Method of geophysical exploration

A method of geophysical exploration for acquiring and processing multicomponent seismic data obtained with seismic sources generating shear waves having time-varying polarizations and seismic receivers recording at least two modes of propagation of the imparted shear waves is provided. More particularly, a method is described for acquiring multicomponent seismic data with torsional seismic sources and multicomponent seismic receivers, as well as a method for processing such multicomponent seismic data so as to ameliorate the effects of shear wave splitting in displayed seismic data. Additionally, principal time-series signals can be obtained which are representative of formation properties along principal axes of an anisotropic formation essentially free of the effects of shear wave splitting.

BACKGROUND OF THE INVENTION 
The present invention relates generally to a method of geophysical 
exploration and more particularly to novel methods for acquiring and 
processing multicomponent seismic data obtained with seismic sources 
generating shear waves having time-varying polarizations. 
Exploration geophysicists have generally considered the earth's subsurface 
formations to be locally homogeneous and isotropic. However, exploration 
geophysicists have recently discovered that the assumptions about the 
general homogeneity and isotropy of the earth's subsurface formations are 
incorrect and that the earth's subsurface formations can exhibit 
pronounced anisotropy, particularly azimuthal anisotropy. Alford et al. in 
U.S. Pat. No. 4,817,061, Alford in U.S. Pat. No. 4,803,666, and Thomsen in 
U.S. Pat. No. 4,888,743, describe geophysical methods for acquiring and 
processing multicomponent seismic data to ameliorate the deleterious 
effects of formation anisotropy on seismic exploration. 
Many seismic sources, such as described by Willis et al. in U.S. Pat. No. 
4,842,094, are considered as having fixed polarizations when they impart 
seismic energy into the earth, although they have the capability of 
imparting shear waves polarized along any selected polarization. With the 
advent of torsional seismic sources generating elliptically polarized 
shear waves as described by Cole in U.S. Pat. Nos. 4,867,096 and 
4,871,045, we have discovered a novel method of geophysical exploration 
which can have a substantial impact on the acquisition and processing of 
multicomponent seismic data, especially in areas where the earth's 
subsurface formations exhibit azimuthally anisotropic characteristics. 
More particularly, the multicomponent seismic acquisition methods can be 
simplified. Consequently, the time required to collect multicomponent 
seismic data can be greatly reduced. These and other benefits of the 
present invention will be further described in more detail below. 
SUMMARY OF THE INVENTION 
According to the present invention, a method of geophysical exploration is 
provided whereby shear wave seismic energy having a time-varying 
polarization is imparted into the earth with a torsional seismic source 
and a first set of seismic signals representative of the earth's response 
thereto is recorded with sets of seismic receivers responsive to at least 
first and second modes of shear wave propagation of the imparted seismic 
energy. The first set of seismic signals can then be processed so as to 
ameliorate the effects of shear wave birefringence and obtain principal 
time-series signals essentially free of the effects of shear wave 
splitting. Additionally, principal time-series signals can be obtained 
which are representative of formation properties along principal axes of 
an anisotropic formation essentially free of the effects of shear wave 
splitting. The step of imparting seismic energy into the earth can be 
repeated with a torsional seismic source, having an opposite polarity to 
that originally employed, and a second set of seismic signals 
representative of the earth's response thereto can be recorded with the 
sets of seismic receivers. By combining the first and second sets of 
seismic signals, one can ameliorate the deleterious effects of shear wave 
birefringence to obtain principal time-series signals essentially free of 
the effects of shear wave splitting and obtain a measure of the azimuthal 
orientation of the principal axes of anisotropic subsurface formations. 
As such, the present invention provides a novel method of geophysical 
exploration especially in providing novel methods for acquiring and 
processing multicomponent seismic data. Specifically, more simplified 
seismic source operation and seismic receiver positioning can be employed 
to ensure the acquisition of multicomponent seismic signals wherein the 
seismic receivers record the earth's response to at least two modes of 
shear wave propagation of the imparted seismic energy. Thereafter, the 
recorded seismic signals can be processed to ameliorate the effects of 
shear wave splitting in displayed seismic data, as well as to obtain 
principal time-series signals representative of the earth's properties 
along principal axes of an anisotropic formation using either a priori or 
analytically derived knowledge of the azimuthal orientation of the 
principal axes of the anisotropic formation. 
These and other advantages of the present invention will be apparent from 
the following detailed description of accompanying drawings.

DETAILED DESCRIPTION OF THE INVENTION 
I. Introduction 
At the outset, brief introductory remarks are provided as an overview to 
assist in understanding the present invention. When formations at depth 
are fractured or cracked, the fractures are often oriented nearly 
vertically, and with one (or more) preferred azimuth. Moreover, oriented 
fractures in formations usually make the formations anisotropic, i.e., the 
rock properties vary with direction. If there is a regional tectonic 
stress or paleo-stress, the fractures can be oriented nearly parallel with 
their planar surfaces substantially perpendicular to the horizontal 
direction of least compressive stress. Such formations can be 
characterized by a vector, perpendicular to the planar surfaces of such 
cracks or fractures, which is called the unique axis. Formations are 
considered to be azimuthally anisotropic if formation properties vary with 
azimuthal direction. Although such parallel fracture systems are used as 
an exemplar of azimuthal anisotropy, it is understood that the following 
discussion is germane to other causes of azimuthal anisotropy. 
In the present invention, the differences in formation characteristics with 
respect to various azimuthal directions (e.g., in the shear modulus, shear 
velocity, etc.) of azimuthally anisotropic formations can be 
advantageously employed. For example, if shear waves travel vertically in 
an azimuthally anisotropic formation so that the polarization (i.e., the 
direction of particle motion) of the imparted shear wave is substantially 
parallel to the fracture strike, the shear wave propagates at 
substantially the shear velocity of the unfractured formation. However, if 
the shear waves travel vertically in the azimuthally anisotropic formation 
so that the polarization of the imparted shear wave is substantially 
perpendicular to the fracture strike, then the shear wave propagates at a 
velocity which depends upon a combination of formation and fracture 
properties, and which can be noticeably less than the shear wave velocity 
of the unfractured formation itself. When shear waves are imparted 
vertically into an azimuthally anisotropic formation so that the 
polarization of the imparted shear wave is oblique to the fracture strike, 
the shear wave is "split" into two separate components, i.e., one parallel 
with the unique axis and the other perpendicular thereto. Such shear wave 
"splitting" is sometimes called shear wave birefringence. 
Only transversely isotropic formations are considered explicitly in this 
explanatory discussion, although more general anisotropic media will show 
similar effects. Transversely isotropic media have one unique axis and two 
equivalent axes (both at right angles to the unique axis). The unique axis 
may or may not be horizontal. Formation anisotropy is most commonly due 
to: 
(1) homogeneous but anisotropic beds (typically shales) which have a 
preferred orientation of mineral grains, due to settling under gravity; 
(2) isotropic beds, thinly layered, so that a sound wave with a wave length 
much longer than the layer thicknesses averages over many layers and 
propagates as if in a homogeneous, anisotropic media; 
(3) horizontal fractures, if the layer is not deeply buried; and/or 
(4) vertical fractures whose planar surfaces are oriented randomly in all 
horizontal directions. 
(5) vertical fracture whose planar surfaces are oriented preferentially in 
a particular horizontal direction. 
These effects may be present in any combination; however, only condition 
(5) leads to azimuthal anisotropy in horizontal beds. 
Transversely isotropic formations generally have their unique axis 
vertical, because the direction of gravity is the ultimate cause of 
anisotropy. However, in the case where transverse isotropy occurs in 
regions having some tectonic stress, a preferred horizontal direction is 
imparted to the fractures. In such a setting, tensile fractures may open 
with their planar surfaces perpendicular to the direction of least 
compressive stress. If the formation is otherwise isotropic, such 
fractures create a transversely isotropic medium whose unique axis is 
horizontal. Formations exhibiting such characteristics are considered to 
be azimuthally anisotropic. The effects of anisotropy on shear wave 
propagation can be used according to the present invention to detect and 
characterize the presence of azimuthally anisotropic formations, and to 
resolve their deleterious effect in seismic data quality. 
To aid in the following discussion, the symbols in the table below have 
been employed: 
TABLE I 
x.sub.i are principal axes, x.sub.1, x.sub.2 of an anisotropic formation; 
x and y are orthogonal axes generally at an arbitrary angle .THETA. to the 
principal axes x.sub.i ; 
A is the amplitude of the imparted shear wave seismic energy; 
A.sub.i is a component of the shear wave energy imparted along the x.sub.i 
axis of the anisotropic formation; 
A.sub..theta. is a component of the shear wave energy imparted at an 
arbitrary angle .theta. to the x.sub.i axis of the anisotropic formation; 
f.sub.i (t) is the earth filter along the x.sub.i axis of the anisotropic 
formation; 
r.sub.i (t) is the principal reflectivity series for shear waves polarized 
along the x.sub.i axis of the anisotropic formation; 
r.sub.i (t)=f.sub.i (t)*r.sub.i (t) 
w(t) is the seismic wavelet of the imparted shear wave; 
S.sub.i (t) is the principal time-series signal along the x.sub.i axis of 
the anisotropic formation; and 
* is a symbol representing the mathematical operation of convolution. 
II. Effects of Anisotropy on the Propagation of Seismic Energy 
Whenever a seismic survey is conducted over a formation which is 
anisotropic, the moveout velocity obtained by standard methods may not be 
equal to the vertical velocity of the medium. This is true even in the 
absence of layering and dip of reflectors. The moveout velocity differs 
from vertical velocity simply because of the angular dependence of the 
wave velocity. The true vertical velocity can be used along with vertical 
travel time to determine a depth to or thickness of a given bed, i.e., to 
convert a time section to a depth section. Hence, if the moveout velocity 
is naively taken to be equal to the vertical velocity, a misestimation of 
depth and/or thickness may result. The discussion below pertains to the 
true vertical velocity and not the apparent or moveout velocity. 
A. Compressional Wave 
The geometry for this example can be best understood with the help of an 
analogy. Imagine that an azimuthally anisotropic formation can be 
represented by a thick deck of cards, standing on their edges. The empty 
planes between the cards represent fractures and the deck is oriented so 
the edges of the cards show on two ends and the top of the deck. Placing 
one's open hand on the top of the deck represents a vertically incident 
compressional (P) wave front. As the hand oscillates up and down 
simulating a compressional wave or longitudinal particle displacement, the 
deck deforms only with difficulty. The fractures have not substantially 
weakened the deck; to deform the deck requires that the cards themselves 
(analogous to the uncracked formations) must be deformed. The high 
resistance to longitudinal deformation implies a large longitudinal 
elastic modulus and hence a large longitudinal velocity. 
B. Shear Wave 
Referring again to the deck of cards analogy, horizontal oscillations of 
the hand can represent a vertically incident shear wave front. For hand 
oscillations generally parallel to the length of the cards, the deck again 
deforms only with difficulty. As discussed before, the fractures do not 
weaken rock for this component of strain. Hence, the effective shear 
modulus .mu..sub.2 and the shear velocity .beta..sub.2 are high. However, 
horizontal hand oscillations generally perpendicular to the length of the 
cards cause the deck to deform easily in shear. The spaces between the 
cards, i.e., the fractures, allow the cards to slide past one another. The 
low resistance to shear implies a low shear modulus .mu..sub.1 and hence a 
low shear velocity .beta..sub.1. 
The contrast between the shear velocities .beta..sub.2 and .beta..sub.1 in 
the card analogy is greater than the contrast found for the azimuthally 
anisotropic formations (because the fractures in the anisotropic 
formations are not continuous throughout the region as in the deck of 
cards); however, the principle is the same. 
For horizontal hand oscillation generally at an oblique angle to the length 
of the deck of cards, the particle displacements of the shear wavefronts 
do not coincide with the principal axes of the deck of cards, and the 
shear waves are subjected to shear wave birefringence or "splitting." That 
is, the shear wave displacements are resolved into two components, one 
along the deck of cards unique axis, i.e., x.sub.1, (perpendicular to the 
cards) and the other along the axis perpendicular thereto, i.e., x.sub.2 
(parallel to the card edges). As a consequence, the imparted shear wave 
energy encounters two different shear moduli, i.e., one (.mu..sub.1) 
perpendicular to the planes of symmetry, and the other (.mu.2) parallel to 
the planes of symmetry. The "split" shear wave energy will travel at two 
different velocities (.beta..sub.1, .beta..sub.2, where .beta..sub.1 
&lt;.beta..sub.2) through the anisotropic formation. It is important to 
understand that oblique polarization results in this splitting, and not in 
unsplit propagation at some intermediate velocity. 
III. Effect of Anisotropy on Recorded Seismic Signals 
A. Shear Wave Seismic Source Having a Fixed Polarization 
Azimuthally anisotropic formations can be considered to have different 
reflectivity series as a function of azimuth. For example, r.sub.1 (t) can 
describe the reflectivity series for shear waves polarized parallel to the 
unique axis of the azimuthally anisotropic formation (i.e., along the 
x.sub.1 axis) and r.sub.2 (t) can describe the reflectivity series for the 
azimuthally anisotropic formation for shear waves polarized perpendicular 
to the unique axis (i.e., along the x.sub.2 axis). Because of the 
differences in shear wave velocities according to each of the two 
principal polarizations, the downgoing shear wavefronts encounter the same 
layer interface at different times, resulting in differing recorded 
reflections. The reflectivity series r.sub.1 (t) can appear as a scaled 
(in amplitude) and stretched (in time) version of r.sub.2 (t), in the 
simple case where the orientation of anisotropy (e.g., of fractures) is 
uniform with depth. The seismic signals recorded by a geophone can be 
described as the convolution of the imparted seismic wavelet with the 
appropriate reflectivity series and with a filter which takes into account 
dispersion, attention, etc. of the earth's formations. 
The effects of azimuthally anisotropic formations on the propagation of 
seismic wave energy can be seen most vividly in the signals recorded using 
seismic source/geophone pairs having various fixed polarizations with 
respect to the principal axes (x.sub.1, x.sub.2) of the anisotropic 
formation. In a first example depicted in plan view in FIG. 1, a seismic 
source S is adapted to impart shear wave seismic energy with displacement 
A.sub.1 parallel to the x.sub.1 axis of the formation according to: 
EQU A.sub.1 =A.multidot.w.sub.1 (t)x.sub.1 (1) 
where 
A=amplitude of the imparted shear wave displacement and 
w.sub.1 (t)=wavelet of the imparted shear wave. 
In this and subsequent figures, the indicated "fracture strike" denotes the 
direction of polarization of the fast shear wave in the anisotropic 
formation, whether or not the anisotropy is caused by a single set of 
oriented fractures. 
A similar analysis could also be provided using a shear wave source having 
the same amplitude and wavelet, and a fixed horizontal line of action 
parallel to the x.sub.2 axis, i.e., 
EQU A.sub.2 =A.multidot.w.sub.2 (t)x.sub.2 (2) 
Responsive to imparted shear wave A.sub.1 a seismic receiver R having a 
matching horizontal polarization R.sub.1 to that of the imparted shear 
wave A.sub.1 (i.e., parallel to the x.sub.1 axis) will record the 
following signal: 
EQU R.sub.1 (t)=A.multidot.f.sub.1 (t)*w.sub.1 (t)*r.sub.1 (t) (3) 
where the filter f.sub.1 (t) accounts for dispersion, attenuation, etc. 
If the seismic receiver R polarization in FIG. 1 is orthogonal to the 
polarization of the imparted shear wave A.sub.1 (i.e., parallel to the 
x.sub.2 axis of the formation) no signal would be recorded, i.e., R.sub.2 
(t)=0. 
Alternatively, if the seismic source S imparts shear wave energy with 
displacement A.sub.2 parallel to the x.sub.2 axis as shown in FIG. 2, a 
seismic receiver R having a horizontal polarization R.sub.2 matching that 
of the imparted shear wave A.sub.2 (i.e., parallel to the x.sub.2 axis) 
would record the following signal: 
EQU R.sub.2 (t)=A.multidot.f.sub.2 (t)*w.sub.2 (t)*r.sub.2 (t) (4) 
If the seismic receiver R in FIG. 2 were to have a polarization which is 
orthogonal to that of the imparted shear waves A.sub.2 (i.e., parallel to 
axis x.sub.1) no signal would be recorded, i.e., R.sub.1 (t)=0. 
If the formation anisotropy is small, the filters f.sub.1 (t) and f.sub.2 
(t) will be similar. For simplicity, one can regard them in this example 
and other examples below to be equal. Similarly, the seismic source 
wavelets w.sub.1 (t) and w.sub.2 (t) may differ under the partial control 
of the survey operator. Again, for simplicity, one can treat them as 
equal. One can rewrite the expressions [f.sub.1 (t)*r.sub.1 (t)] as 
r.sub.1 (t) and [f.sub.2 (t)*r.sub.2 (t)] as r.sub.2 (t). 
In a third example, a seismic source S can impart shear waves having a 
displacement A.sub..THETA. at an oblique angle .theta. to the principal 
axis x.sub.1 as shown in FIG. 3. The natural polarization of the 
anisotropic formation is indicated by formation principal axes x.sub.1 and 
x.sub.2 as before. Assuming the imparted shear wave to be a vector of 
magnitude A in the direction .theta., it can be expressed in formation 
coordinates (x.sub.1, x.sub.2) as follows: 
EQU A.sub..theta. =A cos .theta.w(t)x.sub.1 +A sin .THETA.w(t)x.sub.2(5) 
As the shear wave enters the anisotropic formation, it "splits" into two 
generally, mutually orthogonal components which conform to the two 
possible transverse modes of propagation of the anisotropic formation. The 
rate of separation in time of the split components is dependent upon the 
differences in velocities along the principal axis of the anisotropic 
formation. 
If the seismic receiver R in FIG. 3 had a horizontal polarization aligned 
parallel to the x.sub.1 axis, it would only detect the slower shear wave 
component as follows: 
EQU R.sub.1 (t)=A cos .theta..multidot.r.sub.1 (t)*w(t).multidot.(6) 
If the seismic receiver R in FIG. 3 had a horizontal polarization aligned 
parallel to the x.sub.2 direction, it would record only the faster shear 
wave component as follows: 
EQU R.sub.2 (t)=A sin .theta..multidot.r.sub.2 (t)*w(t).multidot.(7) 
As depicted in FIG. 3 with the seismic receiver R, horizontal polarization 
R.sub..THETA. matching the horizontal polarization of the shear wave 
source S, the seismic receiver R responds to both components of the shear 
wave according to the projection of their polarizations onto the seismic 
receiver polarization. The recorded signal will be: 
EQU R.sub..THETA. (t)=A.multidot.r.sub.1 (t)*w(t) cos .sup.2 
.THETA.+A.multidot.r.sub.2 (t)*w(t) sin .sup.2 .theta. (8) 
or more simply a combination of R.sub.1 (t) as R.sub.2 (t) as previously 
described in Eqs. (6, 7) as: 
EQU R.sub..THETA. (t)=R.sub.1 (t) cos .THETA.+R.sub.2 (t) sin .THETA.(9) 
Consequently, the source S, imparting shear wave energy polarized 
predominantly at an oblique angle .THETA. to the unique axis, can give 
rise to two shear wave components. 
If the seismic receiver R polarization were orthogonal to the polarization 
of the source in FIG. 3, it would respond to different projections of both 
shear wave components, according to their projection onto the seismic 
receiver polarization. That is, the recorded signals would be as follows: 
EQU R.sub..THETA. (t)=A.multidot.r.sub.1 (t)*w(t) sin .THETA. cos 
.theta.--A.multidot.r.sub.2 (t)*w(t) sin .theta. cos .THETA.(10) 
or more simply a combination of R.sub.1 (t) and R.sub.2 (t) as previously 
described in Eqs. (6, 7) as: 
EQU R.sub.0 (t)=R.sub.1 (t) sin .THETA.-R.sub.2 (t) cos .THETA.(11) 
In a fourth example, if the source generates a P-wave which is converted, 
at an interface in the earth's subsurface to a shear wave (following 
conversion principles well-known to those skilled in the art), the 
resulting shear wave of fixed polarization can be treated similarly as in 
the third example above. Although such conversion of compressional waves 
to shear waves requires oblique incidence, in many cases this requires no 
significant changes from the normal-incidence analysis given above. 
B. TORSIONAL SEISMIC SOURCE 
The output of a torsional seismic source having a time-varying horizontal 
polarization can be written: 
EQU A(t)=Aw(t) sin (.PSI.(t))x+Aw(t) cos (.PSI.(t))y (12) 
where x and y are an arbitrary orthogonal coordinate system and .PSI.(t) 
describes the instantaneous polarization of the torsional seismic source 
as a function of time under the control of the source operator. 
The seismic sources described by Eqs. (1) and (2) are special cases of Eq. 
(12), corresponding to .PSI.(t)=90.degree., and .PSI.(t)=0.degree., 
respectively, for all times t (i.e., their polarizations are 
time-invariant). Any arbitrary, horizontal, circularly polarized, 
torsional source can be constructed with an appropriate .PSI.(t) and w(t). 
The treatment below can be generalized to elliptically polarized, 
torsional seismic sources by assigning separate wavelets w.sub.x (t) and 
w.sub.y (t) and separate amplitudes A.sub.x and A.sub.y and if desired, it 
can also be generalized to nonhorizontal, time-varying polarization. 
The torsional source can be deployed either on the surface or downhole. One 
example of practical interest downhole would be a drill bit acting as a 
torsional source. In this case, .PSI.(t)=.omega..multidot.t, where .omega. 
is the angular frequency of the rotating drill bit. 
The output of the torsional source described by Eq. (12) above can be 
rewritten in terms of the anisotropic formation principal axes x.sub.1, 
x.sub.2 by a simple rotation: 
##EQU1## 
where .THETA. is a measure of the angle between the axes x and x.sub.1. 
The components of the shear waves polarized along the axis x.sub.1 are 
principal modes traveling with velocity .beta..sub.1 ; those polarized 
along the axis x.sub.2 are principal modes traveling with velocity 
.beta..sub.2. 
In accordance with one aspect of the present invention, if a pair of 
seismic receivers having horizontal polarizations R.sub.1 and R.sub.2 are 
positioned at generally the same location with their horizontal 
polarizations oriented along the pricipal axes x.sub.1 and x.sub.2 of the 
anisotropic formation, they would record first and second component 
seismic signals R.sub.1 '(t) and R.sub.2 '(t), respectively: 
EQU R.sub.1 '(t)=A[(cos .THETA. sin .PSI.(t)+sin .THETA. cos 
.PSI.(t)].multidot.r.sub.1 (t)*w(t) 
EQU R.sub.2 '(t)=A[-sin.THETA. sin .PSI.(t)+cos .THETA. cos 
.PSI.(t)].multidot.r.sub.2 (t)*w(t) (14) 
More simply, the recorded component seismic signals of Eq. (14) can be 
expressed in compact notation as: 
EQU R'(t)=R.sub.1 '(t)x.sub.1 +R.sub.2 '(t)x.sub.2 (15) 
In general, the polarizations of receivers (R.sub.1 and R.sub.2) may be 
oriented in any two linearly independent directions; the examples cited 
herein discuss the simplest case of orthogonal orientations. 
However, the anisotropic formations' principal axes directions with respect 
to the axes of the seismic receivers (i.e., .THETA.) are generally 
unknown; the determination of their orientation is an objective of the 
present invention. In fact, the geophones' polarizations can be assumed to 
be oriented in an orthogonal coordinate system x, y which is at an 
oblique, yet unknown, angle .THETA. to the principal axes (x.sub.1, 
x.sub.2). In this survey frame, the recorded component seismic signals 
are: 
EQU R.sub.1 (t)=-[A(cos .sup.2 .THETA. sin .PSI.(t)+cos .THETA. sin .THETA. cos 
.PSI.(t))].multidot.r.sub.1 (t)*w(t) 
EQU +[A(sin .sup.2 .THETA. sin .PSI.(t)-cos.THETA. sin .THETA. cos 
.PSI.(t))].multidot.r.sub.2 (t)*w(t) 
EQU R.sub.2 (t)=-[A(cos.THETA. sin .THETA. sin .PSI.(t)+sin .sup.2 .THETA. cos 
.PSI.(t))].multidot.r.sub.1 (t)*w(t) 
EQU +[A(-cos .THETA. sin .THETA. sin .PSI.(t)+cos .sup.2 .THETA. cos 
.PSI.(t))]r.sub.2 (t)*w(t) (16) 
It can be seen in the component seismic signals R.sub.1 (t) and R.sub.2 (t) 
recorded by the seismic receivers R.sub.1 and R.sub.2, respectively, each 
include both principal modes of shear wave propagation, i.e., there are 
multiple events per reflector. Using compact notation, one can rewrite Eq. 
(16) as: 
EQU R(t)=R.sub.1 (t)x+R.sub.2 (t)y (17) 
VI. Field Technique Employing Torsional Seismic Sources 
This section relates to seismic acquisition and processing techniques which 
provide methods for ameliorating the effects of shear wave splitting on 
seismic data as well as detecting of the presence and/or extent of 
fractured rocks in the subsurface, using seismic recordings obtained with 
a torsional seismic source. The present invention is intended to include 
both surface and subsurface methods of seismic exploration. An important 
aspect of the present invention is to describe a method of seismic 
exploration employing torsional seismic sources to estimate the azimuthal 
orientation of the principal axes of subsurface, anisotropic formations 
and to obtain from the recorded seismic data "principal time-series" 
signals which are substantially free of the effects of shear wave 
splitting. 
Looking now to FIG. 4, the method of the present invention will be further 
described. At step 10, shear wave seismic energy, having a time-varying 
polarization, can be imparted into the earth with a torsional seismic 
source. Unlike prior techniques which impart shear wave seismic energy, 
having a fixed polarization, into the earth, the torsional source imparts 
shear wave seismic energy in all directions in accordance with a selected 
time-varying polarization. As such, positioning the torsional seismic 
source so as to impart shear wave seismic energy having a given azimuthal 
relationship to the principal axes of an anisotropic formation is not 
required to achieve shear wave splitting. The earth's response thereto is 
recorded at step 20, with a set of seismic receivers or geophones adapted 
to record at least two modes of shear wave propagation in anisotropic 
formations. In particular, either a set of seismic receivers, having their 
polarizations at an unknown oblique angle .THETA. to the principal axes of 
the anisotropic formation, or a set of seismic receivers having at least 
first and second linearly independent polarizations at unknown angles 
.THETA. and 90-.THETA., respectively (for orthogonal receiver 
polarizations) to the principal axes can be employed to record a first set 
of component seismic signals. 
In anisotropic formations, each of the recorded component seismic signals 
can include two separate (but often overlapping) reflection events, both 
representative of the reflection of the imparted seismic energy from a 
given seismic reflector. The separate reflection events are the result of 
the shear wave "splitting" and thus represent different modes or 
components of propagation of the imparted seismic energy. Although such 
duplicate information might seem helpful, in fact, it confuses the data, 
and renders it difficult to interpret. 
In a first method to resolve such duplication and resulting confusion at 
step 30, one can form weighted sums of the component seismic signals 
R.sub.1 (t) and R.sub.2 (t) obtained with the set of seismic receivers 
having at least first and second linearly independent polarizations as 
described by Eq. (16), at an unknown angle .THETA. to the principal axes, 
according to Eqs. (18, 19): 
EQU sin .THETA.R.sub.1 (t)-cos .THETA.R.sub.2 (t)= 
EQU [A(sin.THETA. sin .PSI.(t)-cos.THETA. cos .PSI.(t))].multidot.r.sub.1 
(t)*w(t) (18) 
EQU and 
EQU cos .THETA.R.sub.1 (t)+sin .THETA.R.sub.2 (t)= 
EQU [A(cos .THETA. sin .PSI.(t)+sin .THETA. cos .PSI.(t))].multidot.r.sub.2 
(t)*w(t) (19) 
Eqs. (18) and (19) now have combinations of the recorded component seismic 
signals (on the left) and principal time-series signals (on the right) 
which contain only one reflection event-per-reflector, i.e., they each 
represent only one mode of shear wave propagation. However, both sides 
also contain the unknown angle .THETA.. 
A variety of different means are available for reducing Eqs. (18) and (19) 
to principal time-series signals independent of the angle .THETA.. One 
general method of obtaining the principal time-series signals independent 
of the angle .THETA. is to repeat the previous acquisition with the 
torsional seismic source polarity reversed at step 40, e.g., by reversing 
the direction of rotation of the torsional source (i.e., by setting 
.PSI.(t).fwdarw.-.PSI.(t)). Once again, the earth's response thereto can 
be recorded with the set of seismic receivers having at least first and 
second polarizations to obtain a second set of component seismic signals 
R.sub.1 (t) and R.sub.2 (t) at step 50. Hereafter, to distinguish the two 
separate sets of component seismic signals, the first set of component 
seismic signals R.sub.1 (t) and R.sub.2 (t) will be labeled as R.sub.1 
(.PSI.) and R.sub.2 (.PSI.), respectively, and the second set of component 
seismic signals will be labeled R.sub.1 (-.PSI.) and R.sub.2 (-.PSI.). 
This change in notation is intended to highlight the change in polarity of 
the torsional source. By similarly weighting and combining at step 60, the 
second set of component seismic signals can be expressed as: 
EQU sin .THETA.R.sub.1 (-.PSI.)-cos .THETA.R.sub.2 (-.PSI.)= 
EQU [A(-sin .THETA. sin .PSI.(t)-cos .THETA. cos .PSI.(t))].multidot.r.sub.1 
(t)*w(t) (20) 
EQU and 
EQU cos .THETA.R.sub.1 (-.PSI.)-sin .THETA.R.sub.2 (-.PSI.)= 
EQU [A(-cos .THETA. sin .PSI.(t)-sin .THETA. cos .PSI.(t))].multidot.r.sub.2 
(t)*w(t) (21) 
The weighted signals of Eqs. (18) and (20) can be combined at step 70 to 
yield: 
EQU sin .THETA.(R.sub.1 (.PSI.)+R.sub.1 (-.PSI.))-cos .THETA.(R.sub.2 
(.PSI.)+R.sub.2 (-.PSI.)) 
EQU =-2A cos .THETA..PSI.(t).multidot.r.sub.1 (t)*w(t) (22) 
Similarly, the weighted signals of Eqs. (19) and (21) can be combined to 
yield: 
EQU cos .THETA.(R.sub.1 (.PSI.)+R.sub.1 (-.PSI.))+sin .THETA.(R.sub.2 
(.PSI.)+R.sub.2 (-.PSI.)) 
EQU =2A sin .THETA. cos .PSI.(t).multidot.r.sub.2 (t)*w(t) (23) 
Finally, the combined signals of Eqs. (22, 23) can then be rearranged to 
yield principal time-series signals S.sub.1 (t) and S.sub.2 (t) as 
follows: 
##EQU2## 
where S.sub.1 (t)=A[w(t).multidot.cos .PSI.(t)]* f.sub.1 (t) * r.sub.1 (t) 
and 
##EQU3## 
where S.sub.2 (t)=A[w(t).multidot.cos .PSI.(t) ]* f.sub.2 (t) * r.sub.2 
(t) 
Each of the principal time-series signals S.sub.1 (t) and S.sub.2 (t) 
represents a seismic signal having one reflection eventper-reflector (not 
including multiples), i.e., it is free of the shear wave splitting effects 
and is independent of the angle .THETA.. Moreover, each of the principal 
time series signals S.sub.1 (t) and S.sub.2 (t) now represents essentially 
the properties of the anisotropic formation along a principal axis 
thereof. The right sides of Eqs. 24 and 25 contain an average of the 
recorded component seismic signals R.sub.1 (.PSI.) and R.sub.1 (-.PSI.), 
i.e., 
EQU R.sub.1 =1/2(R.sub.1 (.PSI.)+R.sub.1 (-.PSI.)) (26) 
and of the component seismic signals R.sub.2 (.PSI.) and R.sub.2 (-.PSI.) 
EQU R.sub.2 =1/2(R.sub.2 (.PSI.)+R.sub.2 (-.PSI.)) (27) 
The principal time-series signal S.sub.1 (t) in Eq. (24) can thus be 
simplified according to: 
EQU S.sub.1 (t)=-tan .THETA.R.sub.1 (t)+R.sub.2 (t) (28) 
Similarly, one can simplify the second principal time-series signal S.sub.2 
(t) in Eq. (25) according to: 
EQU S.sub.2 (t)=cot .THETA.R.sub.1 (t)+R.sub.2 (t) (29) 
In fact, Eqs. (11) and (19) and (20) permit finding the principal 
time-series for special cases of w(t) and .PSI.(t), which can rely on 
special features of these functions and not require the polarity-reversed 
process described above. 
Should a priori knowledge exist regarding the azimuthal relationship 
between formation principal axes and seismic receiver polarizations (i.e., 
the angle .THETA.), the azimuthal dependency in the principal time-series 
signals S.sub.1 (t) and S.sub.2 (t) can be deduced directly. 
At step 80, if the azimuthal angle .THETA. is not known independently, it 
can be estimated by recognizing that (1) .THETA. is independent of time, 
and (2) that r.sub.2 (t) can be physically related to r.sub.1 (t). In 
particular, it may be assumed on physical grounds that r.sub.2 (t) is just 
a stretched version of r.sub.1 (t) according to: 
EQU r.sub.2 (t)=r.sub.1 (t(1+.gamma.)) (30) 
where .gamma.(t) is the average anisotropy down to time t (a smooth 
function of t). 
Then one may simply calculate a plurality of principal time-series signals 
S.sub.1 (t) and S.sub.2 (t) by assuming different values of .THETA. (e.g., 
.THETA.=0, 10, 20, 30, 40, 50, 60, 70, 80, 90) and selecting the angle 
.THETA. for which S.sub.2 (t) appears visually, or by optimizing some 
calculated quantity, as a stretched version of S.sub.1 (t). The trial 
value of .THETA. which produces this result will be close to the actual 
orientation angle .THETA.. More analytically, one can implement this 
technique using the approximation technique described in Thomsen U.S. Pat. 
No. 4,888,743, incorporated by reference herein. Once the principal 
time-series signals S.sub.1 (t) and S.sub.2 (t), independent of the angle 
.THETA., are found, either one is better, for structural interpretation, 
than was the original recorded seismic data, since each has only one 
event-per-reflector. Furthermore, differences in the two principal 
time-series signals gives information about anisotropy, and its 
distribution with depth. 
Alternatively, if seismic receivers having only one polarization at an 
oblique angle .THETA. to a principal axis of the anisotropic formation are 
employed at either step 20 or 50, either the component seismic signal 
R.sub.1 (t) or R.sub.2 (t), as described in Eq. 16, will be recorded. 
However, both component seismic signals includes at least two modes of 
shear wave propagation of the imparted seismic energy. 
Here again, if a priori knowledge exists regarding the azimuthal 
relationship between formation principal axes and the seismic receiver 
polarization, the azimuthal dependency of either R.sub.1 (t) or R.sub.2 
(t) in Eq. 16 can be deduced and either the principal time-series signals 
S.sub.1 (t) or S.sub.2 (t) can be obtained. Alternatively, by simply 
assuming different values for .THETA. and recalling the scaled and 
stretched relationship between r.sub.1 (t) and r.sub.2 (t) the principal 
time-series signal S.sub.1 (t) or S.sub.2 (t) can be determined. 
Having thus described the present invention employing a torsional seismic 
source in combination with sets of seismic receivers adapted to record 
both the fast and slow modes of propagation of shear wave seismic energy 
in an anisotropic formation and methods for ameliorating the effects of 
shear wave splitting, other modifications and improvements thereto may 
become apparent to others skilled in the art. However, the present 
invention is to be limited only by the claims attached herewith.