GB1584060A - Processing well logging data for example for verification and calibration of well logs - Google Patents

Description

(54) PROCESSING WELL LOGGING DATA, FOR EXAMPLE FOR VERIFICATION AND CALIBRATION OF WELL LOGS (71) We, SCHLUMBERGER LIMITED, a Corporation of the Netherlands Antilles, with administrative office at 277 Park Avenue, New York, N.Y., United States of America, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement: The invention relates to methods of processing well logging data derived from borehole exploring devices, and particularly, though not exclusively, to verifying and calibrating logs.

Boreholes are drilled into the earth in search of earth formations bearing fossil fuels in the form of coal or hydrocarbons, minerals such as sulphur and salt, and water which is potable or contains valuable salts. A knowledge of formation characteristics is required to locate and evaluate such earth formations. Important characteristics are the lithology or mineral composition of the formations, the grain structure of the formations, the porosity or volume of pore space between the grains, the contents of these pore spaces, the permeability or capacity for fluid flow between the pore spaces, and the structure of the formation which determines its capacity to trap and accumulate significant amounts of deposits. In order to be of value, a formation must have the correct combination of porosity, permeability, lithology, pore structure and pore contents.A general reference of formation characteristics and their evaluation is a book by E. J. Lynch entitled "Formation Evaluation" and published by Harper and Row in 1962.

An effective method of obtaining information about the characteristics of the earth formations penetrated by boreholes involves investigating apparatus especially adapted for the environment of a borehole. Such apparatus is lowered in the borehole on a wire line after the hole is drilled. This method is known as wire-line logging, or more simply well logging. In well logging, the exploring apparatus is electrically and mechanically connected by means of the wire line to control and recording equipment located at the surface. The investigating apparatus is lowered in the borehole by means of a winch and is then withdrawn slowly while deriving measurements versus depth./These measurements are recorded on a strip of film or paper, with the long dimension of the strip scaled in depth, thus forming a log of the borehole measurement versus depth.Alternatively, the measurements may be recorded in a suitable electronic memory. The exploring apparatus employed to make the measurements and to generate the electrical signals for recording of these measurements is generally of three types, defined by the method employed to make the measurements. The three types of exploring apparata are electrical, sonic and radiation apparata. A discussion of such well logging techniques may be found in a book by Hubert Guyod and Lemay Shane entitled "Geophysical Well Logging" and published in 1969 for Hubert Guyod, Houston, Texas. A discussion of log interpretation may be found in a book by S. J. Pirson, entitled "Handbook for Well Log Analysis" and published by Prentice-Hall in 1963.

Although general log accuracy is progressively improving with time, modern interpretation techniques create new and very stringent requirements for accuracy. This is particularly true of the porosity logs (neutron, density and sonic), but is also true of other logs (such as spontaneous potential logs, resistivity logs, resistivity micrologs, laterologs, electromagnetic logs, various radioactivity logs and logs such as dip, acoustic, geophone, geothermal, photoelectrical and geochemical logs). It may well be that complex log interpretation techniques, such as shale sands and lithology-porosity interpretation techniques require accuracy which is better than what can be reasonably expected from field recalibrations of measurement devices.

The importance and desirability of log calibration has been recognized in the past, and various techniques have been developed for calibration of logs. For example, manual calibration of logging systems by reference to standards is discussed in an article by Cochrane, J.E., entitled Principles of Log Calibration and Their Application to Log Accuracy, and published in the Journal of Petroleum Technology in July 1968 at pages 817 through 826. The technique involves one-point, two-point, or multipoint surface calibration by means of reference signals. In particular, the investigating apparatus which is normally lowered into a borehole to take measurements is placed at the surface in an environment whose characteristics are known, and the difference between the expected and the actual signals generated by the apparatus are recorded at one or more points on its response curve.

These differences are used to correct the actual measurements taken by the apparatus in a borehole. A similar technique is discussed in an article by Maciula, E. A. and Cochrane, J.

E. entitled Quantitative Use of Calibration Data to Correct Miscalibrated Well Logs and published in the Journal of Petroleum Technology in July 1968 at pages 663-670. The technique involves the use of reference signals to determine the offset of a log from an accurate log, and uses this offset as an operator on recorded measurements to convert them to true values.

Another technique is discussed in Jeffries, F. S. and Kemp, E. M., Computer Reconciliation of Sonic Log and Core Analysis in the Boundary Lake Field, Fourth Annual Logging Symposium Transactions, May 23-24, 1963, Oklahoma City, Oklahoma, pages IV-1 through IV-18. The technique involves calibration of sonic logs by reference to porosity data obtained from core analysis.

Another manual approach to calibration of logs is through statistical analysis of logs by a person skilled in log interpretation. This approach involves creating a model of a field, and deciding if a small shift of one or several of the logs from that field would cause them to conform better to the model. The model is the subjective belief of a person who is highly skilled in log interpretation as to what may be the lithology of a particular field. It may be created on the basis of manipulation of porosity readings, as discussed in Burk, J. A. et al., The Litho-Porosity Cross-Plot, SPWLA, Tenth Annual Logging Symposium, May 25-28, 1969, or on the basis of other information such as individual logs from boreholes in the field of interest, or other knowledge of that field.This manual approach requires a person who is highly skilled and highly experienced in interpreting logs (and geological data in general), and involves a high degree of subjectivity. The approach is time-consuming. Additionally, its extension to more than two or three logs is extremely difficult, and emphasizes the importance of the human factor which is necessarily involved in it. This is undesirable, because the use of a greater number of logs adds additional valuable information.

According to this invention there is provided a method of machine processing well logging data derived from borehole exploring devices which investigate earth formations traversed by boreholes, comprising: deriving a plurality of measurements related functionally to a respective plurality of different earth formation characteristics along borehole sections traversing earth formations in a field; forming first data sets, each comprising a defined combination of said measurements; combining at least a defined portion of said first data sets to form a statistical model of the traversed earth formations: and combining second data sets derived from a borehole in the same field with said statistical model to determine what modification of the second data sets may be necessary to bring them into a defined statistical conformity with the statistical model.

In one case, the step of combining second data sets with the statistical model includes: forming second data sets from said borehole, each second data set comprising the same defined combination of measurements as said first data sets; and combining said second data sets with said statistical model to determine a correction for recalibrating at least one of said measurements to bring the second data sets into the defined statistical conformity with the statistical model.

In another case, the step of combining second data sets with the statistical model includes: forming second data sets from said borehole, each second data set being an abbreviated data set comprising an abbreviated combination of said measurements of the first data sets less a missing measurement; and, combining said second abbreviated data sets with said statistical model to generate for each of said second data sets a value of said missing measurement to reconstruct a missing log in said borehole.

In the latter case, the step of combining said first data sets to form a statistical model may include: forming a functionally multidimensional cell memory with each dimension corresponding to a different one of the abbreviated combination of measurements included in a first data set, and with each cell corresponding to a defined abbreviated combination of the measurements included in a first data set: and storing in each of the cells a statistical optimum of the missing measurement for the data sets comprising the defined abbreviated combination of measurements corresponding to that cell to thereby form said statistical model, and in these circumstances, the combining step for each second data set, may include: defining a cell which corresponds to the abbreviated combination of measurements in the statistical model; reading for said second data set the content of said corresponding cell to generate said value of the missing measurement to reconstruct the log.

In a specific example, the creation of a statistical model in a field involves investigating one or more boreholes in the field by borehole investigating apparatus to derive therefrom a plurality of measurements at eahc depth level. As a result of such investigation, there is, for each depth level, a plurality of measurements each of which is functionally related to a different characteristic of the earth formation adjoining the borehole at that depth level.

For example, at each depth level, the plurality of measurements may include a neutron measurement, a bulk density measurement, and a sonic measurement. Data sets are then formed, with each data set comprising the measurements taken at a specific depth level. For example, a data set may comprise the neutron, bulk density and sonic measurements taken at a specific depth level. The data sets are statistically combined with each other to form a statistical model of the field. This includes forming a memory of cells which is functionally a three-dimensional cube of cells, with each dimension of the cube corresponding to one of the three measurements. Each cell of the cube is then uniquely associated with a particular combination of the three measurements, and each data set may be used to address a single cell.The data sets are examined to determine to which cell they correspond, and each cell is caused to store a count of the number of occurrences of the data set corresponding to it.

After all data sets have been so examined, the cells in the three-dimensional cube of cells are storing counts, and the distribution of the stored counts is representative of a statistical model of the field. Prior to being used to address cells, the measurements forming the data sets may be preliminarily processed to improve their quality. Data sets which are obviously erroneous or are of dubious quality may be discarded in order to enhance the statistical conformity of the model to the field.

After the statistical model is created, a log represented by one of the measurements in data sets derived from a borehole in the same field can be calibrated (or - its calibration can be verified) by statistically combining the data sets containing the log with the model created as described above. Each of the last-mentioned data sets is used to address a cell in the same manner as when creating the statistical model. The contents of the addressed cell are added to the current contents of a central accumulator, and the contents of several adjacent cells along the dimension representing the log which is to be calibrated are added to the current contents of respective side accumulators.After all of the data sets containing a representation of the log which is to be calibrated are used in this manner, the central and side accumulators contain counts whose distribution is representative of the desired calibration correction. In particular, the offset from the central accumulator of the peak of the curve for the plot of accumulator contents versus accumulator number represents the calibration correction. If there is no offset, then it is verified that the log needs no calibration.

Reconstruction of a missing log involves obtaining data sets which contain a plurality of measurements for each depth level in a borehole but do no contain measurements representing a particular log. For example, the data set may contain only a neutron measurement and a bulk density measurement, but not a sonic measurement. A log of questionable quality may be considered to be a "missing" log. Reconstruction of the missing log (e.g., the sonic log) involves statistically combining these two-element data sets with the model of the field created on the basis of three-element data sets (e.g., data sets containing neutron, bulk density and sonic measurement). To this end, each of the two-element data sets is used to address a row of cells in the three-dimensional memory storing the model. The row is along the dimension of the missing log.Each of the cells in that row corresponds to a three-element data set which has two elements that are identical to the elements of the corresponding two-element data set. The cells from the row are examined, and the cell which contains the highest count is chosen. The measurement for the missing log is then supplied by replacing the two-element data set with the three-element data set corresponding to the chosen cell.

The method is applicable to multi-dimensional data sets, such as data sets comprising, for example, four measurements, e.g., neutron, bulk density, sonic and resistivity measurements. It is applicable to other combinations of log measurements, preferably measurements which have some inherent mutual interdependence.

Methods of machine processing well logging data in accordance with this invention for verifying and recalibrating logs and reconstructing missing logs will now be described, by way of example, with reference to the accompanying drawings, in which: Figure I is a schematic block diagram of investigating apparatus having a plurality of exploring devices for investigating adjacent earth formations, and of apparatus for recording well logging signals obtained from the exploring devices and for processing these signals for the purpose of creating a statistical model of a field, for the purpose of recalibrating logs on the basis of that statistical model and for the purpose of reconstructing missing logs on the basis of the model; Figure 2 is a brief illustration of the major steps related to creating a statistical model of a field;; Figure 3 is a simplified illustration of a three-dimensional memory of cells for storing the statistical model of a field; Figure 4 is an illustration of the major steps concerned with recalibrating a log; Figure 5 is a schematic illustration of accumulators used in the recalibration Figure 6 is an illustration of a specific use of the accumulators shown in Figure 5; Figure 7 shows a plot formed through carrying out the steps shown in Figure 4; Figure 8 is a detailed illustration of the steps concerned with creating a statistical model of a field; Figure 9 is a detailed illustration of the steps concerned with recalibrating a log; Figure 10 shows a modification of the process shown in Figure 9, said modification serving for concurrent recalibration of three logs; and Figure 11 is an illustration of the steps concerned with reconstructing a missing log by modifying certain steps of Figure 9.

The well logging data to be processed for the purpose of calibrating a log, or for the purpose of verifying the calibration of a log, or for the purpose of reconstructing a missing log, are derived by means of an apparatus of the type illustrated schematically in Figure 1.

Referring to Figure 1, a borehole investigating apparatus 10 is located in a borehole 12.

The apparatus 10 is suspended in the borehole 12 at the lower end of an armoured multiconductor cable 14 and is selectively raised and lowered in the borehole 12 by means of a suitable drum and winch mechanism (not shown) acting on the cable 14. The investigating apparatus 10 includes a suitable sonic exploring device 16 for measuring the acoustic travel time of the formation surrounding the borehole 12. Sonic exploring devices of this type are described in U.S. Patent No. 2,938,592 granted to C. J. Charske et al. on May 31, 1960 and U.S. Patent No. 3,231,041 granted to F. P. Kokesh on January 25, 1966.

The investigating apparatus 10 also includes a neutron exploring device 18 having a radiation source and a radiation detector mounted in a skid 18a for measuring the hydrogen content of the earth formations adjoining the borehole 12, and thus the porosity of said formations. Exploring devices of this type are disclosed in U.S. Patent No. 2,769,918 granted to C. W. Tittle on November 6, 1956 and in French Patent Specification No. 1 583 809. Alternatively, a conventional neutron exploring device can be used in place of the neutron device 18. In a conventional neutron device, neutrons emitted into a formation are captured by certain types of atoms in the formation, which results in the emission of high energy level gamma rays called capture gamma rays. The capture gamma rays are counted by a nearby detector.The investigating apparatus 10 also includes a formation density exploring device 20 for producing well logging measurements which can be utilized to calculate the bulk density of the adjoining formations. The formation density device 20 includes a skid 20a which houses a source and two detectors spaced at different distances from the source. This arrangement of a source and detectors produces signals which correspond to the bulk density of the earth formations adjoining the borehole 12. A formation density measuring device of this type is disclosed in an article by J. S. Wahl, J.

Tittman, C. W. Johnstone and R. P. Alger entitled Dual Spacing Formation Density Log and published in the Journal of Petroleum Technology, December 1964, pages 1411-1416; in an article by J. Tittman and J. S. Wahl entitled The Physical Foundations of Formation Density Logging (Gamma-Gamma) and published in Geophysics on April 1965 at pages 284-294; and in U.S. Patent No. 3,321,625 granted on May 23, 1967 to John S. Wahl. To keep the investigating apparatus 10 centred in the borehole, a pair of extendable wall engaging members 18b and 20b are provided opposite skids 18a and 20a respectively. A borehole caliper may be combined with the arms which extend the skid 18a and 20a to supply a signal representative of the diameter of the borehole 12. To keep the upper portion of the investigating apparatus 10 centred, a plurality of resilient spacers 22 are provided.

Still referring to Figure 1, signals G1 and G2 are derived from the short and long spacing detectors of the formation density measuring device 20. These signals are in the form of pulses whose repetition rates are representative of the measured parameters. The count rate signals G1 and G2 are transmitted to the surface over respective conductors in thearmoured cable 14 and are amplified by a pair of amplifiers 24 and 26 respectively. The outputs of the amplifiers 24 and 26 are applied to a density computer 28 which computes the bulk density Pn of the formations adjoining the borehole 12.If desired, the caliper signal can be applied to the density computer 28 to be used in the computation of the bulk density PB. The resulting bulk density signal Pn is-supplied to a suitable memory 30 which stores the computed bulk density measurements in a manner which allows associating a stored measurement with the depth level in the borehole 12 at which this measurement is taken by the investigating apparatus 10. The memory 30 can be any suitable memory device such as a rotating magnetic or capacitor memory which stores for subsequent readout incoming signals for a sufficient depth interval.The memory 30 is driven at a speed which is a function of borehole depth by a shaft 32 coupled to a rotating wheel 34 which engages the armoured cable 14 to thereby synchronize the memory 30 with - the position of the investigating apparatus 10 in the borehole 12.

The neutron signal N derived by the neutron device 18 is in the form of a series of pulses proportional to the hydrogen content, and thus the porosity of the earth formations adjoining the borehole 12. This neutron signal N is supplied via a suitable conductor in the cable 14 to an amplifier 36 whose output is supplied to a suitable porosity computer 38 which converts the neutron count rate N to a DC signal proportional to the neutron-derived porosity N A device which can serve as the porosity computer 38 is disclosed in the above-mentioned French Patent Specification No. 1 583 809. The neutron-derived porosity signal N is supplied to a suitable memory 40 driven by the shaft 32.The memory 40 is similar to the memory 30 and acts to depth-synchronize the neutron-derived porosity signal stored therein with the bulk density signal output from the density computer 28.

The travel time measurements At derived from the sonic exploring device 16 are supplied via a suitable conductor in the armoured cable 14 to an amplifier 42, and the amplifier output is supplied to a memory 44 which is similar to the memories 30 and 40 and is similarly synchronized by means of the shaft 32 in order to depth-synchronize the recorded sonic logging signals with the bulk density signals and the neutron-derived porosity signals.

Either concurrenfly with recording in the memory 30, or at a subsequent time, the bulk density signals output from the density computer 38 can be supplied to an analog-to-digital converter 46 to be converted therein to digital signals suitable for transmission or for subsequent storage elsewhere. Similarly, the neutron-derived porosity signals which are stored in the inemory 40 may be supplied to a similar analog-to-digital converter 48, and the sonic signals recorded in the memory 44 may be supplied to a similar analog-to-digital converter 50. The digital signals provided at the outputs of the analog-to-digital converters 46, 48 and 50 are supplied to a data link transmitter 52 for transmission via a communication link 54 to a location for further processing of the measurements taken by the investigating apparatus 10.

For processing in accordance with the invented method, the digitized neutron, sonic and density signals transmitted via the communications link 54 are received at a data link receiver 56 and may be supplied to a depth correlator 58, if desired, for fine depth correlation between the individual signals of a triple of measurement signals (neutron, sonic and density) derived at the same depth level in the borehol 12. The output of the depth correlator 58 may be supplied, if desired, to a preliminary processor 60 for carrying out any desired preliminary processing, such as preliminary zero shifting or preliminary scaling by a known factor. The output of the preliminary processor 60 is a series of triples of values called data sets. Each data set comprises a combination of the three measurements (neutron, sonic and density) taken at the same depth level in the borehole 12.For example, if measurements are taken every six inches as the investigating apparatus 10 is drawn up in the borehole 12, there is a data set comprising the three measurements taken at each six-inch interval along the borehole 12. The data sets output from the preliminary processor 60 are stored in a storage device 62 which may be a conventional drum, tape or disk storage device. Two or more boreholes 12 in the same field may be investigated as described above, and the data sets derived therefrom may be stored in the storage device 62. The data sets in the storage device 62 are processed under the control of a central processing unit 64 to generate from these data sets a statistical model of the;field, and this statistical model is stored in a suitable memory 66. The memory 66 may be a conventional core memory, or a conventional disk or drum memory, or the like.When a log from a given borehole 12 in the same field is to be calibrated, data sets which include that log and are stored in the storage device 62 are combined with the statistical model stored in the memory 66 in accordance with the subject invention in order to determine what zero shift, if any, may be required to bring that log into a defined statistical conformity with the model stored in the memory 66.

The result of this determination may be displayed on a display device 68 which may be a conventional computer printer. Under the control of the central processing unit 64 and in accordance with the subject invention, the zero shift may then be applied to the log of interest to calibrate the log on the basis of the determined zero shift.

Calibration of a log from a given field, or verifying the calibration of a log involves two major steps: forming a statistical model of the field by combining a number of logs taken from boreholes in the same field; and combining the log which is to be calibrated with the statistical model to determine what modification thereof, if any, may be necessary to bring it into a defined statistical conformity with the model of the field. The invented method reflects the general principle that when an analyst is comparing logs with an a priori model of a field, and a small shift in one or several logs from the same field would cause them to conform to that a priori model, he would assume the shift to be legitimate and to correspond to a calibration error (zero or scale error).The analyst's basis for this assumption would be statistics from previous logs, plots, etc., as well as the extent of his knowledge and experience, and his subjective beliefs as to what the lithology of the field should be. The statistical model of a field which is created in the method described herein reflects this general principle, but provides for applying it in situations in which it would be impossible or implausible for an analyst to process the available data about a field.

Additionally, the invented method eliminates human error and eliminates subjectivity and personal bias.

To illustrate the problem and to illustrate possible solutions to the problem, an example is given involving the three porosity logs. As will become clear below, the invention is also applicable to other logs and to other combinations of logs, such as four or more logs, or two logs.

For the purposes of illustration, suppose that there is an a priori probability of finding a particular set of the three porosity measurements. In other words, for each triple of the porosity measurements in a three-dimensional space, there is a probability function.

where n is the number of occurrences of the particular triple, and N is the total number of triples. Then let us assume that a small calibration error in one of the logs tends to shift the triple which includes that log to a position of lower probability (the shift tendency is in statistical terms). For each triple of measurements derived at a given depth level from a new borehole in a field, there is a corresponding probability function, and the average probability per level can serve as a measure of the conformity between the triples of measurements from the new borehole and the a priori model defined by the a priori probability functions. Then, calibration can be carried out by maximizing the average probability through a systematic search around an original point.

The choice of an a priori probability is a critical step. It is doubtful that a universal probability function could be found for all logging conditions; even if such a universal probability function could be found, it would be a rather flat function and hence not very useful, since what is needed is a function with relatively steep variations in its domain.

However, for a certain field, and even probably for a certain type of depositional environment, such a probability function should exist, and should possess the necessary properties for calibration purposes.

One method of creating a probability function is to select a set of logs run in reasonably good condition in a desired field (geological environment) and to count the number of occurrences of each unique combination of the three porosity measurements. The accepted a priori probability for a triple of measurements would be the ratio of the corresponding number of occurrences to the total number of triples derived from the field. All mineral combinations normally expected in that field should preferably be included in the set of logs, but this is not an absolute requirement. Undetected small calibration errors in these logs may somewhat flatten the probability function, but it should preserve its main properties. Additionally, small depth mismatches between logs would also somewhat average the function. The probability function can be progressively improved by merging new information deduced from new logs in the same field, preferably logs which are of excellent quality. A borehole including new minerals should not create problems provided that a large portion thereof corresponds to standard lithology.

The major steps in creating a statistical model of a field are illustrated in Figure 2 in terms of steps suitable for execution on a general purpose digital computer. The computer may comprise the central processing unit 64 shown in Figure 1 together with the storage devices 62 and 66 and the display device 68. Although the process may be carried out on a small scale digital computer, by means of multiple transfers of data between bulk storage and fast memory, for the sake of simplicity the process is illustrated below as practiced on a large scale digital computer having a large fast (core) memory. One example of a suitable machine is an International Business Machines System 360/65 general purpose digital computer which has 512K bytes of core memory.

Referring to Figure 2, the first step in building a statistical model of a field is to read at step 70 a data set which comprises a triple of the three porosity measurements taken at a given depth level in a borehole from the field which is of interest. The data set may be read from the storage device 62 in Figure 1, or it may be otherwise formed. It is noted that the data set read at step 70 may comprise other measurements derived from apparatus for investigating earth formations traversed by a borehole.

The data set which is read at step 70 is examined at step 72 to determine if each of its measurements is within specified limits. A data set in which a measurement is abnormally removed from a reasonable range of values for a given field is probably erroneous and invalid and should not be allowed to influence undesirably a statistical model of that field; therefore, if the answer at step 72 is no, i.e., if the data set read at step 70 is not within defined limits, a return is made to step 70 to read another data set. The data set which was determined not to be within the defined limits at step 70 is thus completely discarded.

If the answer at step 72 is yes, i.e., if the data set read at step 70 is within the defined limits, control is transferred to step 74 to calculate a cell address corresponding to the particular combination of measurements comprising the data set read at step 70. The statistical model which is created may be visualized functionally as a three-dimensional memory comprising a cube of cells, where each cell corresponds to a particular combination of the three porosity measurements. A schematic and abbreviated illustration of a three-dimensional memory of cells is shown in Figure 3 where each of the cells is identified by a triple of numbers, each number ranging from 0 to 3.In the example shown in Figure 3, the X dimension of the memory may be the neutron log measurement, the Y dimension of the memory may be the bulk density log measurement and the Z dimension may be the sonic log measurement. Thus, the cell labelled (0, 0, 0) corresponds to a data set in which each of the three porosity measurements is scaled to a zero, the cell labelled (1, 3, 1) corresponds to a data set in which the neutron measurement is scaled to 1, the bulk density measurement is scaled to 3 and the sonic measurement is scaled to 1. The label of a cell may be considered as its address. The cell labels may be given directly in units of the porosity measurements, or the cell addresses may be scaled as defined functions of the values of the porosity measurements of data sets.

Referring back to step 74 of Figure 2, the three measurements of a data set are used to calculate the address of a cell in a cell memory of the type illustrated schematically in Figure 3. After a cell address is calculated, control is transferred to step 76 to increment the current contents of the addressed cell. All cells in the memory may initially contain zero or some other known arbitrary number. If all cells in the memory contain zeros at the start of the steps shown in Figure 2, and the address of a cell is calculated for the first time, the contents of that cell are incremented from zero to one to indicate that there occurred a data set corresponding to that cell. Each time a cell address is calculated at step 74, the cell contents are incremented by one.

After step 76, a test is made at step 78 to determine if there are any remaining data sets. If there are remaining data sets, a return is made to step 70 to read another data set; if there are no remaining data sets, a distribution listing is printed at step 80 by the display device 68 (Figure 1) to show the distribution of the cell contents of the memory illustrated in Figure 3.

In the typical case, most of the memory cells have not been addressed and hence contain no counts. Typically, only up to a few thousand memory cells contain counts.

It is noted that the three-dimensional memory illustrated in Figure 3 need not in fact be a three-dimensional matrix of cells, but may be simulated on a two-dimensional memory such as the fast (core) memory 66 in Figure 1. What is important is only that the memory 66 (Figure 1) has sufficient capacity to have as many word locations as there are cells in the three-dimensional memory discussed above. The required number of word locations is the number of possible unique data sets whose measurements are within the limits defined in step 72 (Figure 2). For example, if there are 50 possible values for each of the three porosity measurements, the memory 66 must have at least 125,000 word locations (i.e., 50 x 50 x 50), each word location (cell) corresponding to a unique data set.

After processing data obtained from one or more boreholes in a given field by means of the method illustrated in Figure 2, the memory 66 contains information which represents a statistical model of the field. This statistical model may be used to calibrate a log obtained from a borehole in the same field, or to verify the calibration of a log, by means of the process whose major steps are illustrated in Figure 4. The calibration and calibration verification process involves statistically combining data sets from a borehole in that field with the statistical model in the memory 66 to determine what modification, if any, of a selected measurement in each of these data sets may be required to bring the selected measurements into a defined statistical conformity with the model.

Referring to Figure 4, steps 82, 84 and 86 are the same as steps 70, 72 and 74 respectively of Figure 2, except that the data sets referred to in Figure 4 contain a measurement representing a log whose calibration is questioned. For example, it may be desired to calibrate or to verify the calibration of the neutron log from a given borehole, and each of the data sets which are processed in steps 82, 84 and 86 contains a neutron measurement representing that log.

In particular, at step 82, a data set is read from the storage device 62 (Figure 1), and if the data set is not discarded at step 84 because of failure to fall within defined limits, it is used at step 86 to calculate a cell address in the same manner as a data set is used at step 74 of Figure 2 to calculate a cell address.

At step 88 of Figure 4, the contents of the cell whose address is calculated at step 86 are nondestructively read out of the cell and are added to the current contents of an accumulator called a "central" accumulator. The central accumulator may be a register, or simply a location in memory in which a running sum is kept of the contents of the cells whose addresses are calculated at step 86.

At step 90, the contents of the several adjacent cells along the dimension of the log which is to be calibrated (e.g., the neutron log dimension) are read out, and each is added to the current contents of a corresponding accumulator from a plurality of accumulators called "side" accumulators.

Figure 5 illustrates a central accumulator 100, a right-side accumulator 102 which is labelled the "(+1)" accumulator, another right-side accumulator 104 labelled the "(+2)" accumulator, a left-side accumulator 106 labelled "(-1)", and a second left-side accumulator 108 labelled "(-2)". The central accumulator 100 stores cumulatively the contents of the cell whose address is calculated at step 86, the right-side accumulator 102 stores the contents of the immediately adjacent cell in the positive direction along the dimension corresponding to the log which is to be calibrated, and the right-side accumulator 104 stores the contents of the cell immediately adjacent to and in the same direction as the cell whose contents are stored cumulatively in the side accumulator 102.The left-side accumulator 106 stores cumulatively the contents of the cell immediately preceding (in the direction of the log which is to be calibrated) the cell whose contents are stored in the central accumulator 100, and the left-side accumulator 108 stores cumulatively the contents of the cell immediately preceding (in the direction of the log which is to be calibrated) the cell whose contents are stored in the left-side accumulator 106. There may be additional left-side and right-side accumulators arranged in a similar manner and serving a similar function. In fact, the embodiment shown in Figure 4 uses five left-side and five right-side accumulators.

Figure 6 illustrates a specific example which is described below by reference to Figures 3, 4 and 5. In this specific example, suppose that the cell labelled (2, 3, 1) in Figure 3 is the cell whose address is calculated at step 86 in Figure 4. The contents of that cell are stored in the central accumulator 100. Then, the contents of the immediately adjacent cell along the dimension of the log which is to be calibrated (i.e., along the QN dimension) are read out and stored in the right-side accumulator 102. This cell is the cell labelled (3, 3, 1) which is immediately to the right side of the cell (2, 3, 1) in Figure 3. If there are other cells to the right of the cell labelled (2, 3, 1) in Figure 3, their contents are stored cumulatively in other respective right-side accumulators.The contents of the cell labelled (1, 3, 1) which cell is immediately preceding the cell (2, 3, 1) in Figure 3, are added cumulatively to the current contents of the left-side accumulator 106. The contents of the next preceding cell, i.e., the cell labelled (0, 3, 1) in Figure 3 are added cumulatively to the side accumulator 108, etc.

When the next data set is used at step 86 of Figure 4 to calculate a cell address, suppose that this new cell address identifies the cell labelled (2, 1, 0) in Figure 3. Then the cell whose contents are added cumulatively to the side accumulator 102 is the cell labelled (3, 1, 0); the cell whose contents are added cumulatively to the side accumulator 106 is the cell labelled (1, 1, 0); and the cell whose contents are added to the current contents of the side accumulator 108 is the cell (O, 1, 0), etc.

Referring back to Figure 4, after all of the data sets containing a measurement for the log which is to be calibrated have been processed through step 90, the test at step 92 indicates that there are no more such data sets. At that time, the accumulators contain cumulative counts, and at step 94 a distribution curve is formed of the contents of these accumulators.

The distribution curve is a plot of the accumulator contents versus the accumulator number relative to the central accumulator. An exemplary distribution curve is illustrated in Figure 7 where the horizontal axis is the accumulator number and the vertical axis is the accumulator contents (actually, the count in an accumulator expressed as a percentage of the total counts in all accumulators). The central accumulator 100 of Figure 5 is labelled 0000 in Figure 7, the left-side accumulator 106 is labelled -001, the left-side accumulator 108 is labelled -002, etc., the right-side accumulator 102 is labelled 0001 in Figure 7, the right-side accumulator 104 is labelled 0002, etc.The line labelled "probability" in Figure 7 indicates numerically, above the corresponding accumulator number on the abscissa, the value plotted along the ordinate (that is, the count in that accumulator expressed as a percentage of the total counts in all accumulators); and the line above that, which is labelled "accumulative cell count", indicates the actual counts stored in the respective accumulators.

A curve 110 may be fitted by conventional curve fitting techniques to the plot represented by the percentage counts in Figure 7. The peak of that curve 110 which is labelled 110a in Figure 7 is a measure of the zero shift which must be applied to the log tested for calibration in order to bring that log into the defined statistical conformity with the statistical model of the field which is stored in the memory 66. In the illustrative example of Figure 7, the peak of the curve 110 is displaced to the left of the central accumulator 100 by 1.61 cell units. This means that a zero shift in neutron porosity units corresponding to 1.61 cell units must be subtracted from each porosity measurement of the log which was tested for recalibration to bring that log into the defined statistical conformity with the model.Referring back to Figure 4, the peak of the curve 110 is found at step 94, the offset of the curve peak from the central accumulator is found at step 96, and the neutron log is calibrated by the determined offset at step 98. At step 100 a print, such as the plot shown in Figure 7 may be provided.

The above discussion gave the specific example of calibrating a neutron log. Similar calibration may be carried out for the bulk density log or for the sonic log. In calibrating the bulk density log for example, a cell address is calculated in a similar manner at step 86 of Figure 4, and at step 88 the several adjacent cells whose contents are read out and added to the current contents of respective accumulators are along the bulk density dimension of the three-dimensional memory shown in Figure 3. Referring to Figure 5, if the cell whose contents are added to the central accumulator 100 is the cell labelled (2, 2, 0), then the cell whose contents are added to the side accumulator 102 is the cell labelled (2, 3, 0); the cell whose contents are added to the side accumulator 106 is the cell labelled (2, 1,0), etc.

Similarly, when calibrating a sonic log, if the cell whose address is calculated at step 86 in Figure 4 is the cell labelled (1, 3, 1), then the cell whose contents are added to the side accumulator 102 in Figure 5 is the cell labelled (1, 3, 2), and the cell whose contents are added to the side accumulator 106 is the cell labelled (1, 3, 0), etc.

A specific example of that part of the method which deals with creating a statistical model of a field is shown in detail in Figure 8. The method shown in Figure 8 can be carried out on a suitable general purpose digital computer, such as an International Business Machines System 360/65 with enough core memory, for example 512K bytes of core memory.

Prior to executing the method illustrated in Figure 8, one or more boreholes in a field are investigated by equipment of the type shown in Figure 1, and data sets of the type discussed above are stored in the storage device 62. Although data sets from a single borehole in the field may be sufficient in some situations, it is preferable to have data sets from several boreholes, for example, at least three or four boreholes. It is preferable to obtain reasonably reliable data sets, e.g., it is desirable to either manually check the calibration of each of the logs obtained from the boreholes or to otherwise ensure that the logs are reasonably well calibrated.

Referring to Figure 8, limits are defined for the values of each of the three porosity logs at step 112. As discussed earlier, this is for the purpose of eliminating obviously erroneous measurements, and to prevent such obviously erroneous measurements from degrading the expected statistical model of the field. For example, it may be known about a specific field that the neutron log measurement should be in the range of - .10 to + .40 neutron porosity log units, that the bulk density measurements should be in the range of 1 to 3.5 bulk density units, and that the sonic measurements should be within the range of 50 to 150 sonic units.

These limits may be defined at step 112, such that any data set which contains a measurement outside the respective limit will be dropped.

At step 114, a data set is read from the storage device 62 (Figure 1) and at step 116 a test is made to determine if a preliminary zero shift has been specified. Such preliminary zero shift may be desired because it is known that a particular log has been shifted by a known amount. For example, it may be known that the instruments involved in recording the neutron log have consistently intrOduced a zero offset of + .05 neutron log units. If that is the case, then it is specified that each neutron measurement should be shifted in the corresponding direction by .05 units. Then, the test at step 116 is positive and control is transferred to step 118 for the purpose of correspondingly offsetting each of the neutron measurements.If no preliminary zero shift has been specified, control is transferred to step 120 where a test is made to determine if a preliminary scaling has been specified.

Preliminary scaling is similar to the preliminary zero shift and may be desired for similar reasons; the only difference is that scaling involves multiplication by a defined factor rather than algebraic addition of a defined offset. If a preliminary scaling has been specified, it is carried out at step 122. Specific methods for carrying out such preliminary zero shifting and scaling are conventional in the well logging art.

If no preliminary zero shift and no preliminary scaling have been specified, or after preliminary zero shift or preliminary scaling, control is transferred to step 124 where a test is made to determine if the data set (after any preliminary zero shift or preliminary scaling) is within the limits defined at step 112. If the data set is not within the defined limits, control is transferred to step 126 where a test is made to determine if any data sets remain. If data sets remain, control is returned to step 114 to read the next sequential data set from the storage device 62 (Figure 1).

If the data set tested at step 124 is within the limits defined at step 112, control is transferred to step 128 where each of the measurements comprising the data set is integer-scaled to form thereby an integer triple (X,Y,Z) which corresponds uniquely to the data set. For example, each of the three measurements of a data set may be given the integer range between 0 and 49, and each integer may be uniquely associated with a specified range of log units. Thus, if the data sets contain neutron measurements in the range of -.10 to +.40 neutron log porosity units as discussed above, the integer 0 is associated with a neutron measurement of - .10 units, the integer 1 is associated with a neutron measurement of - .09 units, the integer 2 is associated with - .08 neutron units, etc.

Similarly, if the bulk density range is from 1.00 to 3.50 bulk density units, the integer 0 is associated with a bulk density measurement of 1.00 unit, the integer 1 is associated with a bulk density measurement of 1.05 units, the integer 2 is associated with a bulk density measurement of 1.10 units, etc. In the same manner, if the sonic measurements range between 50 and 150 sonic log units, the integer 0 is associated with sonic measurements of 50 and 51 units, the integer 1 is associated with sonic measurements of 52 and 53 units, the integer 2 is associated with sonic measurements of 54 and 55 sonic units, etc. After step 128, each data set is represented as a corresponding integer triple (X,Y,Z) wherein each of the elements of the triple is within the integer range of 0 to 49.For example, the data set (-.10, 1, 50) corresponds to the integer triple (0, 0, 0); the data set (-.05, 3, 100) corresponds to the integer triple (5, 40, 25); and the data set (+.40, 3.5, 149) corresponds to the integer triple (49, 49, 49).

At step 130, the integer triple formed at step 128 is used to compute a cell address corresponding to the data set from wkich the integer triple is formed. For example, if each of the elements of the integer triples ranges from 0 to 49, 125,000 cell addresses are needed to provide a cell address for each unique integer triple (i.e, 50 x 50 x 50 cell addresses).If the memory 66 in Figure 1 (e.g., the core memory of a general purpose digital computer) has at least 125K word locations numbered linearly and sequentially from 0 to 124,999, then a cell address CA (word address) may be calculated by the following expression: CA = X + 50Y + 2500Z Thus, the integer triple (0, 0, 0) would result in the cell identified by the linear address 0, the integer triple (1, 1, 0) would result in the linear cell address 51, and the integer triple (1, 1, 1) would result in the linear cell address 2551.

At step 132, the current contents of the cell identified by the address computed at step 130 are incremented by 1.

After step 132, control is returned to step 126 to determine if any data sets for the same borehole remain in the memory 62 (Figure 1). If data sets remain, control is returned to step 114 to read the next sequential data set and to proceed to the following steps. If the manner to the test at step 126 is no, i.e., if all the data sets for a given borehole have been exhausted, control is transferred to step 134 to determine if additional data sets derived from another borehole in the same field are to be added. If the answer is yes, control is returned to step 114 to start reading data sets derived from that borehole. If the manner at step 134 is no, control is transferred to step 136 to print a distribution listing and to end the steps. The distribution listing is a printout of the number of times each integer occurs in the contents of the cells. An example of a distribution list is given in Table 1 below where the column labelled "Class" lists the integers which can be found in the cells of the memory, the column labelled "Frequency of Occurrences" lists the number of cells which contain the integer, and the next two columns to the right bear self-explanatory labels.

Class Freq. of Freq. Cumulative Occurrences List.

(C) (F) (CxF) Frequency 0 121430 0 0 1 1953 1953 1953 2 780 1560 3513 3 413 1239 4752 4 281 1124 5876 5 205 1025 6901 6 133 793 7699 7 106 742 8441 8 82 656 9097 9 79 711 9808 10 46 460 10268 11 45 495 10763 12 46 552 11315 13 27 351 11666 14 24 336 12002 15 19 285 12287 16 17 272 12550 17 11 187 12746 18 12 216 12962 19 8 152 13114 20 10 200 13314 21 3 63 13377 22 2 44 13421 23 6 138 13559 24 3 72 13631 25 2 60 13681 26 5 130 13311 27 1 27 13838 28 1 28 13366 29 3 87 13953 31 1 31 13984 32 1 32 14016 33 1 33 14049 34 1 34 14063 36 2 72 14155 41 1 41 14196 TABLE 1 A detailed example of the portion of the method concerned with calibration of a log or with verifying the calibration of a log is illustrated in Figure 9. In Figure 9, the first ten steps correspond to the first ten steps of Figure 8.In particular steps 138, 140, 142, 144, 146, 148, 150, 152, 154 and 156 of Figure 9 correspond respectively to steps 112, 114, 116, 118, 120, 122, 124, 126, 128, and 130 of Figure 8. The only difference is that the data sets processed in Figure 9 contain a measurement representing a log which is to be calibrated. For simplicity of illustration, it is assumed that the neutron log measurements are to be calibrated, but it should be clear that alternatively, the bulk density measurements or the sonic measurements may be recalibrated.

After step 156 in Figure 9, control is transferred to step 158 where the contents of the cell whose address is computed at step 156 are added to the current contents of a central accumulator. The central accumulator may be one of the general registers of the digital computer, or it may be simply a location in memory which serves as an accumulator.

At step 160, ten additional cell addresses are calculated according to the expression CA = X' + 50Y + 2500Z where (X' = X + D (D = -5, 4, ..., -1, 1, 2 ..., S For example, if the address calculated at step 156 is 20, the ten addresses calculated at step 160 are, respectively: 15, 16, 17, 18, 19, 21, 22, 23, 24 and 25.

At step 162, the contents of the cell addresses computed at step 160 are added to the current contents of respective side accumulators. For example, if there is a central accumulator and ten side accumulators labelled as discussed in connection with Figure 7, the contents of cell 15 are added to the current contents of the accumulator -005, the contents of cell 16 are added to the current contents of the accumulator -004, the contents of cell address 21 are added to the current contents of the accumulator 0001, the contents of cell address 22 are added to the current contents of accumulator 0002, etc.

After step 160, control is returned to step 152 to determine if there are remaining data sets for the same borehole. If the answer is yes, control is returned to step 140 to read another data set, and to proceed again through step 162. If there are no remaining data sets, control is transferred to step 164 to form a plot of accumulator contents versus accumulator number, i.e., a plot of the type illustrated in Figure 7.

At step 166, the peak of a curve fitting the plot is found, as discussed in connection with Figure 7, and at step 168 the displacement of the curve peak from the central accumulator is found in terms of cell units, again as discussed in connection with Figure 7. In the example given in Figure 7, the curve peak is displaced from the central accumulator by -1.61 cell units.

At step 170, the necessary zero shift is computed in terms of logging units by carrying out the reverse of step 154. In this example, one cell unit corresponds to .01 neutron log units, and -1.61 cell units corresponds to an offset of -.0161 neutron log porosity units.

After step 170, control is transferred to step 172 where a printout is provided of a histogram showing the plot formed at step 164 and the values computed at steps 168 and 170.

As an optional procedure, the particular log (i.e., the neutron log) may be calibrated by adding algebraically to each measurement representing that log the zero shift computed in neutron log units at step 170. In this example, calibration is carried out by subtracting from the QN measurement in each data set.

After step 172, or after the optional step 174, control is transferred to step 176 where a test is made to determine if another log is to be calibrated. If the answer is yes, control is returned to step 140 to read from the storage device 62 (Figure 1) the first data set that includes another log which is to be calibrated. If the answer to the test made at step 176 is no, the calibration and calibration verification procedure shown in Figure 9 is ended.

The procedure shown in Figure 9 can be used for any of the three measurements forming a data set. For example, if the bulk density log is to be recalibrated, the cell addresses computed at step 160 are computed according to the following expression: CA = X + 50Y' + 2500Z =Y+D where D = -5, -4 -1, 1, 2 5 Thus, in the case of recalibrating the bulk density log, if, for example, the cell address computed at step 156 is 300 (resulting from an integer triple 0, 6, 0), then the ten addresses calculated at step 160 are, respectively: -50, 100, 150, 200, 250, 350, 400, 450, 500 and 550.

Similar modification is made when recalibrating the sonic log by the procedure illustrated in Figure 9.

When it is desired to calibrate more than one of the three logs which form the data sets, the method illustrated in Figure 9 may be modified to the extent illustrated in Figure 10. In particular, if it is desired to calibrate or to verify the calibration of each of the neutron, bulk density and sonic logs, then the method illustrated in Figure 9 is followed through step 158 thereof, and then instead of executing step 160 illustrated in Figure 9, the steps 160a, 160b and 160c of Figure 10 are executed either simultaneously or sequentially.

Step 160a of Figure 10 corresponds exactly to step 160 of Figure 9. Step 160b of Figure 10 is for calibrating the bulk density log and involves computing the addresses of the cells adjacent the cell whose address is computed at step 156, with the adjacent cells being along the dimension of the bulk density log. Step 160c is for calibrating the sonic log and involves computing the addresses of the cells adjacent the cell whose address is computed at step 156, but along the dimension corresponding to the sonic log. Then, in addition to the ten side accumulators discussed in connection with step 162 of Figure 9, there are two additional and different sets of ten accumulators for storing the contents of the cells whose addresses are computed at step 160b and 160c respectively. Additionally, step 164 of Figure 9 is modified to the extent of providing plots of accumulator contents versus accumulator number for each of the three sets of eleven accumulators each resulting from the execution of steps 158, 160a, 160b and 160c. Steps 166, 168, 170, 172, and 174 of Figure 9 are modified to the extent of treating each of the curves resulting from the execution of steps 160a, 160b and 160c in the same manner as the curve resulting from the execution of step 160 of Figure 9.

An important aspect of the subject invention is that it is applicable to data sets which may have more than three dimensions, i.e., data sets which may comprise more than three different measurements. For example, the methods disclosed herein may be applied to a data set comprising a neutron measurement, a bulk density measurement, a sonic measurement, and another measurement, such as a resistivity measurement. In such case, the statistical model is four-dimensional.One manner of embodying the four-dimensional statistical model in a two-dimensional core memory is to compute cell addresses according to an expression - of the form CA = X + aY + bZ + cR where a, b and c are integer constants and X, Y, Z and R are integer-scaled measurements representing, for example, a neutron, a bulk density, sonic, and a resistivity measurement respectively. If each of the measurements is integer scaled to the range of 0 to 24, the four-dimensional statistical model requires 390,625 cell locations. If a byte of memory is assigned per cell location, then a general purpose digital computer with 512K bytes of core memory is sufficient. If a two-byte word is assigned per cell location, then a 1,024K byte core memory is sufficient.

There are situations where certain logs from a given borehole may be available and may be in-gó-od condition, but a particular log taken in the same borehole may be either in poor condition or nonexistent. The present invention permits the reconstruction of a missing or poor log with the help of other logs from the same borehole and with the help of the statistical model of the field in which the borehole is located. A specific example of a method for.reconstructing a missing or poor log is shown in Figure 11. Prior to proceeding with the method of Figure 11, it is assumed that a statistical model of the field has been created as-discussed in connection with Figure 8, and that at least two logs are available from a specific, borehole for which a log is missing.For example, let us assume that a neutron and a bulk density log are available for a given borehole, but that the sonic log for that borehole is missing. To reconstruct the missing log, data sets are formed as discussed in connection with Figure 9, except that the data sets have only two elements each, namely, a neutron measurement and a bulk density measurement. Then, the steps involved in the reconstruction of a missing log are the same as steps 138 through 154 of Figure 9, the only difference being that the data sets used in the reconstruction of a missing log have only two elements as opposed to the three elements of the data sets used in the method shown in Figure 9.

After step 154, the data sets used in reconstructing a missing log are integer pairs; in.the example given here each data set is scaled to an integer pair (X,Y). Referring to Figure 11, the integer pair is used at step 178 to compute cell addresses according to the expression CA = X + 50Y + 2500Z where Z = 0, 1, 2 ..., 49 The computation at step 178 results in 50 cell addresses. In effect, if the statistical model is visualized as contained in a three dimensional cell cube, the 50 cell addresses are a row along the dimension of the missing log.

At step 180 of Figure 11, the contents of the 50 cells whose addresses are computed at step 178 are examined to determine which cell contains the highest count. If two or more of the cells contain the same counts, it is immaterial which of them is chosen.

After a cell address is determined at step 180, the third element of the cell address (this third element is an integer ranging from 0 to 49) is scaled back to sonic measurement units.

The number in sonic measurement units obtained at step 182 is combined at step 184 with the other two elements of the data set read at step 140 to form a three-element data set (4)N, PB, At). This three-element data set is stored at step 186 in a suitable location in memory, and a return is made to step 140 to read another two-element data set.

After the method discussed above has been repeated for all of the two-element data sets from a given borehole, the result is a plurality of three-element data sets, where the third elements of each of these data sets are a representation of the missing log.

Another technique for reconstructing a- missing log may be used for determining a characteristic of earth formations traversed by a defined borehole in a field when this characteristic cannot be derived from data available from the defined borehole if, for example, the number of different logs which has been run in the borehole is too small. In anexample of this other technique it will be assumed that the characteristic to be derived in a defined borehole of the field is the formation porosity , and that a sonic log At and a gamma ray log GR are available in the defined borehole. In one or several other boreholes of the field the number of logs is sufficient to compute the porosity level by level by processing the well logging data according to a well known method such as the one described in French patent No. 2,102,380 (A.Poupon and R. Gaymard). lt will be remarked here that the characteristic to be determined in the defined borehole may have been derived in another borehole from sources other than well logs such as core analyses, test results or production data. The permeability of earth formations traversed by a borehole may have been derived, for example, from core analyses. The sonic and gamma ray logs are available in the boreholes of the field where the porosity b has been computed.

In this embodiment, a statistical model of the field is created as discussed in connection with Figure 8 except that the read data have the three elements (, At, GR) in step 114, and that only two elements (A, GR) are used to compute a cell address in step (130). In step 132, two numbers are stored in each cell. As before a first number is incremented by one and is representative of the number n of data sets entered in the cell. A second number is incremented by the porosity value and is representative of the total 2:'P of the porosity values entered in the cell.When all the data have been processed the total or second number is divided by the first number in each cell to give the average value 2:/n so that the statistical model may be represented by a two dimensional memory of cells, each cell containing the average value of corresponding to a specific address (At, GR).

In order to determine values of the characteristic for each level of the defined borehole, data sets are formed from the defined borehole as discussed in connection with Figure 9 except that the data sets are abbreviated data sets including only two elements each, namely a sonic measurement At and a gamma ray measurement GR corresponding to the same level of the defined borehole. The following steps are the same as steps 138 to 154 of Figure 9 the only difference being that the data sets have only two elements such as in the above described method for reconstructing a missing log as opposed to the three elements of the data sets used in the method shown in Figure 9. After step 154 the data sets used in determining the characteristic are integer pairs.In the example given here each data set is scaled to an integer pair (X,Y) which is used to compute a cell address according to the expression C A = X + 50 Y The content ( average) of the cell whose address has been computed in the preceeding step is non-destructively read out and is taken as the value of the characteristic corresponding to the current abbreviated data set (At, GR) of the defined borehole. A return is made to the first step to read another two element data set. After this method has been repeated for all of the two element data sets from the defined borehole. the result is a list of values of the formation porosity (P level by level. These values may be recorded as a log of the computed porosity for the defined borehole as a function of depth.As previously discussed the statistical model of the field may be created with cells having addresses with three dimensions or more than three dimensions, the average of the characteristic value being computed for each cell. The abbreviated data sets then comprise the same number of elements as the number of dimensions in order to compute a cell address.

WHAT WE CLAIM IS: 1. Method of machine processing well logging data derived from borehole exploring devices which investigate earth formations traversed by boreholes, comprising: deriving a plurality of measurements related functionally to a respective plurality of different earth formation characteristics along borehole sections traversing earth forma- tions in a field: forming first data sets. each comprising a defined combination of said measurements; combining at least a defined portion of said first data sets to form a statistical model of the traversed earth formations: and combining second data sets derived from a borehole in the same field svith said statistical model to determine what modification of the second data sets may be necessary to bring them into a defined statistical conformity with the statistical model.

2. Method of machine processing well logging data as in Claim I wherein the forming step includes forming data sets each comprising measurements each of which is taken at a defined depth level in a borehole.

3. Method of machine processing well logging data as in Claim 2 wherein the forming step includes forming data sets each comprising measurements taken at the same depth level in a borehole.

**WARNING** end of DESC field may overlap start of CLMS **.

Claims (23)

**WARNING** start of CLMS field may overlap end of DESC **. example, the number of different logs which has been run in the borehole is too small. In anexample of this other technique it will be assumed that the characteristic to be derived in a defined borehole of the field is the formation porosity , and that a sonic log At and a gamma ray log GR are available in the defined borehole. In one or several other boreholes of the field the number of logs is sufficient to compute the porosity level by level by processing the well logging data according to a well known method such as the one described in French patent No. 2,102,380 (A. Poupon and R.Gaymard). lt will be remarked here that the characteristic to be determined in the defined borehole may have been derived in another borehole from sources other than well logs such as core analyses, test results or production data. The permeability of earth formations traversed by a borehole may have been derived, for example, from core analyses. The sonic and gamma ray logs are available in the boreholes of the field where the porosity b has been computed. In this embodiment, a statistical model of the field is created as discussed in connection with Figure 8 except that the read data have the three elements (, At, GR) in step 114, and that only two elements (A, GR) are used to compute a cell address in step (130). In step 132, two numbers are stored in each cell. As before a first number is incremented by one and is representative of the number n of data sets entered in the cell. A second number is incremented by the porosity value and is representative of the total 2:'P of the porosity values entered in the cell.When all the data have been processed the total or second number is divided by the first number in each cell to give the average value 2:/n so that the statistical model may be represented by a two dimensional memory of cells, each cell containing the average value of corresponding to a specific address (At, GR). In order to determine values of the characteristic for each level of the defined borehole, data sets are formed from the defined borehole as discussed in connection with Figure 9 except that the data sets are abbreviated data sets including only two elements each, namely a sonic measurement At and a gamma ray measurement GR corresponding to the same level of the defined borehole. The following steps are the same as steps 138 to 154 of Figure 9 the only difference being that the data sets have only two elements such as in the above described method for reconstructing a missing log as opposed to the three elements of the data sets used in the method shown in Figure 9. After step 154 the data sets used in determining the characteristic are integer pairs.In the example given here each data set is scaled to an integer pair (X,Y) which is used to compute a cell address according to the expression C A = X + 50 Y The content ( average) of the cell whose address has been computed in the preceeding step is non-destructively read out and is taken as the value of the characteristic corresponding to the current abbreviated data set (At, GR) of the defined borehole. A return is made to the first step to read another two element data set. After this method has been repeated for all of the two element data sets from the defined borehole. the result is a list of values of the formation porosity (P level by level. These values may be recorded as a log of the computed porosity for the defined borehole as a function of depth.As previously discussed the statistical model of the field may be created with cells having addresses with three dimensions or more than three dimensions, the average of the characteristic value being computed for each cell. The abbreviated data sets then comprise the same number of elements as the number of dimensions in order to compute a cell address. WHAT WE CLAIM IS:

1. Method of machine processing well logging data derived from borehole exploring devices which investigate earth formations traversed by boreholes, comprising: deriving a plurality of measurements related functionally to a respective plurality of different earth formation characteristics along borehole sections traversing earth forma- tions in a field: forming first data sets. each comprising a defined combination of said measurements; combining at least a defined portion of said first data sets to form a statistical model of the traversed earth formations: and combining second data sets derived from a borehole in the same field svith said statistical model to determine what modification of the second data sets may be necessary to bring them into a defined statistical conformity with the statistical model.

2. Method of machine processing well logging data as in Claim I wherein the forming step includes forming data sets each comprising measurements each of which is taken at a defined depth level in a borehole.

3. Method of machine processing well logging data as in Claim 2 wherein the forming step includes forming data sets each comprising measurements taken at the same depth level in a borehole.

4. Method of machine processing well logging data as in Claim 3 wherein the step of

combining the data sets to form a statistical model includes representing the statistical distribution of the number of occurrences of defined combinations of the plurality of measurements comprising a data set.

5. Method of machine processing well logging data as in Claim 4 wherein the step of combining the data sets to form a statistical model of the traversed earth formation includes: forming a multidimensional cell memory, with each dimension corresponding to a different one of the plurality of different measurements comprising a data set. and with each cell corresponding to a defined combination of the measurements comprising a data set: storing in each of the cells a count of the number of occurrences of the data sets comprising the combination of measurement corresponding to that cell to thereby represent the statistical distribution of the number of occurrences of data sets and to thus form 1 statistical model of the traversed earth formations.

6. Method of machine processing well logging data as in Claim 4 or 5 including integer scaling each of the measurements comprising a data set to convert the data sets to sets of integer numbers.

7. Method of machine processing well logging data as in Claim 4 to 6 including preliminary processing the data sets to improve the quality thereof.

8. Method of machine processing well logging data as in Claim 7 wherein the preliminary processing step includes applying a defined preliminary zero shift to at least one selected measurement of at least a selected plurality of data sets.

9. Method of machine processing well logging data as in Claim 7 or 8 wherein the preliminary-processing step includes preliminarily scaling by a defined factor of at least one of the measurements in the data sets.

10. Method of machine processing well logging data as in any of claims l to 9 wherein the step of combining second data sets with the statistical model includes forming second data sets from said borehole. each second data set coniprisinp the same defined combination of measurements as said first data sets: and combining said second data sets with said statistical model to determine a correction for recalibrating at least one of said measurements to bring the second data sets into the defined statistical conformity with the statistical model.

11. Method of machine processing well logging data as in Claims S and 10 wherein the step of combining data sets with the statistical model includes: providing a central accumulator and a plurality of side accumulators: for each second data set derived from said borehole in the same field. adding the contents of the memory cell corresponding to the combination of measurements comprising the second data set to the current contents of the central accumulator. adding the contents of each of a plurality of adjacent memory cells along a defined dimension to the current contents of a respectively positioned side accumulator: and determining the peak of a curve fitting a plot of the positions of said accumulators versus their contents, and determining the offset of said peak from the central accumulator to thereby obtain a measure of the correction for recalibrating to bring the last mentioned dati sets into the defined statistical conformity with the statistical model.

12. Method of machine processing well logging data as in claim 10 or 11 wherein the step of combining said second data sets include integer scaling of each of the measurements forming a second data set to form thereby a plurality of second data sets each comprising integer numbers.

13. Method of machine processing well logging data as in any one of claims 10 to 1' including preliminarily processing the second data sets prior to said combining step.

14. Method of machine processing well logging data as in claim 13 wherein the preliminary processing step includes selectively applying a defined zero shift and a defined scaling factor to at least one selected measurement in each of a defined plurality of second data sets.

15. Method of machine processing well logging data as in any one of claims l to 9 wherein the step of combining second data sets with the statistical model includes forming second data sets from said borehole. each second data set being an abbreviated data set comprising an abbreviated combination of said measurements of the first data sets less a missing measurement: and.

combining said second abbreviated data sets with said statistical model to generate for each of said second data sets a value of said missing measurement to reconstruct a missing log in said borehole.

16. Method of machine processing well logging data as in claim IS wherein the step of combining said abbreviated data sets includes. for each abbreviated data set defining a plurality of cells which correspond to the abbreviated combination of measurements in the abbreviated data set, and are along the dimension of the missing measurement; determining the cell with the highest contents; and, replacing the abbreviated data set with the data set corresponding to that cell having the highest contents, to thereby generate the missing measurement of that cell having the highest content as the value to reconstruct the log.

17. Method of machine processing well logging data as in claim 15 wherein the step of combining said first data sets to form a statistical model includes forming a functionally multidimensional cell memory with each dimension corresponding to a different one of the abbreviated combination of measurements included in a first data set, and with each cell corresponding to a defined abbreviated combination of the measurements included in a first data set; and storing in each of the cells a statistical optimum of the missing measurement for the data sets comprising the defined abbreviated combination of measurements corresponding to that cell to thereby form said statistical model.

18. Method of machine processing well logging data as in claim 17 wherein the combining step includes, for each second data set defining a cell which corresponds to the abbreviated combination of measurements in the statistical model; reading for said second data set the content of said corresponding cell to generate said value of the missing measurement to reconstruct the log.

19. Method of machine processing well logging data as in one of the claims 14 to 19 wherein said step of deriving a plurality of measurements comprises combining a plurality of well logging data along borehole sections traversing the earth formations for deriving at least one of said measurements.

20. Method of machine processing well logging data substantially as hereinbefore described with reference to Figures 1, 2 and 4 of the accompanying drawings.

21. Method of machine processing well logging data substantially as hereinbefore described with reference to Figures 1, 8 and 9 of the accompanying drawings.

22. Method of machine processing well logging data substantially as hereinbefore described with reference to Figures 1, 8 and 9, and modified substantially as hereinbefore described with reference to Figure 10, of the accompanying drawings.

23. Method of machine processing well logging data substantially as hereinbefore described with reference to Figures 1, 8 and 9. and modified substantially as hereinbefore described with reference to Figure 11, of the accompanying drawings.