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Claims  |
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What is claimed as new and useful is:
1. A method for locating and characterizing subterranean layers comprising
the steps of:
a. detecting at several locations on the earth's surface a first set of
outputs which are proportional to the amplitudes of the reflected seismic
waves generated by a combined seismic wave and electrical current source
while simultaneously detecting at the same locations a second set of
outputs proportional to the voltage induced in the ground by the current
produced at the seismic wave and electrical current source, and while
simultaneously recording the pilot voltage used to generate the seismic
and electrical current pulses, at the combined source, said pilot voltage
being identical in form and proportional to both the source's seismic
pulse and the source's electrical pulse;
b. processing in a multi channel cross-correlator the pilot voltage and the
first and second set of outputs using the pilot voltage as the noise free
reference signal, so as to obtain accurate values for the seismic wave
arrival times, the amplitudes of these seismic arrivals and accurate
values of the induced voltages and the relative time delays of these
voltages;
c. computer processing the outputs of the cross-correlator which contain
the reflection arrival times to obtain the seismic velocity V.sub.n for
all layers by automatically solving the equation
##EQU17##
in which t.sub.n (0) and t.sub.n.sub.-1 (0) are respectively the arrival
time at x = 0 from the bottom and top of the nth layer and in which
.DELTA.t.sub.n and .DELTA.t.sub.n.sub.-1 are respectively the difference
in arrival time between x=0 and x=x for the reflection from the bottom and
the top of the nth layer, the variable x in said equation being known and
input to the computer;
d. computer processing of the outputs of the cross-correlator which contain
the induced voltage values to obtain for all layers the value of bulk rock
resistivity, .rho..sub.r, determined from the n-layer equivalent of the
half space solution
##EQU18##
in which .DELTA..mu. is the potential difference created by the injection
of current I as measured between electrodes located at distances x.sub.n
and x.sub.n.sub.+1 from the surface current pole, said values of
.rho..sub.r being those which best bring into accord in the least squares
sense the seismically determined sequence of layers, .SIGMA.h.sub.n, given
by
##EQU19##
where the quantities are those defined in step c, and the measured induced
voltage values, this accord being brought about by the fact that there is
only one sequence of .rho..sub.r values possible for the measured induced
voltages once the sequence of thicknesses has been seismically
established;
e. computer processing the values of layer resistivity, .rho..sub.r, in
conjunction with values of layer seismic velocity, V, to determine the
pore fluid resitivity, .rho..sub.w, through solution of the relation
##EQU20##
in which a and b are constants determined for the area undergoing
exploration.
2. The method of claim 1 in which step (a) comprises detecting at several
locations on the earth's surface as a first set of output functions of
time the amplitudes of reflected seismic waves generated by a remote
combined seismic wave and electrical current source while simultaneously
detecting as a second set of output functions of time the voltage induced
at various distances by an electrical current waveform which differs from
the source's seismic waveform only in terms of its time base, and while
detecting and storing as a third output function of time the pilot voltage
which is identical in form and proportional to the seismic pulse produced
by the source and which differs from the source's current waveform only in
terms of its time base; and in which step (6) of claim 11 comprises
generating a fourth set of functions of time by altering the time base of
the second set of functions of time until the frequencies present in the
voltage induced by the current source are identical with those contained
in the third function of time and correlating as described in step (b) of
claim (11) the third function of time with the first and fourth set of
functions in such a way as to obtain accurate values of the seismic wave
arrival times and the amplitudes of these arrivals and accurate values of
the voltages and the relative time delays of these induced voltages.
3. The method of claim 1 where in values of pore fluid resistivity are used
in conjunction with values of equivalent salinity, obtained from bore hole
samples, to determine by means of the equation presented in claim 5 the
temperature of the fluid saturating each layer.
4. The method of claim 1 wherein values of pore fluid resistivity obtained
are used in conjunction with temperature values determined from surface
temperature, T.sub.s, heat flow, Q, and seismic velocity, V.sub.k, values
using the relation
##EQU21##
in which .DELTA.Z.sub.k is the thickness of the layer having seismic
velocity V.sub.k, and in which K.sub.w and K.sub.ma are respectively the
thermal conductivity of the fluid phase and rock matrix respectively, and
in which .DELTA.t.sub.w and .DELTA.t.sub.ma are respectively the interval
time for the fluid phase and rock matrix, to determine the equivalent
salinity of the fluids saturating all layers through solution of the
equation
##EQU22##
in which M is the molecular weight of the dissociated salt, .beta. is its
degree of dissociation, u.sub.a.sbsb.1.sbsb.8 and u.sub.c.sbsb.1.sbsb.8
are the ionic mobilities at 18.degree. C for the anions and cations
respectively, .alpha. is a coefficient which takes on the value 0.025 for
most electrolytes, T is temperature in degrees Centigrade, and .rho..sub.w
is the pore fluid resistivity in ohm-meters.
5. The method of claim 1 wherein the values of layer resistivity
.rho..sub.r and layer pore fluid resistivity .rho..sub.w are used to
compute the porosity, .phi., for each layer through solution of the
relation
.rho..sub.r = k.rho..sub.w .phi..sup..sup.-m
in which k and m are constants for the area undergoing exploration.
6. The method of claim 1 wherein the values of layer seismic velocity, V,
obtained are used to compute the porosities of the individual layers or
zones by use of the relation
##EQU23##
in which .phi. is the porosity, V.sub.w and V.sub.ma are respectively the
seismic velocity in the fluid phase and in the solid matrix phase and in
which c is a correction factor to be applied in areas of under-compaction.
7. The method of claim 1 in which the receive transducers consist of a
seismometer and potential measuring electrode housed in a common
container.
8. The method of claim 1 in which the seismic energy source and the
electrical current source are housed in a common container.
9. The method of claim 1 in which the amplitude and sign of reflected
arrivals are used to verify the distribution of velocity as a function of
distance in accordance with the equation
##EQU24##
where d.sub.n.sub.-1 V.sub.n.sub.-1 is the acoustic impedance on the side
of the boundary nearest the source and d.sub.n V.sub.n is the acoustic
impedance on the far side of the boundary and where A.sub.r is the
amplitude of the reflected seismic wave and A.sub.i is the amplitude of
the incident seismic wave. |
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Claims  |
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Description  |
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DESCRIPTION OF THE INVENTION
The invention relates to a geophysical method for determining remotely the
resistivity and equivalent salinity of fluids saturating the subsurface
pore space and in addition determining the quantity of pore space present.
More particularly, the invention relates to the processing in combination
of seismic velocity values and electrical resistivity values these values
being measured remotely. The unique processing of these remotely measured
velocity and resistivity values which forms the substance of the invention
provides realistic estimates of the resistivity and equivalent salinity of
the fluid saturating the pore space and the percentage of pore space as
functions of distance from the remote position of measurement.
The method described finds wide application in the study of groundwater and
is particularly useful for delineating geothermal reservoirs. The salinity
of groundwater within a geothermal province changes laterally only
gradually, therefore localized changes in groundwater resistivity
detectable by means of this invention are caused principally by changes in
reservoir temperature.
The functioning of the invention is postulated on remote detection of the
distance to interfaces separating zones of differing acoustic impedance,
the remote determination of the seismic velocities within these zones and
the remote determination of the electrical resistivity of these zones.
The reflection seismic method of geophysical prospecting remotely
determines the distance to interfaces separating zones having differing
acoustic impedance, where the acoustic impedance, dV, is the product of
the density, d, and the seismic wave velocity, V. This is accomplished by
measuring the distribution in time, t, and space, x, of the seismic energy
reflected from the interfaces separating zones having differing acoustic
impedance.
The electrical resistivity method of prospecting in which an expanding
electrode array is employed is able to remotely determine resistivity as a
function of distance from the point of observation. This is accomplished
by measuring the distribution in space, x, of the voltage differences,
.DELTA..nu., caused by the remote injection of electrical current, I.
Although this invention is not limited to the utilization of this manner
of obtaining resistivity as a function of distance from the remote point
of observation, its functioning is most easily explained by making
reference to an expanding electrode array technique.
It is therefore an object of this invention to detect and process seismic
wave arrival times and voltage differences in such a way as to obtain an
estimate of the resistivity and equivalent salinity of the fluid
saturating the ground at a position remote from the point of measurement.
A still further object is to provide an estimate of the available pore
spaces at points remote from the point of observation. These and further
objects of this invention will become apparent or be described as the
description thereof herein proceeds and reference is made to the
accompanying drawings in which:
FIG. 1 shows the arrival time curves (t vs. x) for reflected seismic energy
arriving from interfaces separating zones of differing acoustic impedance.
Said curves are plotted as a function of distance, x, along the ground
surface measured from the point of origin of the seismic wave.
FIG. 2 shows apparent resistivity, .rho..sub.a, variation as a function of
distance, x, measured from the source of injected current, I. For the
pole-dipole configuration used in this description the apparent
resistivity, .rho..sub.a, is defined by the equation
##EQU1##
in which .DELTA..nu. is the potential difference between electrodes
located at distances x.sub.n and x.sub.n.sub.+1 as measured from the
surface pole. .rho..sub.a is presented in the dimensionless form
.rho..sub.a /.rho..sub.l where .rho..sub.l is the value of .rho..sub.a at
small x.
FIG. 3 shows an accepted empirical relation between porosity and the ratio,
.rho..sub.r /.rho..sub.w, of the bulk rock resistivity to the saturating
groundwater resistivity. This ratio is called the Formation Factor.
FIG. 4 shows an accepted empirical relation between seismic velocity and
rock porosity.
FIG. 5 shows an accepted empirical relation between the ratio, .rho..sub.r
/.rho..sub.w, of the bulk rock resistivity to the saturating groundwater
resistivity and the seismic wave velocity.
FIG. 6 shows schematically the combined electrical current and seismic wave
source required to practice this invention. Also shown is the disposition
of the combined electrical voltage and seismic wave receivers used in the
practice of this invention.
FIG. 7 shows in greater detail the nature of the combined source and
combined receivers. A sectional view of a combined receiver is also shown.
FIG. 8 shows the waveform generated at the source and the waveforms at the
receiver locations. Also shown are correlograms obtained from these
waveforms.
FIG. 9 illustrates the overall functioning of the proposed geothermal
exploration method utilizing electrical resistivity and seismic velocity.
FIG. 10 shows the structure and circuitry of a possible combined electrical
current and seismic wave source.
FIG. 11 depicts a possible pilot voltage source.
FIG. 12 indicates the preferred method of signal processing.
Concerning the theory of operation of the invention, reference is made to
FIGS. 1 and 2 which depict the two events that are occurring
simulataneously at the source. FIG. 1 shows seismic ray paths 11 being
reflected from interfaces 12 and 42 between layers having differing
acoustic impedance. The rays are normal to the expanding wave fronts 13.
FIG. 2 shows current flow lines 14 and their refraction on entering layers
of differing bulk rock resistivities. This refraction influences the
geometry of the electrical potential lines 15 which are normal to the
current lines. The functioning of the invention can be made clear by
indicating how the method of this invention determines the resistivity of
the fluid saturating an arbitrary layer such as layer 40 depicted in FIGS.
1 and 2. In addition it will become clear how the porosity of layer 40 is
estimated. The upper portion of FIG. 1 shows travel time curves 16 for the
seismic arrivals reflected from the interfaces 12 and 42. These travel
times curves represent the numerical solution obtained by numerically
fitting the detected arrival times 17 with the equation
##EQU2##
in which V.sub.n is the seismic wave velocity in layer 40, t.sub.n (0) is
the arrival time at x = 0 of the reflection from interface 42 and
t.sub.n.sub.-1 (0) is the arrival time at x = 0 of the reflection from
interface 12. .DELTA.t.sub.n and .DELTA.t.sub.n.sub.-1 are the incremental
increases in time of arrival of the reflections from interface 12 and
interface 42 observed a distance x from the point x = 0. Slightly more
complex equations can be derived for the case in which the reflectors do
not parallel the upper surface. The important observation is that by
detecting the arrival times of reflected events at the surface, an
estimate of the seismic wave velocity in the interval between points of
reflection can be made for any and all layers.
The upper portion of FIG. 2 shows a theoretical curve 18 for apparent
resistivity, .rho..sub.a, divided by the resistivity of the first layer,
.rho..sub.1, versus distance x. The value of x at which .rho..sub.a
.rho..sub.l values are plotted is given by the quantity (x.sub.n +
x.sub.n.sub.+l 14 where x.sub.n.sub.+l - x.sub.n is the constant distance
between adjacent potential measuring electrodes. This is the type of curve
one obtains for an electrode configuration (pole-dipole) such as that
shown in FIG. 6. For this configuration
##EQU3##
The change in .rho..sub.a /.rho..sub.l as a function of x is brought about
by the fact that the more distant electrodes are being affected by current
which has passed through deeper more resistive layers. If all layers had
the same resistivity the curve would be the straight line defined by
.rho..sub.a /.rho..sub.l = 1. For the case shown the resistivity of the
second layer is twice that of the uppermost layer as indicated by the
plateau in the .rho..sub.a /.rho..sub.l curve at a value of 2 for
intermediate values of x. An equation can be written for the curve
.rho..sub.a /.rho..sub.l versus x for the n-layer case; however, for the
purpose of demonstrating the utility of this invention, it is sufficient
to state that values of the resistivity for the individual layers can be
determined uniquely from the theoretical solution which best fits detected
voltage differences. A preferred method of processing is to use the
seismic reflection input to determine the location of the major interfaces
separating zones having markedly different seismic velocities. Having thus
determined the thicknesses of the major zones, the preferred method uses
these thicknesses in a theoretical resistivity model and adjusts the
resistivities within these seismically determined zones until a "best"
fit, in the least squares sense, is obtained between the resistivity model
and the measured voltage differences.
It should be clear that the success of the invention is contingent upon
obtaining accurate values of seismic reflection arrival times and accurate
values of the voltages which result from the injection of current. In
addition the amplitude and sign of the reflected seismic wave relative to
the incident seismic wave is of interest for it to provide a check on the
distribution of velocity as a function of distance. The ratio of the
amplitude of the reflected energy to the incident must at normal incidence
obey the relation
##EQU4##
where d.sub.n.sub.-l V.sub.n.sub.-l is the acoustic impedance on the side
of the boundary nearest the source and d.sub.n V.sub.n is the acoustic
impedance on the far side of the boundary. In practice density changes are
no more than about .+-.10 percent while seismic velocity may change by
.+-.50 percent. The A.sub.r /A.sub.i ratio can therefore be related to
change in seismic velocity.
In order to accurately obtain these quantities the field arrangement shown
in FIG. 6 is employed and the data recorded on magnetic tape in such a way
that the tape's output will appear as shown in FIG. 8. In FIG. 6, 20
represents the combined seismic wave and electric potential receivers and
36 the distant electrode needed to complete the current injection circuit.
Wires 37 connect the distant electrode 36 to the current source portion of
the combined seismic wave and electrical current source 19. The current
source portion is also connected to the electric pole 38 which is in the
form of a base plate which is placed under vibrator 39 as shown in FIG. 7.
In FIGS. 6 and 7, 19 is an acoustic vibrator similar to that used in
conventional seismic prospecting with the exception that this vibrator not
only provides the seismic input but also acts as a source of electrical
current and 20 represents the combined seismic wave and earth voltage
receivers.
A conventional seismic vibrator consists of a pilot-voltage actuated
electromagnetic driver unit which is activated by electrical current
derived from a pilot voltage that may be obtained from magnetic tape. The
movement of the electromagnetic driver unit operates a hydraulic pilot
valve. The hydraulic pilot valve's function is to control oil flow which
actuates a hydraulic power valve which in turn modulates and controls flow
to the main hydraulic actuator of the vibrator. A motor driven hydraulic
pump is usually required to supply basic hydraulic power. A typical
hydraulic system might consist of a 500 hp motor driving a pump which
delivers 200 gal/min at 3,000 psi. A hydraulic vibrator of the type
described produces an acoustic output which can be essentially identical
in form to the form of the pilot voltage.
Other types of vibrators can be used to practice this invention. For
example an electromagnetic vibrator or an electroviscous vibrator as
exemplified by U.S. patent to Harold K. Chaney and Halvor T. Strandrud,
U.S. Pat. No. 3,416,549 may be used. Both these vibrator types require a
pilot voltage and produce an acoustic output that is essentially identical
in form to the form of the pilot voltage. FIG. 10 shows schematically the
preferred workings of novel combined seismic wave and electrical current
source 19. Pilot voltage and current source 41 provides electrical current
via wires 86 and 87 to the electromagnetic driver unit 55 consisting of
moving coil 56 and magnetic field producing means 57. Moving coil 56
produces a force which if necessary can be hydraulically amplified by
conventional hydraulic amplifier 58 and applied to base plate 38. This
force is proportional to the magnitude of the current flowing through the
electromagnetic driver and has a direction dependent upon the direction of
this current flow.
After passing through the electromagnetic driver unit 55 the current
returns to pilot voltage and current source 41 by passing through base
plate 38, through earth layers 39, 40 etc., through distant electrode 36
and through wire 37. One skilled in the art of geophysical prospecting
will recognize that the combined source 19 just described when developed
as depicted in FIG. 6 can serve as a point source of identical electrical
current and seismic energy.
The selection of the vibrator type is dependent on the allowable level of
distortion, the desired magnitude of force and range of frequency
required. In the case of hydraulic and electroviscous vibrators the pilot
voltage or current produces a force which is then amplified by hydraulic
means, 58.
The operation of the combined source has been described in terms of a
series circuit. Simultaneous excitation can also be accomplished by
operating the electromagnetic driver in parallel with the current source.
This can be brought about as shown in FIG. 10 by changing switches 59 and
59'. Parallel circuit operation is preferred when time base translation of
the injected current is desired.
FIG. 7 shows in cross section a preferred cylindrically shaped receiver.
This receiver consists of a moving coil seismometer 21 affixed atop a
ceramic electrode similar to those presently used in electrical
prospecting. The receiver 20 is implanted in moist ground 22 in such a way
that the conductive salt solution 23 can make contact with the ground
through the porous ceramic container 24. The metal electrode 25 is in
contact with salt solution 23 and forms a reversible electrode with
respect to this salt solution. Excess salt 26 is often provided to
solution 23 in order to assure electrical stability. The electrical output
from the seismometer portion 21 is provided by means of wires 27. The
earth voltage can be assumed to be that of metal electrode 25 and is
monitored by means of wire 28. Insulators 29 provide the necessary
electrical isolation between the seismometer portion of the receiver and
the earth potential monitoring portion.
At the combined seismic wave and electrical current source 19 a pilot
voltage derived from magnetic tape is used to produce the seismic and
electrical pulse and is identical in form and proportional to the
transmitted seismic pulse and to the transmitted electrical current pulse.
This pilot voltage is indicated by the uppermost trace 30 in FIG. 8. As
will be noted, the voltage time histories 31 associated with the injected
current all begin inphase with (at the same time as) the pilot voltage.
Cross-correlation of the pilot signal with the measured voltages provides
a realistic estimate of the amplitude of the voltage due solely to the
injected electrical current. In some instances a delay will be experienced
in the build up of the voltage associated with the injection of current.
The magnitude of this delay can also be determined through
cross-correlation of the pilot signal with the received voltage wave
forms. All earth potential time histories shown in FIG. 8 are measured at
various values of x and are values relative to an arbitrary receiver such
as 20. The value of the reference potential has no effect on the solution
of equation (2). Because reflected seismic energy overlaps, the time
histories 32 of the reflected energy form complicated interference
patterns. Prior art teaches the use of cross-correlation to determine the
amplitude and time of arrival (phase) of reflected seismic pulses. This
art does not anticipate, however, the combined processing of electrical
and seismic data. The right hand portion of FIG. 8 shows schematically the
nature of the correlograms 33 and 34 obtained from this cross-correlation.
It will be shown by discussion of FIG. 12 that correlograms 33 provide a
best estimate of the time of occurrence, amplitude and sign of the needed
electrical voltages and that correlograms 34 provide similar estimates for
reflected seismic arrivals 28. It will also become clear that these values
can be used to automatically determine the seismic velocity and the bulk
rock resistivity within any interval bounded by zones having markedly
different acoustic impedance and electrical bulk rock resistivity. The
term bulk rock resistivity is used to distinguish same from the
resistivity of the groundwater which saturates the interval in question.
Although the preferred method of executing the intent of this invention is
accomplished through simultaneous and coincident application of seismic
and electrical current pulses of identical time domain waveform, in some
applications it is preferable to employ seismic and electrical current
pulses of differing frequency content. When simultaneous pulses of
identical waveform are used, the frequency range contained within the
pulses extends from approximately 1 to 1,000 Hertz. Pulses of differing
frequency content are most often required when the resistivity of the
groundwater which saturates the pores is low and the porosity is high. For
such an environment, high frequency electrical current tends to be largely
confined to the near surface. This effect is often called the "skin
effect". If a sufficiently low frequency is used this effect can, for all
practical purposes, be eliminated. In the practice of this invention the
necessary low frequency current pulse is generated by using as a pilot
voltage for this current pulse a recording of the pilot voltage used to
generate the seismic pulse. This recording is played at some fraction of
the speed at which it was recorded by time base translator 43 (see FIG.
9). Usually a time base expansion of 32 is sufficient to eliminate
problems associated with the skin effect. This expansion causes the 1 to
1,000 Hertz pilot voltage to undergo a downward frequency translation to
0.03125 to 31.25 Hertz. The data obtained with the low frequency current
pulse is recorded on magnetic tape and is translated back to the 1 to
1,000 Hertz range for analysis by time base translator 52 (see FIG. 9).
For the case described this translation is accomplished by playing back
these data at a rate which is 32 times that at which they were recorded.
After this upward frequency translation the seismic and electrical
potential data appear as in the left hand portion of FIG. 8 and the data
analysis proceeds as previously described.
It will now be demonstrated how the method of this invention determines the
resistivity of the groundwater from the values of bulk rock resistivity,
.rho..sub.r, and the seismic wave velocity, V. FIG. 5 shows a plot of data
which was obtained in the following way. First the bulk rock resistivity,
.rho..sub.r, was measured. Then the resistivity of the groundwater
saturating the rock, .rho..sub.w, was measured. Next the ratio of these
two quantities, .rho..sub.r /.rho..sub.w, was calculated. This ratio,
often called the Formation Factor, is the abscissa of the points plotted
in FIG. 5. The velocity, V, of seismic waves was also measured for each
sample. The parameter .rho..sub.r /.rho..sub.w V was calculated and used
as the ordinate for the values plotted in FIG. 5. It will be noted that a
straight line 35 fits these measured data when they are plotted in this
manner. This means that a suitable empirical equation relating these
variables is of the form
##EQU5##
For the data plotted in FIG. 5 the constants a and b take on the values
1.1.times.10.sup.-.sup.3 and 9.1.times.10.sup.-.sup.5 respectively.
It is the intent of the method of this invention to determine the
resistivity of the groundwater, .rho..sub.w, which saturates the zone for
which the seismic velocity and bulk rock resistivity have been
automatically calculated. Equation (4) can be rewritten as
##EQU6##
Equation (5) can be used to determine .rho..sub.w once the bulk rock
resistivity and seismic velocity are known. .rho..sub.w in ohm-meters can
also be converted automatically to equivalent salinity, C, expressed in
parts per million by means of the relation
##EQU7##
in which M is the molecular weight of the dissociated salt, .beta. is its
degree of dissociation, u.sub.9.sbsb.1 .sbsb.8 and u.sub.c.sbsb.1.sbsb.8
are the ionic mobilities at 18.degree. C for the anions and cations
respectively, .alpha. is a coefficient which takes on the value 0.025 for
most electrolytes, and T is temperature in degrees Centigrade. For the
range of concentration anticipated .beta. is equal to 1, representing
complete dissociation.
The validity of the method of this invention can be established further by
a theoretical derivation of equation (5). This derivation is accomplished
by combining Archie's Law
.rho..sub.r = k.rho..sub.w .phi..sup.-.sup.m 7.
as originally proposed by G. E. Archie in 1942 and Wyllie's time-average
equation
##EQU8##
as proposed by M. R. J. Wyllie, A. R. Gregory, and L. W. Gardner in 1956.
The line which corresponds to solutions for equation (7) is shown in FIG.
3 and the line which corresponds to solutions for equation (8) is shown in
FIG. 4. For a model consisting of three sets of straight tubular pores,
each set of pores being at right angles to the directions of the other two
sets, the constants k and m in Archie's Law take on the values 3 and 1
respectively. The parameter, .phi., is the porosity of the rock. It will
be noted that this parameter occurs in both equation (8) and equation (7).
In equation (8) V.sub.ma is the seismic wave velocity in the material
which makes up the solid portion of the rock. This velocity is referred to
as the "matrix velocity." The quantity V.sub.w is the seismic wave
velocity in the fluid which saturates the pore space in the rock. c is a
correction factor which is used to compensate for under-compaction in
loosely consolidated sediments. If the porosity as given by equation (8)
is substituted into equation (7) we obtain for the theoretical model being
discussed
##EQU9##
This equation serves to identify the theoretical basis for the empirical
constants a and b in equation (5). Comparing equations (5) and (9) makes
it clear that
##EQU10##
For all but under-compacted samples the value of c may be taken as equal
to 1. In actual rocks the values of k and m in Archie's Law are known to
assume values which differ from the values 3 and 1 obtained from the
theoretical model. A general form for equation (9) is therefore
##EQU11##
which can be generalized to
##EQU12##
which contains three arbitrary constants, namely g, b, and m. The data of
FIG. 5 suggests that for most applications of the method of this invention
the simpler equation (5), obtainable from (11) by assigning m the value 1,
provides an adequate means for estimating the resistivity of the fluid
saturating the pore space. It should be clear that since values of
V.sub.ma, V.sub.w, and pg,14 c are known, the method of this invention in
conjunction with equation (8) allows the remote determination of the
porosity of an interval between zones having markedly differing acoustical
impedances; for the method provides a value of the seismic velocity, V,
for the interval which can be used in equation (8) to determine the
porosity.
In order to determine equivalent salinity from values of groundwater
resistivity, .rho..sub.w, given by equation (5), it is necessary to
estimate temperature.
The assumption that constant planar heat flow is occurring through the n
layers above the geothermal heat source leads to the equation (12) which
provides the temperature at the base of the nth layer in terms of the
surface temperature, Ts, the heat flow Q, and in terms of the ratio of
layer thickness to thermal conductivity, .DELTA.Z.sub.k /K.
##EQU13##
Elder (1965) uses equation (13) to estimate thermal conductivity
K.sub.k = (1-.phi.)K.sub.ma + .phi.K.sub.w. 13.
In this equation K.sub.ma is the thermal conductivity of the rock matrix,
K.sub.w is the thermal conductivity of water saturating the rock and .phi.
is the porosity.
Wyllie et al (1956) suggested an equation of identical functional form
relating interval time (i.e. the reciprocal of the compressional seismic
velocity), 1/V.sub.k = .DELTA.t.sub.k, to the matrix interval time
1/V.sub.ma = .DELTA.t.sub.ma and the saturating fluid interval time
1/V.sub.w = .DELTA.t.sub.w.
.DELTA.t.sub.k = (1-.phi.).DELTA.t.sub.ma + .phi..DELTA.t.sub.w 14.
where again .phi. is the porosity (see equation (8)). By solving for the
common parameter .phi. in equation (13) and (14) and equating, a linear
equation in thermal conductivity and interval time (reciprocal velocity)
is obtained. This equation is
##EQU14##
For quartz rich sediments the value of K.sub.ma is approximately
2.5.times.10.sup.-.sup.3, while in pyroclastic deposits a value of
5.0.times.10.sup.-.sup.3 is more appropriate. The proper value of K.sub.w
is 1.4.times.10.sup.-.sup.3. An appropriate value for .DELTA.t.sub.ma for
sediments is 55.5.times.10.sup.-.sup.6 and an appropriate value for
pyroclastic matrix interval time is 45.4 .times. 10.sup.-.sup.6. The value
usually used for .DELTA.t.sub.w is 189.times.10.sup.-.sup.6. On
substitution of this value for K.sub.k equation (12) I obtain
##EQU15##
for the temperature at the base of the nth layer. The equivalent salinity
at the base of the nth layer is obtained by inputing this value of T.sub.n
and the value of .rho..sub.w for the nth layer into the computer which
automatically solves equation (6).
The following is given as a specific example of a utilization of
applicant's novel method. Table I provides resistivity and seismic
velocity data obtained by the preferred method described above. Also
included are values of porosity as deduced from the surface measured
velocity values using equation (7) with a value of 1/c equal to 0.79.
TABLE I
__________________________________________________________________________
Location One
Depth Bulk Resistivity
Bulk Velocity
Porosity
Fluid Resistivity
Eq. (7)
Eq. (8)
0 - 10 ft.
2.1 ohm-m 840 ft./sec.
-- --
10 - 610 ft.
3.6 ohm-m 5590 ft./sec.
(73) .288 ohm-m
610 - 2410 ft.
4.7 ohm-m 6420 ft./sec.
58 .277 ohm-m
2410 - 5610 ft.
1.6 ohm-m 8900 ft./sec.
30 .0311 ohm-m
Location Two
0 - 100 ft.
2.7 ohm.m 1500 ft./sec.
-- (1.41) ohm-m
100 - 1600 ft.
7.4 ohm.m 6070 ft./sec.
64 .496 ohm-m
1600 - 3300 ft.
3.2 ohm.m 7580 ft./sec.
43 .119 ohm-m
__________________________________________________________________________
Consider first location one. The seismic data indicate that in this part of
the Imperial Valley of California the subsurface to a depth of 5610 ft.
can be subdivided into four zones. The seismic velocity for all subsurface
zones was determined by equation (1) and is listed in the table. The
resistivity values for all zones were determined by varying the
resistivity within each zone until a "best" fit, in the least squares
sense to the field data was obtained. These "best" values are listed in
the table.
The data Table I demonstrate one of the limitations of the applicant's
method. The correlation upon which equation (5) is based is for water
saturated compacted rock. The uppermost zone at location 1 is only
partially saturated and only partially compacted. This is attested to by a
value of bulk seismic velocity which has a value less than the velocity of
sound in air. Under these conditions equations (5) and (8) cannot be used
to estimate the porosity and pore fluid resistivity.
Considering the next two zones at location one, it is of interest to note
that although their "best" bulk resistivities differ by approximately 30
percent their calculated pore fluid resistivities differ by less than 4
percent. This suggests that both zones possess pore fluids of a very
similar nature. Below these zones a fourth zone is encountered in which
the pore fluid is an order of magnitude less resistive than in the
overlying layers. In this portion of the Imperial Valley it has been
established that hypersaline brine exists at depth. The data for location
one given in Table I clearly indicate that this brine reservoir begins at
a depth of 2410 ft.
The data obtained at location one can be contrasted with those obtained at
location two located approximately 30 miles from location one. The
location two data indicate that the subsurface pore fluids are markedly
different from those at location one. The nearly four fold relative
increase in the pore fluid resistivity at depths of the order of 3,000 ft.
indicates that this portion of the Imperial Valley is underlain by a
different hydrologic regime than that encountered at location one.
Temperature change alone would not be able to affect such a drastic
change. For if the salinity of the pore fluid is 30,000 parts per million,
an increase in pore fluid resistivity from 0.0311 ohm-meter to 0.119
ohm-meter can only be brought about by a decrease in temperature at depth
of approximately 360.degree.F. Since the geothermal gradient is
approximately the same at the two locations, the most logical conclusion
is that the salinity of the pore fluid is much higher at location one than
at location two.
Firm information regarding the geothermal gradient allows prediction of the
equivalent salinity of the pore fluid. Such information is obtainable by
the use of equation (16). Many tables and equations such as equation (6)
are available to convert to equivalent salinity when the resistivity and
temperature of the pore fluid are known. On assuming that surface
temperature and heat flow data lead to a temperature of 150.degree. C (or
300.degree. F) at 3,000 ft., the pore fluid resistivity data of Table I
lead to an equivalent salinity at location one of approximately 60,000
parts per million whereas at location two a value of 12,800 parts per
million is predicted. Such predictions are of prime importance when
systems are being designed to extract useful energy from superheated
brines. The above predictions are consistent with present knowledge of the
hydrologic differences that exist between locations one and two.
The functioning of applicant's invention can be summarized with reference
to FIG. 9 which shows in block diagram form the physical process involved,
with reference to FIG. 11 which depicts a possible pilot-voltage source
and with reference to FIG. 12 which further clarifies the method of
received signal processing.
Pilot-voltage source 41 causes an electromagnetic and seismic disturbance
to be created simultaneously within the earth by seismic wave and
electrical current source 19. The pilot-voltage source 41 can consist of
any electrical means capable of delivering energy sufficient to cause the
production by seismic wave and electrical current source 19 of seismic
waves and induced voltages having amplitudes sufficient to allow their
remote detection. Such pilot-voltage sources can range from simple
mechanically modulated voltage and current sources utilizing commutators
and cams to sophisticated triggerable electronic function generators
wherein the desired values of voltage and current as a function of time
are stored in digital form and are producible sequentially on demand.
The functioning of the pilot-voltage source can perhaps best be envisioned
with reference to the use of a voltage produced from an analogue magnetic
tape. In practice however, a digital or FM tape may be required due to the
possible necessity of producing frequencies presently below the range of
analogue tape systems. FIG. 10 shows diagramatically such a pilot-voltage
source. Magnetic tape 60 is being "read" by tape head 61 the output of
which is amplified by power amplifier 62. The output of the pilot voltage
source is transmitted by means of wires 86 and 87.
In areas where penetration of the electromagnetic disturbance is adversely
affected by the skin effect the time base of the electromagnetic
disturbance produced by 19 is translated by time base translator 43 so as
to create lower frequencies. This translator is shown in block form in
FIG. 9 and can take on forms similar to the pilot voltage source and is
simply a means of monitoring in real-time the pilot voltage and
reproducing in real-time the form of the pilot voltage wherein all
frequencies have been reduced by a consta | | |