electrical potential occurring opposite boundaries between different formations down the borehole. These potentials are of electrochemical ori- gin; their presence requires a contrast in resistivity between the fluid filling the borehole and the naturally- occurring fluid in the formation. The SP log is employed with the resistivity devices for correlation purposes and for defining the boundaries between for- mations. The magnitude of the SP can, under certain circumstances, be used to determine the resistivity, and hence the salinity, of the naturally-occurring formation water.

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70 International Society

10. The microresistivity devices are comprised of the microlog, microlateralog and proximity devices. These are proprietary miniature resistivity probes contained in a pad pressed against and conforming to the bore- hole wall. They provide extremely detailed information on the boundaries between formations intersected by the borehole. They are generally used to locate and delineate porous, permeable beds and to provide an estimate of the porosity of these beds.

I1. The focussed-current resistivity logs are pro- prietary and include the lateralog, guard log and spher- ically-focussed log (also the microlateralog, referred to in paragraph 10). These devices were introduced by the specialist geophysical borehole logging service compa- nies to provide estimates of the true resistivity of highly-resistive formations intersected by the borehole, in the presence of a saline fluid filling the borehole. The presence of fracturing m highly-resistive crystalline rocks is often indicated by a reduction in true resis- tivity.

12. The induction log is a device employing electro- magnetic waves to determine the conductivity (recipro- cal of resistivity) of formations intersected by the bore- hole. Since it does not require an electrically-conductive fluid in the borehole to provide coupling with the adja- cent formation, the induction log can be used in dry boreholes and in those filled with fresh water or oil. The induction device is unique in that the medium im- mediately surrounding the borehole usually contributes little to its response. Since it responds to the presence of thin beds of low resistivity, the induction log may often be used to indicate the presence of fractures in crystal- line rocks.

RADIATION LOGS

13. Radiation probes are used to measure the natural radioactivity of the formations adjacent to the bore- hole, and the response of the latter to bombardment by neutrons or gamma rays. Since the response of these probes is statistical in nature, the speed at which the borehole is logged is critical in obtaining reliable records. Radiation logs comprise essentially the follow- ing: natural gamma ray, neutron and gamma-gamma density probes.

14. The gamma-ray probe measures the natural emission of gamma radiation from formations adjacent to the borehole. Since radioactive elements are present in all rocks and tend to concentrate in clays and shales, the gamma-ray probe can be used for stratigraphic con- trol purposes, reflecting the clay and shale content of sedimentary formations and discontinuities in crystal- line rocks.

15. The neutron probe measures the response of the surrounding formation to bombardment by high- energy neutrons. The latter are slowed down most effec- tively by hydrogen nuclei. Depending'on the type of neutron probe, either gamma rays or capture of the slowed-down neutrons themselves are measured. The response of the probe is largely governed by the con-

for Rock Mechanics

centration of hydrogen nuclei in the surrounding for- mation, and it therefore provides a good indication of porosity.

16. The gamma-gamma density probe measures the response of the surrounding formation to bombard- ment by medium-energy gamma rays. The latter are slowed down and back-scattered by electrons in the formation. The amount of back-scattered gamma radi- ation measured by the probe is inversely proportional to the bulk density of the surrounding formation.

ACOUSTIC LOGS

17. The acoustic or sonic probe measures the velocity of propagation of elastic compressional waves travel- ling through the formation immediately adjacent to the borehole. Shear-wave velocities and the attenuation characteristics of both types of wave may be measured under certain conditions. Measurements of the veloci- ties and attenuation of compressional and shear waves may be correlated with the mechanical properties and degree of fracturing of the formation.

18. The borehole televiewer (or seisviewer), a pro- prietary instrument, measures the amplitude of ultra- sonic waves reflected from the borehole wall. The amplitudes measured are a function of the smoothness of the borehole wall and the presence of discontinuities intersecting the borehole. The resulting record is essen- tially an expanded black-and-white picture of the bore- hole wal [.

MISCELLANEOUS LOGS

19. The caliper probe continuously measures the average borehote diameter over its length. The caliper log is required to correct the interpretation of other logs which are affected by changes in borehole diam- eter. Changes in the borehole diameter may also indi- cate changes in lithology encountered. Certain caliper probes are sufficiently sensitive to locate individual fractures intersected by the borehole.

20. The temperature probe measures the temperature of the borehole fluid adjacent to the formations of interest. Anomalous temperatures will be measured under certain circumstances: e.g., if there is ground- water or.gas flow into the borehole.

21. The directional survey provides the dip and dip direction of the borehole.

22. The continuous dipmeter (or diplog), a pro- prietary instrument, measures the dip and dip direction of discontinuities intersected by the borehole. It employs either three or four identical miniature electric logs mounted in rubber pads at equal intervals around the borehol¢ circumference. During operation of the dipmeter, the rubber pads are forced into contact with the borehole wall. The information is recorded in digi- tal form and computer-processed to yield dips and dip directions of discontinuities intersected at intervals along the borehole. The inclinometer, included as an integral part of the dipmeter probe, records the data necessary to determine the magnitude and direction of

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Suggested Methods for Geophysical Logging 71

any borehole deviation. This knowledge is combined with relative dip and caliper data to determine the true formation dip and azimuth.

23. The TV log provides a picture of the borehole wall, with the cylindrical surface expanded to fill an oscilloscope screen. The picture may be videotaped for further analysis. Successful use requires an empty or clear-water filled borehole.

PROCEDURE: BOREHOLE DRILLING

24. Boreholes may be drilled by either of two methods, percussion or rotary-hydraulic, or by a com- bination of both. The rotary-hydraulic method is most widely used, although percussion drilling is still employed in areas underlain by hard rock. For geo- physical logging, the borehole should be of a diameter such that there is sufficient clearance for the largest probe employed to pass freely without fear of sticking. Since the downhole probe usually contains a number of sensing devices, each recording measurements at a dif- ferent position on the probe, the length of the borehole will determine to what depth it can be logged. The recording point may be several metres above the l:ottom of the probe.

25. In order to prepare a borehole for logging, it is necessary to have it filled with a fluid, usually drilling mud or water. The type of borehole fluid is of particu- lar importance in electric logging, for which it is advis- able to use water or water-based drilling fluid of fairly low salinity to obtain good records.

26. Often it is necessary to support the borehole wall with casing. Lining of the borehole with steel casing restricts the range of useful geophysical measurements essentially to those of the radiation logs. The presence of plastic casing, unless it has a large number of ports communicating with the formation, inhibits the re- sponse of the resistivity and SP logs.

L OGGING PROCEDURE

27. The boreholes will usually be logged as the probe is raised in the borehole. The speed at which the bore- hole is logged depends on the type of measurement being made, ranging from approximately 4 m/min for the radiation and caliper logs to 30 m/rain for the elec- tric and sonic logs. Particular attention should be paid to the nature of the borehole fluid if satisfactory electric logs are to be recorded. If the borehole is steel-cased, only the radiation logs will be effective opposite the cased sections of the borehole.

28. In order to evaluate the quality of the geophysical borehole logging in a borehole it is advisable to incor- porate a 'repeat section' of 10-30 m, which is logged a second time later in the programme.

29. It must be stressed that the success of any geo- physical borehole logging programme is dependent on the correct choice of probes for the lithologic con- ditions expected to be encountered, and upon the tech- nical quality of the borehole logging records them- selves. It is important, therefore, to ensure that the

borehole logging equipment used is in satisfactory con- dition, and that certain criteria whereby the standard of logging records is judged are met. Specialist geophysi- cal borehole logging companies will usually welcome such checking, since it will be in addition to the strin- gent precautions they design themselves to ensure opti- mum results.

INTERPRETATION

30. The interpretation of geophysical borehole logs calls for specialist experience. The interpretation gener- ally will be more reliable when the results of logging a borehole with several different types of probe are con- sidered together. Specialist geophysical borehole log- ging organizations generally offer the services of pro- fessional log analysts.

31. A clear distinction should be made between the geophysical measurements themselves, those physical or mechanical properties computed indirectly using theoretical formulae and those properties derived in- directly on the basis of an established correlation between the computed and the required property. Theoretical formulae should only be applied after care- ful examination of their validity for the case in ques- tion; established correlations are generally to be pre- ferred.

32. The first step in the interpretation is to make any necessary corrections to the probe readings for bore- hole diameter and for borehole fluid characteristics. The various geophysical observations in each of several boreholes may then be compared and correlated to de- termine the subsurface geometry of structural features intersected by the boreholes. If dipmeter or borehole televiewer surveys have also been made in the bore- holes, the interpretation is made considerably easier, and quite complicated structural features may then be identified.

33. The mechanical properties of strength and defor- mability of the formations encountered can be esti- mated from the sonic and density logs. The results of field trials have indicated that the electric and neutron logs can, under certain circumstances, yield information on the strength of crystalline rocks.

34. Cross-plots of the measurements made by differ- ent logging devices (e.g. neutron-sonic and density- sonic logs) can yield much useful information on the lithology, degree of fracturing and porosity of forma- tions adjacent to the borehole. Considerable effort has been devoted by the specialist geophysical borehole logging companies to the applications of computer- generated cross-plots to different aspects of log inter- pretation.

SERVICES AVAILABLE

35. Services available from specialist geophysical log- ging organizations fall iffto the following three groups. It should be noted that the logging systems described under I and II below may be purchased.

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72 International Society for Rock Mechanics

(I) Shallow-depth {to 200 m), hand-operated, portable logging systems capable of measuring and recording single-point resistance. SP and, in some cases, natural gamma radiation as a function of depth in boreholes of approximately 50mm dia. The probes are approxi- mately 41 mm in diameter. Typically, such a unit would weigh 80 kg.

1II) Medium-depth (to 1000mk motor-operated. portable borehole logging systems capable of recording the following logs as a function of depth in boreholes of approximately 75 mm dia:

(a) Electrical resistivity, SP and single point resist- ance; probe dia 38-50 mm.

(b) Gamma ray and neutron; probe dia 43 mm. (c) Density tborehole compensated); probe dia

43 mm. (d) Sonic (borehole uncompensated); probe dia

54 mm. (e) Caliper; probe dia 32 mm. (f) Temperature; probe dia 37 mm.

Typically, such a unit would weigh 200kg skid- mounted. It should be noted that the hazard associated with the neutron and density logs precludes their use by other than licensed personnel.

{III) Full-size. mobile truck or skid-mounted, bore- hole logging systems offering a complete range of log- ging services for deep boreholes. The records are usually obtained in digitized form for subsequent com- puter analysis. Since these systems were originally de- veloped for use in the oil industry, the probe sizes generally used are larger (greater than 100 mm in dia) than those referred to above under group II, and conse- quently require boreholes of 140 mm or greater in di- ameter. However. the following small-diameter probes have recently been developed for use with these systems in boreholes of approximately 75 mm in dia.

(i) Electrical resistivity and SP; probe dia 38 mm. (ii) Induction, electrical resistivity and SP; probe

dia 56 mm. (iii) Gamma ray and neutron; probe dia 43 mm. [ivj Density (borehole compensated); probe dia

43 mm. (v) Sonic (borehole uncompensated); probe dia

43mm. Sonic (borehole compensated); probe dia 50 mm.

(vi) Caliper; probe dia 44 mm. (vii) Temperature; probe dia 43mm.

These services are provided by a small group of specialist borehole logging companies only.

36. It should be noted that. when the services of specialist borehole logging companies are employed, the customer is invariably responsible for recovering or replacing logging probes lost due to caving of the bore- hole or to some other misfortune. In the case of neu- tron or density probes, such a loss can also involve a serious safety hazard.

37. In addition to the logs described above, the major specialist logging companies offer the services of the two proprietary geophysical borehole probes which measure the dip and dip direction of discontinuities

intersecting the borehole. These are the dipmeter tor diplog) and the borehole televiewer lot seisviewerl.

38. The smallest dipmeter offered by the specialist logging companies has a dia of 100 mm and can oper- ate in boreholes of 113 mm dia or larger. Usually, how- ever. boreholes of 140 mm alia or larger are required for dipmeter surveys. The dipmeters generally incorporate a borehole directional survey. The smallest borehole televiewer is 86 mm in dia and can operate in boreholes of 100 mm dia or larger. Other televiewer probes are larger, and require boreholes of at least 120 mm dia.

NOTES

(I) Reference

Sheriff R. J. Glossary of terms used in well logging. Geophysics 35,. 11t6--1139 [1970).

PART 2. SUGGESTED METHODS FOR SINGLE-POINT

RESISTANCE AND CONVENTIONAL

RESISTIVITY LOGS

SCOPE

I The single point resistance tog consists of a record of the electrical resistance between a reference electrode B grounded at the surface, and a second electrode A located in a probe free to move in an electrically-con- ductive fluid-filled borehole. The resistance measured reflects the resistivities of formations adjacent to the borehole. It is possible, therefore, to obtain a qualitat- ive measure from a single point resistance log of the variation of formation resistivities as the probe is raised m the borehole.

2. The conventional (normal and lateral) resistivity logs are recordings of the apparent resistivities of the formations adjacent to an electrically-conductive fluid- filled borehole. They are obtained by passing a current into the formation between two electrodes A and B. and measuring the potential difference between two further electrodes M and N.

3. For the normal device, electrodes A, M and N are located in the probe in the borehole, and electrode B may be grounded at the surface or placed in the bore- hole at a distance greater than the spacing AN. Elec- trodes B and N are assumed to be at infinity, since their distance from electrode A is much greater than the dis- tance AM. The spacing AM is approximately half the radius of investigation of the normal device. Although a number of different spacings are used, those of 0.4 m (16 in.) for the 'short normal' and 1.6 m (64 in3 for the 'log normal' are commonly used.

4. For the lateral device, electrodes A, B and M are located in the probe in the borehole, with the distance AB being small compared with AM. Electrode N is

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Suggested Methods for Geophysical Logging. 73

assumed to be at infinity and is grounded at the surface or in the borehole with the distance AN much greater than AM. The midpoint between electrodes A and B is considered as the reference point 0, with OM the spac- ing which is approximately the radius of investigation of the lateral device. Although a number of different spacings OM are used, those of 5.7 m (18 ft 8 in.), or less frequently 1.8 m (6 It), are commonly used.

5. Normal resistivity togs (usually the short normal) may be used in correlations, lithologic determinations and to indicate boundaries of beds. The short normal may also be used to measure the resistivity of porous, permeable zones invaded by the mud filtrate, while the long normal yields a value of resistivity intermediate between that of the invaded zone and of the true forma- tion resistivity. Under certain circumstances, the short normal may be used to obtain an estimate of the poro- sity of porous, permeable zones.

6. The lateral device may be used to provide an esti- mate of the true formation restivity, provided the re- sponse is not affected by mud filtrate invasion effects. In contrast to the response of the normal logs, that of the lateral device is not symmetrical opposite uniform beds, and it is highly distorted in thin beds.

APPARATUS

7. The apparatus consists essentially of the following: (a) Single point resistance: a movable probe in which

electrode A is located. Ib) Normal resistivity: a movable probe with elec-

trode A located near the base, electrode M at 0.4 or 1.6 m (or some other spacing) above A, and electrode N at a distance many times the spacing AM.

(c) Lateral device: a movable probe with electrode B located near the base, electrode A above B (0.8 m for the 5.7 m spacing OM), electrode M 5.7 m above the midpoint of electrodes A and B, and electrode N at a distance much greater than OM.

(d) An electronic circuit with which to apply a con- stant current between electrodes A and B.

(e) A galvanometer with a recorder to measure the potential difference between electrodes M and N in the case of the resistivity devices and between A and B for the single-point resistance log.

(f) Electronic circuits for scale selecting. ~* (g) A power or manually-operated winch and multi-

conductor armoured cable connecting the probe to the surface, together with a means of measuring the depth of the probe in the borehole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchronism between depth in the borehole and that displayed on the recorder.

(h) A fluid resistivity meter.

PROCEDURE

8. As soon as the borehole has been drilled and filled with electrically-conductive fluid, the probe is lowered

* N u m b e r s refer to Notes at the end of Par t 2.

in the borehole. The fluid should be circulated immedi- ately before logging is commenced. While the probe is lowered in the borehole, a suitable scale for displaying the record is chosen.

9. The probe is then raised at a constant rate over the uncased length of the borehole, and measurements of the apparent resistance or resistivity are recorded con- tinuously. The rate of travel in the borehole is approxi- mately 4-30 mmin. These logs are usually recorded with others, such as the SP log.

10. The resistivity of the mud filtrate or water is measured in a fluid resistivity meter at a given tempera- ture. The mud filtrate resistivity may also be calculated if its salinity is known.

CALCULATION AND INTERPRETATION OF RESULTS

11. In porous, permeable formations, the apparent resistance or resistivity measured by the device depends on a number of factors, such as the true formation resistivity R,, invaded zone resistivity Ri, diameter of the invaded zone d~, resistivity of the adjacent forma- tions Rs, drilling fluid resistivity R,,, bed thickness e, electrode spacing and borehole diameter d. The shape of the curve recorded is influenced by the ratio of the formation thickness to the electrode spacing. For the normal resistivity and single-point resistance devices, the curves are symmetrical about the centre of the for- mation; for the lateral devices, however, the curves are asymmetrical.

12. Qualitative interpretations of these logs, such as the identification of lithology, correlations of forma- tions between boreholes and the positioning of forma- tion boundaries require no calculations.

13. For quantitative interpretation, the true forma- tion resistivity can be obtained directly from the resis- tivity togs if the formation is a t least 5 times {for the normal device) and 3 times (for the lateral device) thicker than the spacing, and provided the diameter of invasion and the borehole are small compared with the spacing. Otherwise, the apparent resistivity measured must be corrected for formation thickness, effects of adjacent formations and for borehole and invasion di- ameters. These corrections may be made using depar- ture curves or interpretation charts.'-

14. The formation factor F is defined as the ratio of the resistivity of a fully water-saturated porous, per- meable formation to the resistivity of the water saturat- ing it. The formation factor is related to the formation porosity q~ by the Archie relation F = a 6 - " , in which the value of a is approximately unity and m is approxi- mately 2. The formation factor may, under certain cir- cumstances, be estimated from the ratio of the apparent resistivity measured by the normal device to the resis- tivity of the borehole fluid escaping to the formation. It is also given by the ratio of the true resistivity of the formation to the resistivity of the formation water fully saturating it.

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74 International Society for Rock Mechanics

R E P O R T I N G OF RESULTS

15. The report should contain the following data: (a) The borehole location and length, diameter, incli-

nation and direction, also the characteristics of the drilling fluid and location of any casing.

(b) The resistance or resistivity logs to an appropriate scale, together with core or cutting logs where avail- able. fully annotated with details of instrument settings.

(c) Possible correlations with other logs. (d) Correlations of apparent resistivity made by dif-

ferent logs at a particular point. (e) Calculations of true formation resistivity, invaded

zone resistivity and the porosity of porous, permeable zones.

NOTES

Ill The horizontal scale may vary from 20 to 1000f~M for the whole recording track for the resistivity devices and to 200fl for the single.point resistance log. Depth scales are usually 1/200 or 1/1000. but scales such as 1/50 or I 100 are used in logging shallow bore- holes. Other depth scales are 1/120. 1/240 and 1/600.

12) References Dresser Atlas. Log Review l: Review of Well Logging Principles.

Dresser Atlas Inc.. Houston 11971). Pirson S. J. Handbook of Well Log Analysis for Oil and Gas Formation

Et'aluation. Prentice-Hall. Englewood Cliffs. NJ (19631. Schlumberger. Log Interpretation: Vol. I. Principles. Schlumberger

Inc.. New York {19721. Schlumberger. Lo# Interpretation Charts. Schlumbcrger Inc.. New

York (1972). Schlumberger. Log Interpretation: Vol. II. Applications. Schlumberger

Inc.. New York 11974~.

PART 3. SUGGESTED

METHOD FOR THE SPONTANEOUS

POTENTIAL LOG

SCOPE

1. The Spontaneous Potential or Polarization curve (SP), is a record of the potential difference between a movable electrode in the borehole and a fixed surface electrode, due to electrochemical (membrane and liquid junction) and electrokinetic potentials in porous, per- meable formations in mud or water-filled and uncased boreholes, when the resistivities (and salinities) of the formation water and of the mud filtrate {or borehole water) are different.

2. This method can be used for geologic correlation, to locate bed boundaries, to detect permeable zones and to measure the formation water resistivity. The readings of the SP curve opposite shales and clays usually give a straight line called the 'shale base line'; opposite porous, permeable formations a deflection of the curve occurs, usually in the negative direction.

Numbers refer to Notes at the end of Part 3

APPARATUS

3. The apparatus consists essentially of the following: (a) A movable electrode or probe in the borehole and

a fixed electrode grounded at the surface. Both elec- trodes must be made of stable metals, e.g. oxidized lead. to avoid bimetallic corrosion.

(b) A power or manually-operated winch and isolat- ing cable connecting the electrode to the ground sur- face, together with a method for measuring the depth of the electrode in the hole. T h e movement of the cable should be coupled to the recorder to ensure synchro- nism between actual depth of the probe in the borehole and that displayed on the recorder.

(c) A galvanometer, usually with a recorder and elec- tric circuits for sensitivity adjustments, scale selecting ~* and positioning the base line.

(d) A fluid resistivity meter.

P RO CED U RE

4. Once the hole has been drilled and filled with elec- trically-conductive fluid, the fixed electrode is grounded at the surface ~usually in the mud pit/tank or in a special mud-filled holel and the movable electrode is lowered along the borehole. The fluid should be circu- lated and conditioned before logging.

5. When lowering the electrode, the horizontal scale is chosen so that the largest deflection does not go off-scale, and the base line is positioned in the same way. Care should be taken to avoid disturbance due to such external influences as electric welders and trains, electrolytic corrosion of nearby cased wells, chemical changes in the borehole fluid and magnetization of the winch.

6. The electrode is raised at a constant rate along the uncased length of the borehole and measurements are recorded continuously. The rate of travel in the hole is about 4 to 30 m/rain. Usually this log is recorded together with other logs, such as the resistivity or sonic logs.

7. The resistivity of the mud filtrate or water is measured in the fluid resistivity meter at a given tem- perature if it is necessary to determine the formation water resistivity or salinity. It is also possible to calcu- late the mud filtrate resistivity if its salinity is known.

CALCULATION AND

I N T E R P R E T A T I O N O F RESULTS

8. Deflections and the shape of the SP curve depend on several factors, such as the relationship between mud filtrate and formation water resistivities, thickness and resistivity of the permeable bed, mud resistivity, diameter of the zone invaded by the mud filtrate, bore- hole diameter and resistivity of the adjacent formations.

9. Deflections of the SP curve are either to the left or to the right of the baseline associated with shales or clays. If in a porous, permeable zone the formation water resistivity Rw is lower than the borehole water or

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Suggested Methods for Geophysical Logging 75

mud filtrate resistivity R,,.r, the deflection is to the left (negative). Such is usually the case for deep boreholes drilled with fresh-water drilling fluids. If Rw is larger than R,,,.r the deflection is to the right (positive). This is usually the case for the upper zones of the borehole or in shallow boreholes opposite fresh-water bearing for- mations, or when using salt-water muds. The actual position of the base line has no meaning in itself.

10. Correlations, the location of bed boundaries or a qualitative identification of permeable beds do not require calculations; these are provided by deflections from the shale base line. The points of inflection of the curves provide the exact level of bed boundaries.

11. Calculations of the formation water resistivity R,~ may be made using the following expression, which is valid for porous, permeable formations when they are uninfluenced by the presence of disseminated clay min- erals,

SP = 0.238- T . log (R"r)e (Rw)e '

in which T is the absolute temperature of the forma- tion; (R,.¢)~ and (Rw)~ are equivalent resistivities which take into account the departure of actual chemical ac- tivity from that predicted from salt content; SP is the deflection in millivolts read directly from the log oppo- site thick beds. For thin beds, corrected values of SP must be used. 2 The influence of disseminated clay min- erals upon the interpretation of the SP log is discussed in the literature. 3

R E P O R T I N G OF RESULTS

12. The report should include the following data: (a) The borehole location and length, diameter, incli-

nation and direction, also the characteristics of the drilling fluid and location of any casing.

(b) the SP log at an appropriate scale, together with core or cutting logs where available, fully annotated with details of instrument settings.

(c) Possible correlations with other logs. (d) Indications of the permeable beds. (e) If calculated, results of the formation water resis-

tivity or salinity, together with details of data used in their calculations and any assumptions made.

NOTES

(I) Horizontal sensitivities may vary from 10 to 500mV for the whole recording track. Depth scales are usually 1/200 or 1/1000. but scales such as 1/50 or l/t00 are used in logging shallow boreholes. Other depth scales are 1/120, 1/240 and 1/600.

(2) For this correction, the relationship between adjacent formation resistivity R5 to mud resistivity R,. borehole diameter and bed thick- ness are needed.

(3) References

Dresser Atlas. Log Review I: Review of Well Logging Principles. Dresser Atlas Inc., Houston (1971).

Pirson S. J. Handbook of Well Log Analysis for Oil and Gas Formation Ecaluation. Prentice-Hall, Englewood Cliffs, NJ (1963).

Pirson S. J. Geologic Well Log Analysis. Gulf, Houston (1970).

* Numbers refer to Notes at the end of Part 4.

Schlumberger. Log Interpretation: Vol. I. Principles. Schlumberger Inc., New York 119721.

Schlumberger. Log Interpretation Charts. Schlumberger Inc.. New York 11972).

PART 4. S U G G E S T E D M E T H O D FOR THE

I N D U C T I O N LOG

SCOPE

1. The induction log is a record of the response of formations adjacent to the borehole to an alternating magnetic field, which is created by a high-frequency alternating-current transmitter coil located in the probe. The magnetic field induces secondary currents in electrically-conductive formations. These currents in turn create magnetic fields, which induce signals in a receiver coil located in the probe. The receiver signals are essentially proportional to the conductivity (reci-. procal of resistivity) of the formation. Any signal pro- duced by direct coupling of transmitter and receiver coils is balanced out in the measuring circuits.

2. The induction log may be used in empty boreholes, or with conductive or non-conductive 1fresh water or oil) fluids in the borehole. It may also be used in bore- holes with non-conductive casing. Theory of the re- sponse of the induction log shows that. provided it is of high resistivity, the medium immediately surrounding the borehole contributes very little to its response; the log therefore reflects the true resistivity of the surround- ing formations.

APPARATUS

3. The apparatus consists essentially of the following: (a) A movable probe in the borehole with between

two and six coaxial coils. One of these is the main transmitter coil and another is the receiver coil, spaced between 0.7 and 1.0 m apart. The remaining coils are employed to improve radial and vertical investigative characteristics of the device.

(b) An electronic circuit to provide a high-frequency (20-60 kHz) alternating current of constant intensity for the transmitter coil.

(c) An electric circuit to select signals of the correct phase and to amplify them before transmitting to the surface for measuring with a galvanometer and display- ing on a recorder.

(d) Electronic circuits for scale selecting ~* and cali- bration adjustments.

(e) A winch and multi-conductor armoured cable connecting the probe to the surface, together with a means of measuring the depth of the probe in the bore- hole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchro- nism between actual depth of the probe in the borehole and that displayed on the recorder.

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76 International Society for Rock Mechanics

if) A mechanical centralizer for the probe in the bore- hole.

(g) A fluid resistivity meter.

PROCEDURE

4. As soon as the borehole has been drilled, the probe is lowered in the borehole. While the probe is lowered in the borehole, a suitable scale for displaying the record is chosen.

5. The probe is then raised at a constant rate over the section of the borehole to be logged, and measurements are recorded continuously. The rate of travel in the borehole is approximately 4--30 m/min. The induction log is usually recorded with others, such as the short normal and SP logs, or a second induction log of differ- ent coil spacing and a lateralog.

6, The resistivity of the mud filtrate or water is measured in a fluid resistivity meter at a given tempera- ture. The mud filtrate resistivity may also be calculated if its salinity is known.

CALCULATION AND INTERPRETATION OF RESULTS

7. In porous, permeable formations, the resistivity measured by the induction log is close in value to the true resistivity of the formation, provided the formation has not been deeply invaded by the drilling fluid, When the formation has been deeply invaded, the apparent resistivity recorded by the device deviates from the true resistivity. The amount by which it deviates depends upon the depth of invasion, and upon the contrast between the resistivity of the invaded zone and the true resistivity of the formation. Interpretation under these circumstances is facilitated when a shallow-investiga- tion device, such as the short normal resistivity log, is run together with the induction log. z

8. The formation factor F, defined by the ratio of the true resistivity of the formation to that of the connate water fully saturating it, may also be determined if the connate water resistivity is obtained from the SP log. The formation factor is related to the formation poro- sity ~b by the Archie relation F -- aq~-', in which the value of a is approximately unity and m is approxi- mately 2.

9. Fracture zones in rocks of low porosity drilled with fresh water are often identified by the induction log.

I0. The bed definition is good when the formauon thickness is greater than the spacing between the main transmitter and receiver coils.

REPORTING OF RESULTS

11. The report should contain the following data: (a) The borehole location and length, diameter, incli-

nation and direction, also the characteristics of the drilling fluid and location and description of any cas- ing.

lb) The induction log conductivity and resistivity measurements to appropriate scales, together with core or cutting logs where available, fully annotated with details of instrument settings.

tct Any other logs of the borehole, in order to facili- tate interpretation of the induction log in porous, per- meable formations and to establish possible corre- lations.

Id} An interpretation of the results in terms of peru- nent geological characteristics of the formations sur- rounding the borehole.

NOTES

t ll The horizontal scale is calibrated linearly in units of conducti- vity Imitlisiemens/m. mS/m) or of resistivity (ohm. m, f~m). Often both the resistivity and conductivity are recorded and displayed simul- taneously on the log. In certain cases the resistivity scale is logarith- mtc, and covers four decades typically from 0.1 to 1000fire. This presentation enhances the interpretation of low resistivities, while preventing high resistivities measured from going off scale. Depth scales are typically 1,/200 or 1/1003. but scales such as 1/50 or 1 100 are used in logging shallow boreholes. Other depth scales are 1/120. 1/240 and 1/600.

12} References Dresser Atlas. Log Reriew I: Reriew of Well Logging Principles.

Dresser Atlas Inc., Houston ~1971). Moran 1. H. & Kunz K. S, Basic theory of induction logging. Geophy-

sics 27. 829-858 11962). Schlumberger. Log Interpretation: Vol. I, Principles. Schlumberger

Inc.. New York 11972). Schlumberger. Loy Interpretation Charts. Schtumberger Inc., New

York 119721. Schlumberger. Log Interpretation: Vol. II. Applications. Schlumberger

Inc,. New York {1974).

PART 5. SUGGESTED METHOD FOR THE GAMMA-RAY LOG

SCOPE

1. The gamma-ray log provides a continuous measurement of the natural radioactivity of formations intersected by the borehole. In most sedimentary rocks, the log reflects the shale and clay content of formations. This is because the radioactive elements tend to con- centrate in rocks containing clay minerals. Sandstones, limestones and dolomites tend to have a low level of radioactivity, unless radioactive contaminants such as volcanic ash or granite wash are present. Because of absorption, most of the gamma rays counted by the log originate within the first 150ram of formation sur- rounding the borehole.

2. In mineral exploration, the gamma-ray log .is employed to detect and evaluate deposits of radioactive minerals such as potash and uranium ore.

3. The gamma-ray log may be employed in wells with steel casing, since the presence of steel easing only partly reduces the total number of gamma rays counted. However, corrections must be made to account for the presence of casing.

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Suggested Methods for Geophysical Logging 77

4. The gamma-ray log may be employed in empty boreholes.

APPARATUS

5. The apparatus consists essentially of the following: la) A probe containing the device for detecting

gamma rays originating in the formation adjacent to the borehole, together with a preamplifier. Scintillation counters are usually preferred for this purpose for their short active length and efficiency, although Geiger- Mtiller counters are still used.

Ib) An armoured cable to transmit the signal to the surface, and on which to suspend the probe.

(c) Electronic circuits for averaging the signal, for time-constant selecting and for calibration purposes.

(d) A recorder displaying the gamma-ray intensity in API units as a function of depth, t*

le) A power or manually-operated winch with a means of measuring the depth of the probe in the bore- hole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchro- nism between actual depth of the probe in the borehole and that displayed on the recorder.

P R O C E D U R E S

6. Since the rate of emission of gamma rays is statisti- cal in nature, the rate of counting by the detector will depend upon the basic time unit over which the count- ing takes place. Fluctuations in the rate of counting will be smaller if the counting time or time constant (T.C.) is longer, or if the level of radioactivity is higher. The T.C. is selected to an appropriate value (normally between 2 and 4 sec) to avoid high statistical fluctuations in the rate of counting.

7. The probe is raised in the borehole at a sufficiently slow speed, which depends on the T.C, selected and on the minimum bed thickness to be detected. Normally the speed is chosen so that the probe travels approxi- mately 0.3 m during one T.C. (e.g. 9 m/min for a T.C. of 2 sec). It is recommended that the log be run over cer- tain sections of a few metres of the borehole twice to check the statistical fluctuations.

8. If a quantitative interpretation is to be made, cali- bration must be performed, before or after running the log, with a gamma-ray source of known intensity at a fixed distance from the detector in the probe. It is recommended that the API recommended practice be used for this purpose.-'

10. The response of the gamma-ray log is influenced also by the conditions existing within the borehole. such as the presence of casing and borehole diameter, since the materials present between the detector and the adjacent formations absorb gamma rays. The log must therefore be corrected for hole diameter, probe eccentri- city in the borehole, casing and cement thickness and density of the fluid filling the borehole." A correction must also be made on the depth scale to account for the time constant lag of the gamma-ray log response.

11. Some gamma-ray logs permit the analysis of the spectrum of energy levels of gamma-ray emission from the surrounding formations. In this way the presence of different radioactive elements (e.g. potassium, thorium and uranium) may be detected.

R E P O R T I N G OF RESULTS

12. The report should contain the following data: (a) The borehole location and length, diameter, incli-

nation and direction, also the characteristics of the drilling fluid and location and details of any casing and cement.

(b) Details and calibration procedures followed. (c) The gamma-ray log to an appropriate scale in

API units, together with core and cutting logs where available, fully annotated with details of instrument settings.

(d) An interpretation of the results in terms of perti- nent geological characteristics of the formation sur- rounding the borehole, noting any assumptions and corrections made to the gamma-ray tog.

NOTES

(I) 16.SAPI units are equivalent to [~g Ra-equiv.ton. The hori- zontal scale varies from 100 to 200API units for the whole scale. Depth scales are usually 1200 or 1, 1000. but scales of 1 50 or 1 100 may be used in shallow boreholes. Other depth scales are 1 120. 1:2-10 and 1/600.

(2) References

American Petroleum Institute. Recommended Practice Jbr Standard Calibration and Form for Nuclear Logs. API RP 33 (1959).

Dresser Atlas. Log Review I: Reriew of Well Logging Principles. Dresser Atlas Inc., Houston [1971).

Pirson, S. J. Handbook of Well Log Analysis for Oil and Gas Forma- tion Evaluation. Prentice-Hall, Englewood Cliffs, N.J. t19631.

Schlumberger. Log Interpretation: Vol. I, Principles. Schlumberger Inc.. New York (1972).

Schlumberger. Log Interpretation Charts. Schlumberger Inc.. New York (1972).

Schlumberger. Log Interpretation: Vol. II. Applications. Schlumberger Inc., New York [1974).

C A L C U L A T I O N AND I N T E R P R E T A T I O N OF RESULTS

9. In the absence of radioactive mineral deposits, the gamma-ray log responds to the presence of clays, shales and acidic volcanic rocks. In sedimentary rocks the gamma-ray log may often be correlated with the clay mineral content.

* Numbers refer to Notes at the end of Part 5.

PART 6. S U G G E S T E D M E T H O D FOR THE

N E U T R O N LOG

SCOPE

1. The neutron log responds to the amount of hydro- gen in the formations surrounding the borehole. In water- or hydrocarbon-saturated porous formations,

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78 International Society for Rock Mechanics

where disseminated clay minerals are absent, the neu- tron log may be used to estimate the porosity. In crys- talline rocks the log may be used to detect fracture zones close to the borehole. It should be noted that where water of crystallization or hydrogen chemically combined in formation materials is present, it contrib- utes to the response of the neutron log.

2. Fast neutrons emitted by a high-energy source located in the probe bombard the formation adjacent to the borehole, On emission from the source the neu- trons are slowed to thermal velocities by collisions with atomic nuclei, of which hydrogen nuclei are the most effective, After the neutrons have been slowed down they are captured by atomic nuclei in the formation. and a gamma ray of capture is emitted by the capturing nucleus, These gamma rays of capture or slowed-down neutrons are counted by a detector mounted in the probe. For the long spacings commonly used. the counting rate increases for decreased hydrogen content. because the fast neutrons travel further from the source before being slowed down and captured.

3. The neutron log may be employed in boreholes with steel casing, since the presence of steel casing only partly reduces the sensitivity of the neutron log. How- ever, corrections must be made for the presence of casing.

4. The neutron log may be employed in empty bore- holes.

5. When used in combination with the gamma-ray log, the neutron log provides a means for identifying lithologies and for obtaining the porosities of porous zones. In combination with the density or acoustic logs, the neutron log can also be used to indicate the pres- ence and degree of fracturing in crystalline rocks.

APPARATUS

6. The apparatus consists essentially of the following: (a) A probe containing a shielded source of fast neu-

trons ~*, a detector or detectors of gamma rays of cap- ture or of slow neutrons, together with preamplifiers. The distance from source to detector is usually 170 mm or less for short spacing, or 300 mm or greater for the long spacing apparatus more commonly used. Two detectors with these spacings are used with some neu- tron logs.

(b) An armoured cable to transmit the signals from the detector or detectors to the surface, and on which to suspend the probe.

(c) Electronic circuits for averaging the signal, for time-constant selecting and for calibration purposes.

(d) A recorder displaying the gamma-ray or slow- neutron intensity in API units as a function of depth. 2

(e) A winch with a means of measuring the depth of the probe in the borehole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchronism between actual depth of the probe in the borehole and that displayed on the recorder,

* N u m b e r s refer t o N o t e s a t t he e n d o f P a r t 6.

PROCEDURE

7. Since the rate of formation of slow neutrons and of emission of gamma rays of capture is statistical in nature, the rate of counting by the detector or detectors will depend upon the basic time unit over which the counting takes place. Fluctuations in the rate of count- ing will be smaller if the counting time or time constant (T.C.) is longer, or if the level of measured radioactivity is higher. The T.C. is selected to an appropriate value (normally between 2 and 4 secJ to avoid high statistical fluctuations in the rate of counting.

8. The probe is raised in the borehole at a sufficiently slow speed, which depends on the T.C. selected. Nor- mally the speed is chosen so that the probe travels approximately 0.3 m during one T.C. (e.g. 9 m/min for a T.C. of 2 secl.

9. In certain situations it may be desirable to raise the probe in the borehole in discrete steps, obtaining a count while the probe is maintained at a constant depth. In this case the total count should be at least 2500 gamma rays of capture or slowed-down neutrons to reduce fluctuations to approximately + t~',o.

10. If a quantitative interpretation is to be made. calibration must be performed, before or after running the log, with a standard neutron log calibrator. This secondary standard must have previously been cali- brated itself in an equivalent of the API neutron log calibration pit.

CALCULATION AND INTERPRETATION OF RESULTS

11. The response of the neutron log in API units is converted to porosity, with calibration and correction curves to account for borehote effects and lithology. 3 The calculated porosity reflects the total hydrogen present, in the case of partial water saturation on the one hand and the presence of water of crystallization on the other, the porosity calculated will, respectively, be artifically low or artificially high.

12. The records of neutron logs with two or more detectors are usually processed automatically to yield a linearly-scaled recording or porosity directly.

13. A correction must be made on the depth scale to account for the lag in the neutron log response due to the time constant chosen.

REPORTING OF RESULTS

14. The report should contain the following data: (a) The borehole location and length, diameter, direc-

tion and inclination, also the characteristics of the drill- ing fluid and location and details of any casing and cement.

(b) Details of the neutron source and detectors used, and of the calibration procedures followed.

(c) The neutron log to an appropriate scale in API units or units of porosity, together with core and cut- ting logs where available, fully annotated with details of instrument settings.

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Suggested Methods for Geophysical Logging 79

(d) Any other logs of the borehole, in order to facili- tate interpretation of the neutron log.

(e) An interpretation of the results in terms of perti- nent geological characteristics of the formations sur- rounding the borehole, noting any assumptions and corrections made to the neutron log.

NOTES

Ill Plutonium-Beryllium or Americium-Beryllium sources of fast neutrons are normally employed, because of their long half life and freedom from emission of gamma rays. Radioactive sources are dan- gerous: they should be handled only in their shields and always with care.

[2} One AP[ neutron unit is arbitrarily defined as 1/1000 the differ- ence between instrument zero and the deflection opposite a limestone flndiana) of porosity 0.19 contained in a pit at Houston. The horizon- tal scale is linear in API units, with a range of 3200 for the whole scale or in units of limestone porosity in the range typically - 0 . 1 0 to 0.30. Depth scales are usually 1/200 or 1/1000, but scales of 1/50 or 1 100 may be used in shallow boreholes. Other depth scales are 1/120, 1 240 and 1:600.

(3) References

American Petroleum Institute. Recommended Practice for Standard Calibration and Form for Nuclear Logs, API RP33 0959).

Dresser Atlas. Lo 9 Review I: Review of Well Loqgin9 Principles. Dresser Atlas Inc., Houston (1971).

Pirson, S. J. Handbook of Well Lo 9 Analysis for Oil and Gas Forma- tion Evaluation. Prentice-Hall, Englewood Cliffs, NJ (1963).

Schlumberger. Lo 9 Interpretation: Vol. I, Principles. Schlumberger Inc., New York 11972).

Schlumberger. Log Interpretation Charts. Schlumberger Inc., New York (1972).

Schlumberger. Lo 9 Interpretation: Vol. It, Applications. Schlumberger Inc., New York (1974).

PART 7. S U G G E S T E D M E T H O D FOR THE G A M M A - G A M M A

DENSITY LOG

SCOPE

1. The gamma-gamma density log responds to the gamma rays emitted by a source within the probe and back-scattered by the formations surrounding the bore- hole. The back-scattered gamma rays counted by a detector are inversely proportional to the bulk density of the material surrounding the probe.

2. Medium-energy gamma rays emitted by a source located in the probe bombard the formation adjacent to the borehole. The gamma rays are back-scattered by collisions with electrons in the formation, and some of these reach the detector. The source and detector are arranged so that the number of gamma rays counted is inversely proportional to the electron density of the surroundings. Since the bulk density is proportional to the electron density for most elements of low atomic mass, the gamma-gamma log provides a measure of the bulk density of the surroundings.

3. Since the gamma rays are absorbed by the forma- tion quite close to the borehole, conditions close to the

* Numbers refer, to Notes at the end of Part 7.

probe have an appreciable effect on the response of the density log. To compensate for these effects a two- detector arrangement is often used, and the probe is held against the borehole wall during logging.

4. The density log may be employed in empty bore- holes.

5. When used in combination with the gamma-ray log, the density log provides a means for identifying formation lithology and the presence of porous forma- tions, and for determining their porosity. In combina- tion with the neutron or acoustic logs, the density log can also be used to indicate the presence and degree of fracturing in crystalline rocks.

APPARATUS

6. The apparatus consists essentially of the following: (a) A probe containing a shielded source of medium-

energy gamma rays t*, a detector or detectors Of back- scattered gamma rays, together with preamplifiers. The probe is provided with some mechanical device for ensuring it is in contact with, or close to, the borehole wall during logging.

(b) An armoured cable to transmit the signals from the detector or detectors to the surface, and on which to suspend the probe.

(c) Electronic circuits for averaging the signal, for time-constant selecting and for calibration purposes. With two detectors, automatic compensation of the data is made, and the bulk density of the formation is calculated directly.

(d) A recorder displaying the bulk density as a func- tion of depth.-'

(e) A winch with a means of measuring the depth of the probe in the borehole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchronism between actual depth of the probe in the borehole and that displayed on the recorder.

P R O C E D U R E

7. Since the rate at which back-scattered gamma rays strike the detectors is statistical in nature, the rate of counting will depend upon the basic time unit over which the counting takes place. Fluctuations in the rate of counting will be smaller of the counting time or time constant (T.C.) is larger. The T.C. is selected to an appropriate value (normally between 2 and 4sec) to avoid high statistical fluctuations in the rate of count- ing.

8. The probe is raised in the borehole at a sufficiently low speed, which depends on the T.C. selected. Nor- mally the speed is chosen so that the probe travels approximately 0.3 m during one T.C. (e.g. 9 m min for a T.C. of 2 sec).

9. Under certain conditions it may be desirable to raise the probe in the borehole in discrete steps, obtain- ing a count while the probe is maintained at a constant depth. In this case the total count of back-scattered

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80 International Society for Rock Mechanics

gamma rays should be at least 2500 to reduce fluctua- tions to approximately + 1~/o.

10. A caliper log is usually run with the density log to permit corrections to be made for any roughness of the borehole wall.

l 1. Before or after each logging run, the probe should be carefully checked and calibrated with appropriate secondary calibration devices, e.g. in blocks of aluminum, magnesium and sulphur.

CALCULATION A N D

I N T E R P R E T A T I O N O F R E S U L T S

12. The density probe equipped with two detectors provides a direct record of the bulk density of the for- mations intersected by the borehole. In this case. cor- rections must be made only for borehole roughness.

13. For single-detector density probes, the readings are converted to bulk density using calibration curves. In uncased boreholes with the probe applied against the borehole wall, corrections must be made for bore- hole diameter, density of drilling fluid and. if present, drilling mud-cake thickness. In cased boreholes, or when the probe is not applied against the borehole wall. special calibration curves must be employed. In cased boreholes, the thickness and density of casing and of materials between the casing and borehole wall should be carefully evaluated for a quantitative inter- pretation.

14. The formation bulk density p~ is related to the porosity ~ through the relation

@ = P= - Pb

Prn - - Pf"

in which p,, = density of matrix material, py = density of fluid filling the pore spaces. Given the matrix and pore fluid densities, the porosity can be calculated)

15. A correction must be made on the depth scale to account for the lag in the density log response due to the time constant chosen.

REPORTING OF RESULTS

16. The report should contain the following data: (a) The borehole location and length, diameter, direc-

tion and inclination, also the characteristics of the drill- ing fluid and location and details of and casing and current.

(b) Details of the gamma-ray source and detectors used, and of the calibration procedures followed.

(c} The density log to an appropriate scale of bulk density, together with core and cutting logs where available, fully annotated with details of instrument settings.

(d) Any other logs of the borehole, in order to facili- tate interpretation of the density logs.

(e) An interpretation of the results in terms of perti- nent geological characteristics of the foundations sur-

" Numbers refer, to Notes at the end of Part 8.

rounding the borehole, noting any assumptions and corrections made to the density log.

NOTES

Ill t3"Caesium or 6°cobalt sources of g a m m a rays are normally employed, the former providing g a m m a rays of one energy level and the latter two. Radioactive sources are dangerous: they should rse handled only in their shields and al~ays with care.

I21 The horizontal scale is linear in bulk density, with a range from 2000 to 3000kg-m -3. Depth scales are usually t 2 0 0 or 1 [000. but scales of 1 50 or 1. 100 may be used in shallow borehotes. Other depth scales are I..'120. I;240 and I '600.

13) References Dresser Atlas. Log Review l: Reriew of Well Logging Principles.

Dresser Atlas Inc.. Houston 11971). Schlumberger. Log Interpretation: Vol. l. Principles. Schlumberger

Inc., New York {19721. Schlumberger. Log Interpretation Charts. Schlumberger Inc.. New

York (1972). Schlumberger, Log Interpretation: VoL II. Applications. Schlumberger

Inc.. New York (1974). Ti t tman J. & Wahl J. S. The physical foundations of formation den-

sity logging (gamma-gamma) . Geophysics 30. 284--294 (1965).

PART 8. S U G G E S T E D M E T H O D FOR THE

ACOUSTIC OR SONIC LOG

SCOPE

1. The acoustic or sonic log provides a measure of the time of travel of compressional waves over a certain interval of the formation immediately adjacent to the borehole. From the travel time, the velocity of propaga- tion of compressional waves in the formation can be calculated. With appropriate devices and under suitable geological conditions, the velocities Of propagation of shear and other secondary waves, and the attenuation characteristics may be measured.

2. Variations in the velocity of compressional waves may be correlated with changes in lithotogy and the porosity of formations adjacent to the borehole. Knowledge of the compressional and shear wave velo. cities, together with the density of the formation, en- ables the dynamic elastic properties of the formation to be calculated. ** The attenuation characteristics of com- pressional and shear waves may be correlated with the mechanical properties and degree of fracturing and fis- suring of the formation.

APPARATUS

3. The apparatus consists essentially of the following: (a) A transmitter of pulses of acoustic waves mounted

at one end of the probe. An acoustic receiver or receivers, with associated preamplifiers, are mounted a fixed distance at the other end of the probe, where they are acoustically insulated from the transmitter. The borehole compensated acoustic log consists of two

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Suggested Methods for Geophysical Logging 81

transmitters of acoustic waves, one above and one below two pairs of receivers.

(b) A winch and multi-conductor armoured cable, through which pass the electronic signals to and from the probe. The winch should be equipped with some method for measuring the depth of the probe in the borehole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchro- nism between actual depth of the probe in the borehole and that displayed on the recorder.

(c) Surface electronics for conditioning and a recorder for displaying the signal or signals from the acoustic receiver or receivers.'

PROCEDURE

4. The borehole must be filled with a liquid, usually water or drilling mud. before the sonic log is run. The liquid is essential for acoustically' coupling the trans- mitter and receivers in the probe to the formation sur- rounding the borehole. The probe is first lowered to the depth at which logging is to commence. It is then raised at a constant rate of 5 - 3 0 m m i n along the uncased length of the borehole and measurements are recorded as a function of depth.

5. The measurements can take any of several forms: ta) Transit time display at the surface. The time of

transit At of compressional waves over a certain dis- tance of the formation, the receiver spacing, is plotted as a function of depth.

(b) Variable intensity display at the surface. The amplitudes of the elastic waves reaching the receiver are recorded photographically as a function of depth. The amplified signal from the receiver modulates the inten- sity of an oscilloscope electron beam, the trace of which is photographed.

(c) Waveform display at the surface. The complete wave train at discrete intervals up the borehole is dis- played on an oscilloscope screen and photographed.

CALCULATION AND INTERPRETATION OF RESULTS

(c) Wat'e fl?rm display at the surJ'c~ce

The compressional and often the shear-wave arrivals at a particular depth can be identified, and an~ necess- ary corrections applied for the borehole size and liquid filling the borehole. The compressional and shear-wave velocities and attenuation characteristics may then be calculated as a function of depth. If the density of the formation is also known 3, the dynamic elastic constants can also be calculated as a function of depth.

7. The velocities and attenuation of acoustic waves in rocks depend upon a number of factors, including the rock type, porosity, persistence and aperture of fissures, degree of fracturing, etc. A number of specialist geo- physical borehole logging service companies have out- lined t the procedure and prepared charts for the evalu- ation of porosity in sedimentary rocks from sonic logs. Other publications relate to the evaluation of fractures and determining the mechanical properties of the adja- cent formation.

REPORTING THE RESULTS

8. The report should include: (a) The borehole location and length, diameter, incli-

nation and direction, also the characteristics of the drilling fluid and the location and details of an) casing.

(b) Details of the equipment used and method of dis- play of the results. The spacings of the transmitter and receiver or receivers in the probe must be reported.

(c) The records obtained at an appropriate scale, together with core and cutting logs where available, fully annotated with details of instrument settings.

(d) Tabblated values of derived parameters, together with the formulae or correlations used in their deri- vation, with full details or references to the limitations of these calculations and the assumptions made.

(e) An interpretation of the results in terms of perti- nent geological characteristics of the formations sur- rounding the borehole.

6. (a) Transit time display at the surface

The travel times are measured from the display, and any necessary corrections applied for the boreholes size and liquid filling the borehole. The compressional-wave velocity can then be calculated as a function of depth.

(b) Variable intensity display at the surfilce

The compressional and often the shear-wave arrivals at a particular depth can be identified and any necess- ary correction applied for the borehole size and liquid filling the borehole. This is facilitated by running the log a second time with a different spacing between the transmitter and receiver. The compressional and shear wave velocities may then be calculated as a function of depth. If the density of the formation is also known, 3 the dynamic elastic constants can also be calculated as a function of depth.

NOTES

(1) References

Geyer R. L. & Myung J. I. The 3-D velocity log: a tool for in situ determination of the elastic moduli of rocks. Proc. 12th S.vm p. Rock Mechanics 71-107, A.I.M.E., New York (1971).

Schlumberger Lo 9 Interpretation: Vol I, Principles. Schlumberger Inc., New York (1972).

Schlumberger. Log Interpretation Charts. Schlumberger Inc., New York {1972).

Schlumberger. Log lnterpremtiopl: Vol. II, Applications. Schlumberger Inc., New York (1974).

Society of Professional Well Log Analysts. 4cou.~tic Logqinq: SPWLA Reprint Volume, S.P.W.L.A., Houston [19781.

Tixier M. P., Loveless, G. W. and Anderson R. A. Estimation of formation strength from the mechanical properties log. J. Petrol. Technol. 27, 283-293 (1975). (2) The horizontal scales for the transit time display are typically

linear from 500 to 100 l~sec/m. Depth scales are typically 1,200 or 1/1000, but scales such as 150 or 1.,100 are used in logging shallow boreholes. Other depth scales are 1:120, 1/240 and 1600.

(3) Requires the running of a density log in addition to the acoustic log.

R.~.~.S. 18, l - -F

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82 International Society for Rock Mechanics

PART 9. SUGGESTED METHOD FOR THE

CALIPER LOG

SCOPE

1. The caliper log provides a measure of the diameter of a borehole as a function of depth. The borehole di- ameter or changes in diameter are required to provide the accurate interpretation of the results from many of the other types of logging device. The caliper log is therefore run with almost all combinations of other log- ging devices. Changes in borehole diameter indicate the build-up of mud cake opposite porous, permeable for- mations or the tendency of boreholes to cave opposite incompetent formations. Changes in diameter can also indicate the presence of gross fissures or 'vuggy' zones, 'squeezing' of marls or clays, and dissolution of soluble salts by the drilling fluid.

APPARATUS

2. The apparatus consists of the following: (a) A number (between 3 and 6) of arms radiating

from a central probe. These arms can either be retracted so that they are flush with the probe, or they can be spring-loaded so that they are in contact with the borehole wall when the probe is raised in the bore- hole. The distance each arm protrudes from the probe is measured mechanically and the distance converted to an electrical signal, which in turn is transmitted to the surface.

(b) A winch and multi.conductor armoured cable through which pass the electronic signals from the probe. The winch is equipped with some method for measuring the depth of the probe in the borehole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchronism between actual depth of the probe in the borehole and that displayed on the recorder.

(c) Surface electronics for conditioning the signals from the several arms on the probe and displaying the mean borehole diameter, and with some devices the individual measures for different arms with correspond- ing directions, as a function of depth of the probe in the borehole)*

PROCEDURE

3. The caliper probe should be accurately calibrated before running in the borehole by placing metal rings of known internal diameter around the measuring arms. The actual diameters should be recorded. At least two rings should be used, one greater and one smaller than the expected maximum and minimum borehole diam- eters. This procedure should be repeated on completion of the logging process. If the measuring probe has a direction indicator it should also be tested before and after completing the logging process.

* Numbers refer to Notes at the end of Part 9.

4. With the arms retracted, the probe is lowered m the borehole to the desired depth at which logging is first to be performed. After releasing the arms. the probe is then raised at a constant rate of 4-20 m/ram along the uncased length of the borehole. Measure- ments of diameter are recorded and displayed continu- ously as a function of depth of the probe in the bore- hole.

REPORTING OF RESULTS

5. The report should include: (a) The borehole location and length, inclination and

direction, and drill bit diameter, It should also include the characteristics of the drilling fluid and the location and diameter of any casing.

(b) Details of the equipment used, and the logging speed.

(c) The record of borehole diameter, or difference between measured diameter and drill bit diameter, as a function of depth to a suitable scale.

(d) If a record is made of the cross-section shape of the borehole as a function of depth, this should be illus- trated at regular intervals.

NOTES

(1) Depth scales are typically 1/200 or I 1000, but scales such as 1/50 or 1/00 are used in logging shallow boreholes. Other depth scales are I 120. 1~ 240 and 1 600.

PART 10. SUGGESTED METHOD FOR THE

TEMPERATURE LOG

SCOPE

1. The temperature log provides a measure of the temperature of the borehole fluid as a function of depth. The differential temperature log provides a measure" of the difference in temperature between two points in the borehole fluid.

2. If the drilling fluid filling the borehole has been allowed to rest a sufficiently long time it tends to come to thermal equilibrium with the surrounding forma- tions. In the absence of any disturbing influences, the temperature then measured at a point in the borehole is close to that of the surrounding formation, and with depth will generally reflect the geothermal gradient (in boreholes deeper than about 2Ore), which is very ap- proximately 1~C increase in temperature per 40 m in- crease in depth. If. however, there are disturbing influences, such as the influx of groundwater or gas to the borehole or the setting of cement grout, these occurrences will be reflected by abnormal changes in the temperature recorded.

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Suggested Methods for Geophysical Logging

APPARATUS

3. The apparatus consists of the following: ta) A probe containing one or several resistance

thermometers, or preferably thermistors, spaced at fixed intervals.

(b) A winch and multi-conductor armoured cable through which pass the electronic signals from the thermistors. The winch should be equipped with some method for measuring the depth of the probe in the borehole. The movement of the probe in the borehole should be coupled with the recorder to ensure synchro- nism between actual depth of the probe in the borehole and that displayed on the recorder.

(c) Surface electronics for conditioning the signals from the thermistors and displaying the temperature or temperatures difference as a function of the depth of the probe in the boreholes. ~*

PROCEDURE

4. After first ensuring the borehole is filled with fluid, the temperature probe is lowered down the borehole as slowly as is practicable and consistent with the time constants of the thermometers or thermistors while the measurements are made. This procedure reduces the disturbing effect of the passage of the probe on the thermal regime within the drilling mud. Measurements of temperature or temperature difference are recorded and displayed continuously as a function of depth of the probe in the borehole.

REPORTING OF RESULTS

5. The report should include: (a) The borehole location and length, diameter, incli-

nation and direction. It should also include the charac- teristics of the drilling fluid, the time allowed for the borehole fluid to rest and its level in the borehole, and the location of any casing and its diameter.

(b) Details of the equipment used, including the log- ging speed and time constants of the thermometers or thermistors.

(c) The record of temperatures or temperature differ- ences as a function of depth to a suitable scale.

NOTES

(1) Depth scales are typically 1/200 or 1 1000, but scales such as l 50 or 1,100 are used in logging shallow boreholes. Other depth scales are 1,120, I 240 and 1600.

PART 11. REFERENCES

I. GENERAL GEOPHYSICAL BOREHOLE LOGGING

Allaud L. A. & Martin M. H. Schlumberger: Tire History of a Techni- que. Wiley, Ne~ York (1977L

Baltosser R. W. & Lawrence H. W. Application of well logging tech- niques in metallic mineral mining. Geophysics 35, 143-152 (1970).

* Numbers refer to Notes at the end of Part 10.

83

Bond L. O., Alger R. P. & Schmidt A. W. Well log applications in coal mining and rock mechanics. Trans. Soc Min. En~4r~. Am. Soc. Min. Engrs 2N), 355 362i1971L

Dresser Atlas. Log Review 1 Reriew of Well Loqgin 9 Principles. Dresser Atlas Inc., Houston 11971t.

Evans H. B. Status and trends in logging. Geophysics 35, 93-112 (1970).

Jennings H. Y. & Timur A. Significant contributions in formation evaluation and well testing. J. Petrol. Technot. 25, 1432-1446 (1973).

Kelley D. R. A Summary oj" Major Geophysical Logging Methods. Pennsylvania Geological Survey Bulletin M6I, Penn Geological Survey, Harrisburg, PA 11969).

Lynch E. J. Formation Evaluation. Harper & Row. New York (1962~. Pirson S. J. Handbook of Well Log Analysis for Oil and Gas Formation

Evalu,ttion. Prentice-Hall, Englewood Cliffs, NJ (1963). Pirson S. J. Geologic Well Log Analysis. Gulf, Houston 11970). Pickett G. R. Applications for borehole geophysics in geophysical

exploration. Geophysics 35, 81-92 (1970). Schlumberger. Log Interpretation: Vol. I, Principles. Schlumberger

Inc., New York (19721. Schlumberger. Log Interpretation Charts. Schlumberger Inc., New

York 11972). Schlumberger. Log Interpretation: Vol. II, Applications. Schlumberger

Inc., New York (1974~. Schlumberger. Serrices Catalog. Schlumberger Inc., Ne~, York 11977). Sherriff R. E. Glossary of terms used in well logging. Geophysics 35,

1116-1139 (1970). Society of Petroleum Engineers of A.I.M.E. Well Logging: SPE

Reprint Series No. I. A.I.M.E.. New York 11971). Society of Professional Well Log Analysts. Acoustic Logging:

SPWLA Reprint Volumes. S.P.W.L.A., Houston (19781. Tixier M. P. and Alger R. P. Log evaluation of non-metallic mineral

deposits. Geophysics 35, 124 142 (1970). Wyllie M. R. J. The Fundamentals of Well Log Interpretation. 3rd ed.

Academic Press. New York 11963).

2. STRUCTURAL APPLICATIONS OF GEOPHYSICAL BOREHOLE LOGGING

Allaud L. A, & Ringot J. The high resolution dipmeter tool. The Log Analyst 10, No. 3 (19691.

Campbell R. L. Stratigraphic applications of dipmeter data in mid- continent, Am. Ass. Petrol. Geol. Bull. 52, 1700-1719 11968).

Cox J. W. The high resolution dipmeter reveals dip-related borehole and formation characteristics. Trans. S.P.W.LA. I lth Annual Log- ging Syrup., Dl-D26 I1970).

Dyck J. H., Keys W. S. & Meneley W. A. Application of geophysical logging to groundwater studies in Southern Saskatchewan. Can. J. Earth Sci. 9, 78-94 I1972).

Evans H. B. See reference in Section 1 (1970). Gilreath J. A. & Maricelli J. J. Detailed stratigraphic control through

dip computations. Am. Petrol. Geol. Bull. 48, 1902-!'910 (1964). Holt O. R. & Hammack G. W. The diplog. In Log Review 1: Review

of Well Logging Principles, Sect. 9. Dresser Atlas Inc., Houston {1971).

King M. S., Stauffer M. R. & Pandit B. I. Quality of rock masses by acoustic borehole logging. Proc. III Int. Congr. I.A.E.G., Sec. IV, Vol. l, pp. 156-164 (1978).

Myung J. I, & Baltosser R. W. Fracture evaluation by the borehole logging method. Proc. Idth Syrup. Rock Mechanics. pp. 31-56. A.S.C.E., New York f1972).

Pirson S. J. See reference in Section 1 (1970). Zemanek J., Caldwell R. L., Glenn E. E., Hotcomb S. V., Norton L. J.

& Straus A. J. D. The borehole televiewer--a new logging concept for fracture location and other types of borehole inspection. Trans. Soc. Petrol. Engrs Am. Inst. Min. Engrs. 246, 762-774 119691.

Zemanek J., Glenn E. E.. Norton L. J. & Caldwell R. L. Formation evaluation by inspection with the borehole tele',ie~er. Geophysids 35, 254-269 (1970).

3. MECHANICAL PROPERTIES FROM GEOPHYSICAL BOREHOLE LOGS

Ambraseys N. N. & Hendron A. J. Dynamic beha~iour of rock masses. In Rock Mechanics in Engineering Practice tEdited by Stagg K. O. and Zienkie~icz O. C,). Chap. 7, pp. 20_~-236. Wiley, New York (19681.

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84 International Society for Rock Mechanics

Carroll R, D. Rock properties interpreted from sonic velocity logs. I. Soil Mech. Fdns Dit'. Am. Soc. cir. Engrs 92, 43-51 {1966).

Carroll R. D. The determination of the acoustic parameters of volca- nic rocks from compressional velocity measurements, Int. J. Rock Mech. Min. Sci. 5, 557-579 (t969).

Coon R. F. & Merritt A, H. Predicting in situ modulus of deforma- tion using rock quality indexes, in Determination of the In Situ Modul,ls of Defornattion o f Rock. Publication STP 477. pp. 154-173. A.S.T.M.. Philadelphia 11970).

Deere D. V. Geological considerations. In Rock Mechanics in Engin- eering Practice (Edited by Sta u K. G. and Zienkiewicz O. CA Chap. 1. pp. 1-20. Wiley. New York (1968).

Ggyer R. L. & Myung J. i, The 3-D velocity log; a tool for in situ determination of the elastic moduli of rocks. Proc. 12th Syrup. Rock Mechanics pp. 7t-107, A.I.M.E.. New York (1971).

Headron A. J. Mechanical properties of rock. In Rock Mechanics in Engineering Practice (Edited by Stag S K. G. and Zienkiewicz O. C.). Chap. 2, pp. 21-53. Wiley. New York (1968).

Kin$ M. $., Stauffer M. R. & Pandit B. I. S¢¢ reference in Section 2 11978).

Kokesh F. P.. Schwartz R. J. Wall W. B. & Morris R. L. A new

approach to sonic logging and other acoustic measurements. J. Petrol. Technol. 17, 282-286 "19651.

Lawrence H. W. In situ measuremem of the elastic properues of rocks. Proc. 6th Syrup. Rock Mechu~Tics. pp. 381-390. University of Missouri. Rolla 1964).

Morris R. L., Grine D. R. & Arkfeld T, E. Using corn presslonal and shear acoustic amplitudes for the location of fractures. J. Petrol. Technol. 16, 623-632 11964).

Myung J. I. & Hetander D. P. Correlation of elastic moduli dynami- cally measured by m situ and laboratory techniques. Trans. $.P,W.L.A. I Jth Annual Logging Syrup.. HI-H25 (1972).

Myung J, I. & Baltosser R. W. See reference in Section 2 ~19721. Pickett G. R. Acoustic character logs and their applications in forma-

tion evaluation. Trans. $oe. Petrol. Engrs. Am. Inst. Min. £ngrs 228, 659-667 ~ 1963).

Stowe R. L. Comparison of in situ and laboratory test results on granite. Tr~ms, $oc. Min. Engrs 152, 194-199 [1972).

Tixier M. P.. Loveless G. W. & Anderson R. A. Estimation of forma- tion strength From the mechanical properties log. J. Petrol. Tech- nol. 27, 283-293 i1975).