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BACKGROUND OF THE INVENTION
This invention relates generally to improved methods and apparatus for
investigating subsurface earth formations traversed by a borehole, and
more particularly to an improved technique for processing formation
measurements to obtain displacements between measurements for use in
correlating logs.
It is often desirable to correlate or compare curve shapes of two or more
well logging curves which have been generated either during the same or
different traversals of the logging instrument through the same borehole
or, alternatively, during traversals through adjacent boreholes to locate
corresponding data points on the curves.
One example of the reason for this may be to check or compare a re-logging
of a well against a prior log of the same or different parameters to
insure that all measurements are on depth. Another example might be in
field studies where well-to-well depth correlations are desired. Yet
another example might be in the case of formation dip measurements wherein
a plurality of measurements are made during one borehole pass.
In the latter case, a logging instrument is provided having four movable
arms spaced ninety degrees apart in azimuth, each having a pad in contact
with the borehole wall which carries an electrode system for making a
shallow focused formation resistivity measurement.
Normally, the shapes of each logging curve measurement thus generated by
the pads are similar since they are measuring characteristics of portions
of the formation relatively adjacent one another.
However, due to such things as the logging sonde not always being oriented
perpendicular to formation beds (for example because the beds are inclined
relative to the sonde), although the shapes of each measurement may appear
similar, they may appear offset in depth. This is because one of the
measuring pads will reach the bed and thus generate a characteristic
signature prior to another pad.
As is well known in the art, the amount of such offsets in the pad signals
relative to one another provides valuable information about the amount and
direction of formation dip. Thus, once again it is necessary to find ways
to compare or correlate the logging curve shapes to determine the offsets.
Several methods have been attempted over the years to correlate two or more
logging curves. The oldest method was simply optical correlation by an
experienced individual whereby visual comparisons were simply made between
portions of the logs. While this method was often very reliable, it was
obviously extremely time consuming, particularly if high resolution was
desired or large depth intervals were involved, and moreover, the method
further depended upon the subjective human abilities of the particular
analyst.
Another group of methods known as "fixed interval correlation" utilized a
statistically defined cross-correlation coefficient in comparing
successive intervals of finite length on two measurement curves as a
measure of curve similarity.
Fixed interval correlation has also evidenced several difficiencies in log
analysis applications including insufficient depth resolution and
computational inefficiency inasmuch as a large number of computations was
required. The method was also particularly unsuited to formation dip
measurements exhibiting unreliability in complicated stratification, for
example, and loss of dip variations when smaller than the correlating
interval.
Moreover, this correlation interval was preset and thus not adapted
continuously to the current geological context, causing missed
correlations and limitations on resolutions. Still further, because the
dip calculations were attributed to an interval and not to the bedding,
only bulk directional properties over each particular interval were
described rather than the basic cause of correlation, e.g., bedding. Thus,
true correlations were often missed or high cross-correlation coeffients
were noted for curve features which did not correlate.
Still another log correlation method commonly referred to as
"point-to-point" correlation has been attempted. In this method, pattern
recognition or classificiation is employed whereby pattern vectors of each
curve to be correlated are analyzed against a "catalog" of standard
patterns.
However, although improvement in depth resolution may have been noted, this
method too has been found deficient particularly with formation dip
applications in its noise susceptibility, e.g., failure to distinguish
between regular and random features in data which result in excessive
scatter and gaps in formation dip determinations.
Accordingly, the present invention overcomes these and other deficiencies
of the prior art by providing an improved method and apparatus for
utilizing statistical and frequency distribution of the measurement data
to determine well log correlations.
SUMMARY OF THE INVENTION
A plurality of well logging curves to be correlated are generated, each
over a respective borehole interval. The data for each curve is
pre-processed in accordance with an algorithm whereby, for each curve, an
activity function is derived and a corresponding activity curve of the
following form as herein defined:
##EQU1##
An activity function noise level cutoff is empirically determined and all
maxima above the cutoff on each activity function are identified and
matched to depth-correlative data points on the corresponding logging
curve from which the respective activity function was derived.
All possible pairs of such data points meeting predetermined conditions are
then identified, wherein each data point of each pair corresponds to a
different logging curve, and wherein each such pair simultaneously
satisfies the constraints that: the difference in depth at which each
point of the pair was generated does not exceed a predetermined maximum;
the points of each pair are either both on the positively sloping portions
or both on the negatively sloping portions of their respective
corresponding logging curves; and the shapes of the corresponding sloping
portions of the logging curves including the points of each pair must be
"similar" as defined by a predetermined function of the activity function
values corresponding to the sloping portions and having the herein defined
form of A.sub.1 /A.sub.2 .ltoreq.F, A.sub.2 /A.sub.1.ltoreq.F.
Once all possible pairs of data points meeting the above-noted conditions
are matched for all two-curve combinations, for each pair of curves
selection of optimal point-to-point correlations or pairs from the
universe of all possible pairs is made by dynamic programming
optimization, wherein equations of the following form and herein defined
are solved:
##EQU2##
In a particular preferred embodiment of the invention, the plurality of
logging curves is comprised of a plurality of micro-resistivity
measurements each derived from a different respective pad of a dip meter
logging tool.
It is therefore an object of the present invention to provide an improved
method and apparatus for correlation of well logs.
It is another object of the present invention to provide an improved
point-to-point well logging correlation method and apparatus.
It is yet a further object of the present invention to employ a transform
function related to statistical and frequency distribution of logging
measurements to determine well logging correlation.
Still a further object of the present invention is to provide an improved
method and apparatus for detection of formation bedding plane dips.
Yet another object of the present invention is to provide an improved
automated formation dip analysis method and apparatus having improved
depth resolution, computational efficiency, noise immunity, and ratios of
correlations to sample intervals.
These and other objects and advantages of the present invention can be
understood from the following detailed description in conjunction with the
drawings wherein:
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a side elevational view, partly in cross-section, of a dip meter
logging system in accordance, with the present invention.
FIG. 2A depicts an illustrative pair of transform functions of the present
invention and their correlative logging curves.
FIG. 2B is a schematic depiction of an illustrative set of maximum possible
pairs of similar features.
FIG. 2C is a schematic depiction of an illustrative set of optimal
correlation pairs selected from the maximum possible pairs depicted in
FIG. 2B.
FIG. 3 illustrates the steps for producing activity transform functions
depicted in FIGS. 2A-C for the dip meter system of FIG. 1.
FIG. 4 illustrates the steps for determining the maximum possible matching
pairs of similar features on curve pairs depicted in FIG. 2B.
FIG. 5 illustrates the steps for selecting optimal correlation pairs of
FIG. 2C from the maximum possible pairs of FIG. 2B.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to the drawings in detail, particularly to FIG. 1, therein is
illustrated schematically a typical borehole surveying operation in which
a portion of the earth 10 is shown in vertical section. Well 11 penetrates
the earth's surface. Typical earth formations are illustrated by shale
formations 12 and 13 and intervening sand formation 14 having formation
interfaces 15 and 16. Disposed within well 11 is a formation surveying
instrument 17 commonly known as a dip meter tool. Dip meter tool 17
includes an elongated body member 18 having a plurality of arm members 19,
20, 21 and 22 disposed symmetrically about body member 18. Mounted on each
arm member 19-22 is a corresponding probe pad 23, 24, 25 and 26 for
contacting the sides of borehole 11 to obtain formation data. (In the view
of FIG. 1, arm member 22 and probe pad 26 are obscured from view by body
member 18, arm member 20 and probe pad 24.)
Each probe pad 23-26 includes an emitting electrode 27 for emitting
currents into the surrounding earth formations. Each probe pad 23-26 also
has a metal guard electrode 28 which encircles and is concentric with
emitting electrode 27. Emitting electrode 27 is electronically insulated
from guard electrode 28. Guard electrode 28 functions to insure that the
potential difference across the entire pad remains near zero so that
emitted current is focused into the formation.
The measured voltages and currents are processed by electronic circuitry
(not shown) located within body member 18. Also located within body member
18 is telemetry circuitry for transferring data between tool 17 and
surface processing circuitry 29. A more detailed description of various
techniques associated with the measurements herein discussed can be found
in the articles "The Micro Laterolog" and "The Laterolog" by H. G. Doll,
published in the Journal of Petroleum Technology in January 1953 and
November 1951, respectively, which are herein incorporated by reference.
Dip meter tool 17 is suspended in well 11 by multi-conductor cable 30 which
contains the required conductors for electrically connecting tool 17 with
surface processing circuits 29 through slip rings 31 located on the end of
drum 32. Cable 25 is wound or unwound from drum 32 in raising and lowering
tool 17 to traverse well 11. As tool 17 traverses well 11 the movement of
cable 30 is measured by a suitable measuring device and coupled to depth
indicator 33. The depth information from depth indicator 33 is coupled to
signal processing circuits 29 and recorder 34. Therefore, each sample of a
measured signal corresponds to one increment in depth and displacements
determined between such signals are indicative of depth displacements.
The elements of FIG. 1 are shown diagrammatically, and it is to be
understood that the associated circuits and power supplies are provided in
a conventional manner. It is also to be understood that the instrument
housing will be constructed to withstand the pressures, mechanical, and
thermal abuses encountered in logging a dip well and to provide adequate
space therewithin to house the necessary apparatus to conduct the
surveying operation. Further, while the tool of FIG. 1 is described as
having four movable arms spaced 90 degrees apart, the present invention is
not limited to any specific number of arms, or even the dip meter tool
depicted herein. The dip meter tool 17 has been depicted for convenience
because it simultaneously generates four resistivity logs 23A-26A whereby
the curve correlating features of the present invention may be described.
However, it is specifically contemplated that the correlating methods and
apparatus of the present invention may be adapted to two or more other
well logging curves.
On a well logging operation such as illustrated in FIG. 1, tool 17 is
caused to traverse well 11. Current is emitted from emitting electrode 27
located in each probe pad 23-26. Guard electrode 28 on each respective
probe pad 23-26 confines the emitted currents into the desired focused
pattern. Measured survey signals indicate changes in formation
characteristics adjacent each pad. The resultant survey signals are
processed in subsurface electronic circuitry and transmitted through
electrical conductors within cable 30, through slip rings 31, to signal
processing circuits 29 for processing. It should be recognized that the
signals can be processed at the well site or the signals may be
transmitted by a transmission system to a remote computer location for
processing. Additionally, the signals may be recorded on a suitable
recording medium, such as, for example, magnetic tape for later
processing.
The measurements from the dip meter tool 17 are useful in identification of
faults, cross bedding, said bars, reef, channels, deformation around salt
domes, and other structural anomalies, There are two basic sets of data
necessary for calculating dip angle and direction. These are at least
three points to establish a plane, and a system for determining the
orientation of the plane with respect to vertical and true north.
Referring still to FIG. 1, a brief description will be given of how this
data is derived within a borehole. Housed within body member 18 of FIG. 1
is an orientation section which continuously establishes the position of
tool 17 with respect to the vertical and to magnetic north. The azimuth or
direction of pad 23 is measured by a magnetic compass 40. Attached
directly to compass 40 is the wiper arm of a potentiometer. Relative
movement of the compass needle due to rotation of tool 17 varies the
measured resistance of the potentiometer. The resistance of the
potentiometer is directly related to the azimuth of the number one probe
pad. A gimbal type suspension system supports the compass assembly 40,
thereby allowing the compass needle to remain in a horizontal plane to
permit accurate orientation measurements to be made in deviated wells.
This azimuth information signal 40A is delivered uphole on cable 30.
Deviation of tool 17 from vertical is also continuously measured. Tool 17
utilizes a weighted pendulum system 41 suspended on swivel pivots and
allowed to hang vertically. When tool 17 deviates from vertical pendulum
41 varies the resistance of a potentiometer. Changes in the resistance of
the potentiometer are calibrated to indicate the magnitude of deivation of
tool 17. Derivation signal 41A is also sent uphole on cable 30.
The direction of deviation from vertical of tool 17 is measured by pendulum
system 42 which continuously aligns itself in a vertical plane passing
through the well. Pendulum system 42 is connected to the wiper arm of a
360 degree potentiometer. Movement of pendulum system 42 changes the
resistance of the potentiometer, indicating on a calibrated scale the
angle of deviation with respect to the number one probe pad. Since the
orientation of pad 23 is continuously measured as described previously,
the azimuth of deviation is easily determined.
The systems described to measure tool 17 position within the well utilize
low torque potentiometers. Each device is extremely sensitive to slight
changes in the position of tool 17, yet is constructed to withstand the
severe abuse encountered in well surveying operations. Further details as
to how to obtain and use the reference measurements may be found in the
article "Automatic Computation of Dipmeter Logs Digitally Recorded on
Magnetic Tape" by J. H. Mercer, et al and published in the July 1962 issue
of the Journal of Petroleum Technology, which is incorporated herein by
reference.
Still referring to FIG. 1, therein are illustrated the four probe pads
23-26 of tool 17. Probe pads 23-26 are in a radially spaced apart
symmetrical relationship and placed in a common plane perpendicular to the
longitudinal axis of tool 17. As tool 17 traverses up the well 11, the
four probe pads trace a path along the borehole wall. These pads 25, 26,
24, 23 will intersect the formation bedding plane 16 on the borehole wall
respectively at the four elevational locations indicated at x, y, y and z,
corresponding to probe pads 25, 26, 24, 23, respectively. As indicated,
the mechanical arm assembly assures that the pad paths are located on
opposite sides of the borehole for each diagonally opposing pair of pads.
The signal response for each of probe pads 23-26 is illustrated by
correlation curves 23A, 24A, 25A, and 26A as the tool 17 traverses up the
borehole 11. These signals from each pad 23-26 are transmitted to the
surface on cable 30 as signals 23A-26A, respectively. The change in the
character of correlation curves 23A, 24A, 26A, 25A, indicated by
respective inflection points z, y, y and x correspond to depths at which
formation bedding plane 16 intersects well 11. As illustrated, as tool 17
travels up well 11 probe pad 25 intersects formation bedding plane 16
first at x resulting in a change in the measured signal response, shown at
x of correlation curve 25A. Similarly, probe pad numbers 24 and 26 next
intersect formation bedding plane at y resulting in a change in the
measured signal response for pads 24 and 26, shown as Y on respective
correlation curves 24A and 26A.
As tool 17 continues to move upward in well 11 pad 23 intersects formation
bedding plane 16 at point z, being indicated by a change in the measured
signal response for pad 23, shown as Z on correlation curve 23A. It should
be recognized that correlation curves 23A-26A can be used to determine
displacement between the points of intersection of the formation bedding
plane 16 along the wall of well 11. Thus, displacement may be determined
for pads 23A and 24A or 26A using points A and Y of correlation curves 23A
and 24A or 26A, for pads 23A and 25A using points Z and X of correlation
curves 23A and 25A, respectively and so on.
In addition to the displacement between signal responses, the radial
distance between the measure points on probe pads must be determined. The
radial distances are measured independently between opposing pad pairs 23
and 25, and 24 and 26 by a borehole caliper circuit, shown at 43. This
circuit transmits uphole as signal 43A the caliper measurement signal 43B
from the caliper in tool 17 connected to arms 19-22. It is known that the
position of any three points provide the definition of a plane penetrated
by a borehole. Any two related displacements from a pad and the
corresponding diameters thus define the three points and can be used to
determine dip and azimuth values. A more detailed description of the
determination of dip and azimuth values can be found in U.S. Pat. No.
4,303,975 by V. R. Heep which is incorporated herein by reference.
From the foregoing it will be appreciated that at least two logging data
curves have been generated, and in accordance with the present invention
it is now desired to compare shapes of the curves to determine
displacement. For illustrative purposes and simplicity, curves 23A and 25A
will be utilized having corresponding peaks z and x, respectively, which
correspond to differing elevations Z and X within borehole 11 where
formation bedding 16 intersects borehole 11. It will also be noted from
the preceeding discussion that the elevational distance .DELTA. between
these points Z and X will be proportional to the distance .DELTA.
separating the corresponding peaks Z and X on respective pad signals 23A
and 25A.
Referring now to FIG. 2A, there will be seen depicted therein
micro-resistivity pad signals or "logging curves" 23A and 25A with
corresponding peaks Z and X indicated thereon. Additionally, peaks M and N
have been indicated on curves 23A and 25A corresponding to the additional
bedding interface 15 of FIG. 1. The purpose for these additional peaks is
to illustrate that in the depth correlation of logs there are many points
which may be correlated in that the entire curve shapes will be generally
similar.
It is thus desired as part of the subject invention to identify as many
matched data pairs such as Z-X and M-N on respective curves such as 23A
and 25A as possible. As indicated in the background of the invention these
pairs will ideally thus correspond to the true correlative data points
generated at the same borehole elevations in the case of two repeat logs
through the same borehole. This information can then be used to make
depths of the two logs correspond.
Alternatively, in the case of the dip meter measurement presently being
described, the distance such as .DELTA. between the two correlation pairs
such as X minus Z is valuable information directly indicative of formation
dip.
Moreover, in explaining the present invention, reference will be made to
correlating only two curves for simplicity. However, particularly in view
of the fact that generation of four curves has been described already, it
should be readily apparent that it is contemplated that the methods to be
carried out would be applicable to all combinations of curves desired to
be correlated such as the four micro-resistivity curves of the dip meter
measurement.
In what follows, reference will be made first to FIGS. 2A-2C for a general
graphical and intuitive description and explanation of the present
invention, followed thereafter by more detailed representative and
illustrative flow diagrams of FIGS. 3-5 implementable by a digital
computer in a conventional manner.
The method of the present invention whereby optimally correlated, matched
data pairs are identified between all combinations of curves to be
correlated can best be described in two stages: first the selection of all
possible and feasible points on curves 23A and 25A which may be candidates
for pair matchings (signifying possible depth correlation between the two
points of each pair); second, the selection of the actual optimally
correlated data pairs from the universe of all possible feasible pairs.
Taking first the selection of all possible pairs and still referring to
FIG. 2A, at first one seemingly rational scheme for picking distinctive
points on curves 23A and 25A for comparison might be the derivatives of
each curve (which would indicate distinctive, unique inflection points).
However, in practice the simple derivative is not suitable because it will
give large values even for low amplitude noise.
Referring still to FIG. 2A, there will be seen two additional curves 23B
and 25B corresponding respectively to logs 23A and 25A. Each curve is a
function of its respective log and will be referred to as the "activity"
function defined by:
##EQU3##
where A(d) is the "activity" of the log signal at depth d;
r(i+d) is the logging signal at depth i+d
r(d) is the signals arithmetic average of the log over N samples at depth
d, or
##EQU4##
i+d indicates N samples at depth d, half of them higher and half of them
lower at this depth; and
K is a normalization coefficient.
In the preferred embodiment N is selected to be from 7 to 11 measurement
points with 9 having been found preferable in many instances. Also, with
respect to dip meter measurements, it is typical to have a data sampling
rate of 64 samples per foot.
The activity function, behaving as a filter or pre-processing function
rather than acting upon discrete points as in the derivative, has the
property that, unlike with the derivative, a smoothing effect is exhibited
with low values resulting for low amplitude noise. Activity maximums may
be used for characteristic log points for correlation and, in fact, will
indicate characteristic points of bed boundaries on microresistivity
readings. Moreover, by selecting an established noise cutoff level based
upon an entire class of logs such as micro-resistivity logs, for example,
activity maxima levels falling below this level, which indicate no
significant information was recorded, are disregarded.
Thus, referring to FIG. 2A again, it will be seen that each activity maxima
establishes a characteristic point on its corresponding original log
(designated by a cross) with maxima below the noise level (not shown)
being disregarded. These crosses will thus indicate all possible
point-to-point matches, in accordance with the activity function criteria,
on the two log curves 23A and 25A which may be correlated.
In theory, any crossed point on curve 23A could correspond to any crossed
point on 25A, the total number of such corresponding matches equally the
product of the number of crosses on each curve. Intuitively, it will be
noted that it is necessary to apply some criteria in addition to the
activity function to reduce this total number of characteristic points to
a more manageable portion implementable efficiently on a computer for
picking final correlation point pairs.
Fortunately, three such constraints exist to reduce the number of possible
matches considerably. The first of these is that the difference in the
depths at which two correlation points on two curves were derived must not
be greater than a given maximum for the given logs. This constraint
corresponds physically to the fact that there will be a maximum expected
separation in borehole elevation such as .DELTA. of FIG. 1 between two
correlating points which may be the maximum expected dip angle in the area
and referred to as the search limit.
The second criteria is that for a point on each of two curves to be
considered a potentially correlated pair, both points must lie on
respective curve segments having the same slope and sign, e.g., either
positive or negative.
The third criteria is that for a point in each of two curves to still be
considered a potentially correlating pair, the curve segments on which
each point lie must have a similar "shape" to be hereinafter defined.
Referring now to FIG. 2B, the significance of the preceding criteria may be
seen graphically. Depicted therein are the curves 23A, B, and 25A, B of
FIG. 2A, with all potentially correlating crossed point-pairs on curves
23A and 25A which meet the foregoing criteria being interconnected by a
straight line.
Referring to points 71 and 72 for the moment, it can be seen, for example,
why line 70 (which was drawn in only for illustrative purposes) might not
properly appear due to the criteria.
First, in accordance with the first criteria, the vertical distance
represented by line 73 may exceed the corresponding maximum expected dip
angle in the area where the two logs 23A and 25A were derived.
Next, in accordance with the second criteria, it will be noted that points
71 and 72 lie on portions of curves 23A and 25A, respectively, having
different slopes, violating this criteria.
In accordance with the third criteria, the points 71 and 72 are not
situated on slopes of curves having similar shapes and thus, even
intuitively, should not be candidates for a match. It should be noted that
if any one of the above criteria is not met with respect to a potential
point pair, the pair is rejected and not shown interconnected with the
line. Thus, it will be appreciated that a significant reduction is
possible in the number of potential matches from the total of AxB (wherein
A and B are the number of crossed points respectively in curves 23A and
25A) to a number which, in the case of dip meter logs, for example, is
often found to be in practice a reduction by a factor of 1/10.
With reference to the third criteria, further detail is required. Whereas
the first two criteria are numerically definable, the third, at least
initially, does not appear so in that the criteria requires a seemingly
subjective condition, e.g., "similarity" of two slope segments containing
the matched pair candidate. However, it has been found that each slope
within the vicinity of the respective candidate-point has primarily only
steepness (or "gradient") and width. Since the slope characteristics are
adequately represented by the activity function (which is a function of
gradient and width), the activity function at these points may be used to
express the third criteria of "shape" numerically. Thus, two slopes in the
vicinity of two corresponding selected points on two corresponding curves
are "similar in shape" if their respective activity function values do not
differ by more than a predetermined amount, or:
A.sub.1 /A.sub.2 .gtoreq.F
A.sub.2 /A.sub.1 .gtoreq.F
where F is a parameter predetermined for each class of logs which controls
maximum allowable curve dissimilarity and is found to be four in the case
of diplogs; and wherein A1, A2 are activity values for the selected points
being tested on the first and second slopes.
Once, as indicated in FIG. 2B, all possible paired point-to-point matches
are selected by derivation and application of the activity functions, and
then (in accordance with the three criteria reduced) the number of
possible correlation pair-points is reduced, the second stage of the
present invention is then applied wherein the final selection of the
actual optimally correlated paired-points is made as shown in FIG. 2C.
Thus, referring now to FIG. 2C in comparison to FIG. 2B, several things may
be noted. First, FIG. 2C is a graphical representation of the actual point
pairs (selected from the universe of possibly correlating pairs depicted
in FIG. 2B) which have been optimally correlated in accordance with the
method of the present invention depicted in the flow diagram of FIG. 5.
Each such pair is interconnected by a line which has a counterpart line in
FIG. 2B.
It can be seen that the number of such point pairs has been substantially
reduced from those shown in FIG. 2B. Also, it will be noted that unlike in
FIG. 2B wherein lines connecting possible correlating point pairs cross,
there is no such line crossing in FIG. 2C. This corresponds to the | | |
