U.S. patent application number 11/638861 was filed with the patent office on 2008-06-19 for computing an absorption parameter for a mode-converted seismic wave.
Invention is credited to Ralf Ferber, Stephen Morice.
Application Number | 20080144437 11/638861 |
Document ID | / |
Family ID | 39466520 |
Filed Date | 2008-06-19 |
United States Patent
Application |
20080144437 |
Kind Code |
A1 |
Ferber; Ralf ; et
al. |
June 19, 2008 |
COMPUTING AN ABSORPTION PARAMETER FOR A MODE-CONVERTED SEISMIC
WAVE
Abstract
To survey a subterranean structure, measured seismic data is
processed using an algorithm for deriving a single-mode absorption
parameter. A first absorption parameter for a mode-converted
seismic wave is computed based on an output of the algorithm. The
first absorption parameter represents an absorption effect of the
mode-converted seismic wave by the subterranean structure, where
the mode-converted seismic wave is reflected from the subterranean
structure in response to a source seismic wave of a different mode
than the mode-converted seismic wave.
Inventors: |
Ferber; Ralf; (Horsham,
GB) ; Morice; Stephen; (New Plymouth, NZ) |
Correspondence
Address: |
WesternGeco L.L.C.;Jeffrey E. Griffin
10001 Richmond Avenue
HOUSTON
TX
77042-4299
US
|
Family ID: |
39466520 |
Appl. No.: |
11/638861 |
Filed: |
December 14, 2006 |
Current U.S.
Class: |
367/40 |
Current CPC
Class: |
G01V 1/36 20130101 |
Class at
Publication: |
367/40 |
International
Class: |
G01V 1/16 20060101
G01V001/16 |
Claims
1. A method of surveying a subterranean structure, comprising:
processing measured seismic data using an algorithm for deriving a
single-mode absorption parameter; and computing a first absorption
parameter for a mode-converted seismic wave based on an output of
the algorithm, wherein the first absorption parameter represents an
absorption effect of the mode-converted seismic wave by the
subterranean structure, and wherein the mode-converted seismic wave
is reflected from the subterranean structure in response to a
source seismic wave of a different mode than the mode-converted
seismic wave.
2. The method of claim 1, wherein processing the measured seismic
data comprises processing the measured seismic data for a
mode-converted seismic wave.
3. The method of claim 2, wherein computing the first absorption
parameter comprises computing a mode-converted absorption Q that is
based on a cumulative effect of a first absorption Q for the source
seismic wave traveling from a seismic source to a subsurface
reflector in the subterranean structure, and a second absorption Q
for the mode-converted seismic wave traveling from the subsurface
reflector to a seismic sensor.
4. The method of claim 3, further comprising computing an R
parameter that is equal to a total travel time divided by the
mode-converted absorption Q, wherein the total travel time is equal
to a sum of a travel time of the source seismic wave from the
seismic source to the subsurface reflector, and a travel time of
the mode converted seismic wave from the subsurface reflector to
the seismic sensor.
5. The method of claim 4, further comprising deriving an amplitude
transfer function to represent amplitude dissipation caused by the
absorption effect, wherein the amplitude transfer function is based
on the R parameter.
6. The method of claim 1, wherein processing the measured seismic
data comprises processing measured seismic data for a single-mode
P-wave to produce a first absorption Q for the single-mode P-wave,
the method further comprising processing further measured seismic
data for a single-mode S-wave to produce a second absorption Q for
the single-mode S-wave.
7. The method of claim 6, further comprising: determining a first
travel time of the source seismic wave from a seismic source to a
subsurface reflector in the subterranean structure; and determining
a second travel time of the mode-converted seismic wave from the
subsurface reflector to a seismic sensor.
8. The method of claim 7, further comprising computing an R.sub.P
parameter as a function of two times the first travel time based on
the absorption Q for the single-mode P-wave, and computing an
R.sub.S parameter as a function of two times the second travel time
based on the absorption Q for the single-mode S-wave.
9. The method of claim 8, further comprising: averaging the R.sub.P
and R.sub.S parameters to obtain an average R; and deriving an
amplitude transfer function based on the average R, wherein the
amplitude transfer function represents amplitude dissipation caused
by the absorption effect.
10. The method of claim 7, wherein determining the first and second
travel times are based on: (1) a total travel time of the source
seismic wave and the mode-converted seismic wave; and (2) velocity
functions of the P-wave and the S-wave.
11. An article comprising at least one storage medium containing
instructions that when executed cause a computer to: receive
measured data provided by at least one seismic sensor, the measured
data relating to a mode-converted seismic wave reflected from the
subterranean structure, the mode-converted seismic wave having a
mode different from a mode of a source seismic wave produced by a
seismic source; and apply an algorithm for deriving a single-mode
absorption parameter to compute an absorption parameter for the
mode-converted seismic wave based on the received measured
data.
12. The article of claim 11, wherein receiving the measured data
comprises receiving S-wave data that is reflected from the
subterranean structure in response to a source P-wave.
13. The article of claim 11, wherein receiving the measured data
comprises receiving P-wave data that is reflected from the
subterranean structure in response to a source S-wave.
14. The article of claim 11, wherein computing the absorption
parameter comprises computing an overall absorption Q that
represents a cumulative effect of a first absorption Q for the
source seismic wave and a second absorption Q for the
mode-converted seismic wave.
15. The article of claim 14, wherein the instructions when executed
cause the computer to further compute an R parameter that is equal
to total travel time of the source seismic wave and the
mode-converted seismic wave divided by the overall absorption
Q.
16. The article of claim 15, wherein the instructions when executed
cause the computer to further derive an amplitude transfer function
based on the R parameter, wherein the amplitude transfer function
is to be used in at least one of simulating an absorption effect of
the subterranean structure, and compensating for the absorption
effect of the subterranean structure.
17. A computer comprising: at least central processing unit (CPU);
and software executable on the at least one CPU to: process
measured seismic data using an algorithm for deriving a single-mode
absorption parameter; and compute a first absorption parameter for
a mode-converted seismic wave based on an output of the algorithm,
wherein the first absorption parameter represents an absorption
effect of the mode-converted seismic wave by the subterranean
structure, and wherein the mode-converted seismic wave is reflected
from the subterranean structure in response to a source seismic
wave of a different mode than the mode-converted seismic wave.
Description
TECHNICAL FIELD
[0001] The invention relates computing an absorption parameter for
a mode-converted seismic wave, where the mode-converted seismic
wave is reflected from a subterranean structure in response to a
source seismic wave of a different mode than the mode-converted
seismic wave.
BACKGROUND
[0002] Seismic surveying is used for identifying subterranean
elements, such as hydrocarbons, fresh water, and so forth. In
performing seismic surveying, seismic sources are placed at various
locations on an earth surface or sea floor (or in a wellbore), with
the seismic sources activated to generate seismic waves directed
into a subterranean structure. Examples of seismic sources include
explosives, air guns, or other sources that generate seismic
(acoustic) waves. In a marine environment, seismic sources and
sensors can be towed in water by a sea vessel.
[0003] The seismic waves generated by a seismic source travel into
the subterranean structure, with a portion of the seismic waves
reflected back to the surface (earth surface, sea floor, or
wellbore surface) for receipt by seismic sensors (e.g., geophones).
These seismic sensors produce signals that represent detected
seismic waves. Signals from the seismic sensors are processed to
yield information about the content and characteristic of the
subterranean structure.
[0004] As seismic waves travel through an earth formation, the
seismic waves are subject to dissipation due to conversion of the
energy of the seismic waves into heat by the earth formation. A
seismic wave typically has multiple frequencies. The dissipation
effect varies at different frequencies, with higher dissipation
occurring at higher frequencies of the seismic wave. As a result,
the seismic waves lose more amplitude at higher frequencies than at
lower frequencies.
[0005] Conventionally, when processing measured seismic data, an
inverse filtering technique is applied to correct the dissipation
(absorption) effects. Typically, the inverse filter increases
amplitudes of seismic waves at higher frequencies to counter the
dissipation effect.
[0006] There are two types of seismic waves: P-wave (also referred
to as a compression wave, which extends in the direction of
propagation of the seismic wave); and S-wave (also referred to as a
shear wave that extends in a direction generally perpendicular to
the direction of propagation of the seismic wave). The dissipation
(absorption) effect of a seismic wave is represented by an
absorption parameter Q, also referred to as a seismic quality
factor. Conventional techniques for estimating absorption
parameters typically compute pure-wave (or single-mode) absorption
parameters; in other words, a P-wave absorption parameter Q is
computed based on a P-wave reflected from a subterranean structure
in response to a source P-wave; and an S-wave absorption parameter
Q is estimated from an S-wave reflected from a subterranean
structure in response to a source S-wave. Techniques for surveying
subterranean structures based on estimating pure wave absorption Qs
suffer from reduced accuracy, since the surveying does not take
into account all available data.
SUMMARY
[0007] In general, according to an embodiment, a method of
surveying a subterranean structure includes processing measured
seismic data using an algorithm for deriving a single-mode
absorption parameter, and computing an absorption parameter for a
mode-converted seismic wave based on an output of the algorithm,
where the mode-converted seismic wave is reflected from the
subterranean structure in response to a source seismic wave of a
different mode then the mode-converted seismic wave.
[0008] Other or alternative features will become apparent from the
following description, from the drawings, and from the claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 is a schematic view of marine seismic surveying
arrangement in which some embodiments of the invention can be
employed.
[0010] FIGS. 2A-2B and 3A-3B illustrate examples of single-mode
seismic waves and mode-converted seismic waves.
[0011] FIG. 4 is a flow diagram of a process of computing an
absorption parameter using a technique according to an embodiment
of the invention.
[0012] FIG. 5 is a flow diagram of a process of computing an
estimated absorption parameter in accordance with another
embodiment of the invention.
[0013] FIG. 6 is a block diagram of an arrangement including a
computer in which some embodiments of the invention may be
implemented.
DETAILED DESCRIPTION
[0014] A seismic surveying technique according to some embodiments
is able to estimate an absorption parameter for a mode-converted
seismic wave based on output of a tool that applies an algorithm
for deriving a single-mode (pure wave) absorption parameter. The
absorption parameter (e.g., absorption Q) represents the absorption
(or dissipation) effect experienced by a seismic wave traveling
through a subterranean structure. An absorption Q is also referred
to as anelastic attenuation or seismic quality factor. Note that
the term "absorption parameter" can alternatively refer to an R
parameter, which is equal to travel time divided by absorption Q.
The R parameter is discussed further below.
[0015] Seismic waves have two modes: a compression mode in which
the seismic wave includes a P-wave or compression wave that extends
in the direction of propagation of the seismic wave; and a shear
mode in which the seismic wave is an S-wave or shear wave that
extends in a direction generally perpendicular to the direction of
propagation of the seismic wave. A source seismic wave produced by
a seismic source (e.g., an explosive, an air gun, etc.) is directed
into a subterranean structure, which can have a subsurface
reflector (e.g., an interface to a layer of hydrocarbons, a layer
of water, or another layer of interest). The seismic wave is
reflected from the subsurface reflector, where the reflected
seismic wave can be measured by a seismic sensor (or plural seismic
sensors) (e.g., geophones or other seismic sensors). In many cases,
mode conversion can occur upon reflection from the subsurface
reflector. For example, a source P-wave can be reflected as an
S-wave, or alternatively, a source S-wave can be reflected as a
P-wave. A reflected seismic wave that has a mode different than the
mode of the source seismic wave is referred to as a mode-converted
seismic wave.
[0016] Thus, a reflected S-wave produced from reflection of a
source P-wave is one example of a mode-converted seismic wave.
Similarly, a reflected P-wave produced from reflection of a source
S-wave is another example of a mode-converted seismic wave. Often,
a seismic wave reflected from a subterranean structure includes
both P-waves and S-waves. The mode-converted wave is the one of the
reflected P-waves and S-waves having a different mode from the
source seismic wave.
[0017] As noted above, a seismic surveying technique according to
some embodiments estimates absorption parameters for mode-converted
seismic waves, which allows the seismic surveying technique to take
into account absorption effects associated with mode-converted
seismic waves. Considering absorption effects of reflected
mode-converted seismic waves, as well as absorption effects of
reflected pure (or single-mode) seismic waves, allows the seismic
surveying technique to be more accurate than conventional surveying
techniques (which typically just compute pure wave absorption
parameters).
[0018] The surveying technique according to some embodiments can be
applied to marine seismic surveying, land seismic surveying, seabed
seismic surveying, and borehole (wellbore) seismic surveying. With
land seismic surveying, seismic sources and seismic sensors are
placed at the earth surface to survey the subterranean structure
underneath the earth surface. With seabed seismic surveying,
seismic sources and seismic sensors are placed on the sea floor to
survey a subterranean structure underneath the sea floor. With
borehole surveying, seismic sensors and/or sources are placed in
the borehole to survey a subterranean structure behind the wall of
the borehole.
[0019] FIG. 1 illustrates an example marine seismic surveying
environment. In FIG. 1, the subterranean structure includes
subterranean layers 102 and 104 underneath a sea floor (or seabed)
106. In some examples, the subterranean layer 102 can include an
earth formation, while the subterranean layer 104 can include a
hydrocarbon layer, a water layer, or some other layer of interest.
An interface 108 between the subterranean layers 102, 104 is a
subsurface reflector that reflects seismic waves.
[0020] FIG. 1 also shows a number of seismic sources 110 and
seismic sensors 112 in the body of water 118. The seismic sources
110 and seismic sensors 112 can be towed by a sea vessel 114 at the
sea surface 116. For example, the seismic sources 110 and seismic
sensors 112 can be attached to support cables (not shown) that are
connected to the sea vessel 114. A seismic source 110 creates
seismic waves in the body of water 118, and a portion of the
seismic waves travels downwardly through the body of water 118 and
into the subterranean layer 102. Some portion of the seismic waves
is reflected upwardly by the interface 108 between the subterranean
layers 102, 104. The reflected seismic waves can be received by the
seismic sensors 112, which produce measured seismic data to be
processed. The measured seismic data can be in the form of a
seismogram, a seismic trace, or in some other format.
[0021] If a computer 120 is provided on the sea vessel 114, then
the computer 120 can be used to process the seismic data produced
by the seismic sensors 112. Alternatively, the data recorded by the
seismic sensors 112 can be processed later when the sea vessel 114
returns to land. In yet another alternative, the sea vessel 114 can
communicate (such as by wireless communication) the measured
seismic data to a remote computer for processing at the remote
computer.
[0022] In other implementations, the seismic sources 110 and
seismic sensors 112 can be located on the sea floor 106, instead of
being towed by the sea vessel 114. In a land surveying context, the
seismic sources 110 and seismic sensors 112 are provided on the
earth surface. In a borehole surveying context, the seismic sources
110 and/or seismic sensors 112 are positioned in the borehole.
[0023] As noted above, a reflected seismic wave can be a
mode-converted seismic wave that has a different mode then the
source seismic wave. For example, in FIG. 2A, a seismic source 110
produces a source P-wave that is reflected from a subsurface
reflector 200 (e.g., interface 108 in FIG. 1) as a reflected S-wave
(mode-converted seismic wave), where the reflected S-wave is
detected by a seismic sensor 112. This is contrasted to the
scenario of FIG. 2B, where a source P-wave generated by the seismic
source 110 is reflected by the seismic reflector 200 as a reflected
P-wave.
[0024] Similarly, as depicted in FIG. 3A, a source S-wave produced
by a seismic source 110 can be reflected by the subsurface
reflector 200 as a reflected P-wave (mode-converted seismic wave)
that is detected by the seismic sensor 112. On the other hand, FIG.
3B shows a reflected S-wave reflected from the subsurface reflector
200 in response to a source S-wave.
[0025] FIGS. 2B and 3B are examples of single-mode scenarios, since
the reflected wave in each case has the same mode as the source
wave. On the other hand, FIGS. 2A and 3A are examples of
mode-converted (or mixed) scenarios, since the reflected wave in
each case has a different mode than the source wave.
[0026] Both the source seismic wave and the reflected seismic wave
are subject to absorption (dissipation) effects caused by
transformation of the energy of the seismic waves to heat by
subterranean formation(s) through which the seismic waves
propagate. Each of the source and reflected seismic waves is
associated with a respective absorption parameter (e.g., absorption
Q).
[0027] Eq. 1 below defines an amplitude function A.sub.R(f) of a
seismic wave, where the amplitude function is dependent upon both
frequency (f) and R (which depends upon Q(t)).
A R ( f ) = exp ( sgn .pi. fR ) , ( Eq . 1 ) R = t Q ( t ) . ( Eq .
2 ) ##EQU00001##
[0028] Q(t) represents the absorption Q that is a function of
travel time of the seismic wave. The value t is the total travel
time in both directions (the travel time of the source seismic wave
to the subsurface reflector 200, plus the travel time of the
reflected seismic wave from the reflector to the seismic sensor).
The parameter R is calculated according to Eq. 2 above, with R
being a value equal to t (total travel time) divided by Q(t). It is
noted that the term "absorption parameter" refers to either the
absorption Q, represented by Q(t), or R. The amplitude transfer
function defines how the absorption effects of the subterranean
structure reduce amplitudes of seismic waves at different
frequencies f.
[0029] The phase function of the seismic data is as expressed as
follows:
.PHI. R ( f ) = sgn 2 f ln ( f c f ) R . ( Eq . 3 )
##EQU00002##
[0030] The phase function defines how the absorption effects of the
subterranean structure changes the phase of the seismic wave. In
both Eqs. 1 and 3 above, the value of "sgn" varies depending upon
the application of the amplitude function A.sub.R(f) and the phase
function .phi..sub.R(f). The value of "sgn" is -1 if the amplitude
and phase functions are used for absorption simulation (to simulate
the absorption effects of a subterranean structure on the source
and reflected seismic waves). On the other hand, the value of "sgn"
is equal to +1 when the amplitude and phase functions are used for
correction of measured seismic data (i.e., when A.sub.R(f ) and
.phi..sub.R(f) are used as inverse filters to be applied to the
measured seismic data to compensate for absorption effects).
[0031] Once Q(t) is known, then R can be derived according to Eq.
2, and from R, the transfer and phase functions can be implemented
as respective compensation filters (inverse filters) to be applied
to measured seismic data to compensate for absorption effects,
where the absorption effects are represented by Q(t) or R. Note
that according to Eq. 1, absorption increases (amplitude decreases)
with both frequency and two-way travel time. Similarly, as
indicated by Eq. 3, phase velocity increases with frequency up to
an upper cut-off frequency f.sub.c and is constant thereafter.
[0032] Eqs. 1 and 3 above express amplitude and phase functions in
the single-mode scenario (where absorption Q is the same in both
the direction of propagation of a source seismic wave and a
direction of propagation of the reflected seismic wave). However,
in the mixed or mode-converted scenario, as depicted in FIGS. 2A
and 3A, the equations have to be modified somewhat to account for
the fact that the absorption Q for the mode-converted seismic wave
is different from the absorption Q for the source seismic wave.
However, it is noted that mode-converted absorption follows
identical mathematical rules as single-mode absorption. The
absorption effects for the source seismic wave and the reflected
mode-converted seismic wave are cumulative; in other words, the
absorption effect for the source seismic wave traveling from the
surface to the subsurface reflector, and the absorption effect of
the reflected seismic wave traveling back from the subsurface
reflector to the surface, are cumulative, in the sense that the
overall absorption can be described by the multiplication of both
the amplitude transfer function associated with the source seismic
wave and the amplitude transfer function for the reflected,
mode-converted seismic wave.
[0033] For example, assuming the source seismic wave is a P-wave,
and the reflected, mode-converted seismic wave is an S-wave, then
the amplitude function in this mixed scenario is represented as
follows:
A ( f ) = exp ( sgn .pi. f R P ( 2 t P ) 2 ) exp ( sgn .pi. f R S (
2 t S ) 2 ) = exp ( sgn .pi. fR PS ( t PS ) ) , where ( Eq . 4 ) R
PS ( t PS ) = R P ( 2 t P ) + R S ( 2 t S ) 2 , and ( Eq . 5 ) t PS
= t P + t S . ( Eq . 6 ) ##EQU00003##
[0034] Eq. 4 replaces R in Eq. 1 with R.sub.PS, where R.sub.PS
represents the mode-converted absorption parameter R. Eq. 5
indicates that R.sub.PS is made up of the average of R.sub.P and
R.sub.S Eq. 5 provides the link between the effective
mode-converted absorption parameter R.sub.PS (based on the total
travel time of the P-wave and the S-wave) and the P-wave R.sub.P
and S-wave R.sub.S as functions of two-way travel times (2t.sub.P
and 2t.sub.S). The total travel time t.sub.PS is the sum of the
travel time (t.sub.p) of the source P-wave, and the travel time
(t.sub.s) of the mode-converted S-wave, as expressed in Eq. 6
above.
[0035] Eqs. 4-6 thus describe the absorption effects for a seismic
wave traveling down to the subsurface reflector as a P-wave for a
one-way travel time t.sub.P, undergoing one-way absorption
described in terms of the ratio of the two-way P-wave travel time
2t.sub.P and Q for P-waves (represented by Q.sub.P(2t.sub.P)), and
traveling upwardly to the seismic sensor for a certain one-way
travel time t.sub.S, undergoing one-way absorption described in
terms of the ratio of the two-way S-wave travel time (2t.sub.S) and
the Q for S-waves (represented by Q.sub.S(2t.sub.S)). It is noted
that
R P ( 2 t P ) = 2 t P Q ( 2 t P ) , and R S ( 2 t S ) = 2 t S Q ( 2
t S ) . ##EQU00004##
Note also that the functions R.sub.P and R.sub.S together describe
two-way absorption.
[0036] The phase function for the mixed scenario can be similarly
derived such that
.PHI. ( f ) = sgn 2 f ln ( f c f ) R PS ( 2 t PS ) , ( Eq . 7 )
##EQU00005##
where Eq. 7 differs from Eq. 3 in that R in Eq. 3 has been replaced
with R.sub.PS in Eq. 7. (In the reverse scenario where the source
seismic wave is an S-wave, and the reflected mode-converted seismic
wave is a P-wave, then the parameters above are replaced as
follows: R.sub.PS.fwdarw.R.sub.SP, and
t.sub.PS.fwdarw.t.sub.SP).
[0037] From the foregoing, it can be seen that the amplitude and
phase functions for the mode-converted scenario can be readily
derived once the absorption parameter R.sub.PS is derived. As
described above, mode-converted absorption follows identical
mathematical rules as single-mode absorption. Therefore, in
accordance with some embodiments, R.sub.PS can be derived from
measured seismic data (e.g., seismogram, seismic trace, etc.) for
the mode-converted seismic wave using single-mode absorption
parameter estimation techniques.
[0038] FIG. 4 shows a process of characterizing absorption effects
in a mixed scenario (mode converted scenario). First, measurement
data of the mode-converted seismic wave is received (at 202). Next,
the absorption Q for the mode-converted seismic wave is estimated
(at 204), using a single-mode (or pure wave) Q estimation
technique. There are various known single-mode Q estimation
techniques, including those described in WO 2006/025824, entitled
"Method for Estimating Absorption Parameter Q(T)," published Mar.
9, 2006, by Ralf Ferber. In other implementations, other
single-mode Q estimation techniques can be employed.
[0039] The mode-converted absorption Q estimated at 204 is
represented as Q.sub.PS (for the case where the source seismic wave
is a P-wave, and the reflected seismic wave is an S-wave). From
Q.sub.PS, the mode-converted absorption parameter R.sub.PS can be
computed (at 206) as follows:
R PS ( t PS ) = t PS Q ( t PS ) . ##EQU00006##
[0040] Once R.sub.PS(t.sub.PS) is known, the amplitude and phase
functions for the mode converted scenario can be derived (at 208),
according to Eqs. 4 and 7 above. As noted above, the amplitude and
phase functions can be used to perform either simulation to
characterize absorption effects of a subterranean structure, or to
build inverse filters to correct measured seismic data to
compensate for absorption effects.
[0041] FIG. 5 shows another technique of characterizing absorption
effects in a mode-converted scenario, according to an alternative
embodiment. In this alternative embodiment, the mode-converted
seismic wave Q is estimated from the P-wave Q and the S-wave Q
(from which the P-wave R and S-wave R can be readily derived
according to Eq. 2). Thus, according to the FIG. 5 embodiment, the
P-wave Q is computed (at 302) from P-wave measurement data, and the
S-wave Q is computed (at 304) from the S-wave measurement data.
Note that both the P-wave Q and the S-wave Q are single-mode
absorption Qs, which are both estimated using single-mode Q
estimation techniques, such as those described in WO
2006/025824.
[0042] From the P-wave Q and the S-wave Q, the values of R.sub.P
and R.sub.S can be respectively derived (at 306). Assume further
that the travel time t.sub.PS is available for the mode-converted
seismic wave. From the above-data, the mode-converted wave
absorption parameter R.sub.PS is computed (at 308) from the P-wave
and S-wave absorption parameters R.sub.P and R.sub.S according to
Eq. 5 above.
[0043] Note, however, that Eq. 5 requires that the one-way travel
times, t.sub.P and t.sub.S have to be computed. To compute the
one-way travel times, t.sub.P and t.sub.S, from the two-way travel
time t.sub.PS, the average P-wave and the S-wave two-way travel
time velocity functions V.sub.P(t) and V.sub.S(t) are needed. The
one-way P-wave travel time can be determined by solving the
following equation for t.sub.P:
t P V P ( 2 t P ) - t PS - T P V S ( 2 ( t PS - t P ) ) = 0. ( Eq .
8 ) ##EQU00007##
Eq. 8 above has just the P-wave one-way travel time t.sub.P as an
unknown, and can be solved by a line search algorithm or some other
technique. Once t.sub.P is known, the S-wave travel time t.sub.S
can be readily derived according to Eq. 9 below:
t.sub.S=t.sub.PS-t.sub.P. (Eq. 9)
Both one-way travels times t.sub.P and t.sub.S are then used to
compute R.sub.PS(t.sub.PS) using Eq. 5. Having computed
R.sub.PS(t.sub.PS), the mode-converted seismic wave Q function can
be derived as follows:
Q PS ( t ) = t PS R PS ( t PS ) . ( Eq . 10 ) ##EQU00008##
[0044] In addition, as with the technique of FIG. 4, the amplitude
and phase functions can be derived (at 310) once R.sub.PS is
known.
[0045] More generally, with either of the FIG. 4 or FIG. 5
technique, measured seismic data is processed using an algorithm
for deriving a single-mode absorption parameter. In the FIG. 4
technique, the measured seismic data processed is the measured
mode-converted seismic data. In the FIG. 5 technique, the measured
seismic data processed is the measured single-mode P-wave data and
S-wave data. Based on an output of the algorithm for deriving a
single-mode absorption parameter, an absorption parameter for a
mode-converted seismic wave is computed, wherein the mode-converted
absorption parameter represents an absorption effect of the
mode-converted seismic wave by the subterranean structure.
[0046] FIG. 6 shows an example of computer 400 in which an
absorption effect characterization module 402 according to some
embodiments can be executed. The absorption effect characterization
module 402 can perform the tasks represented by either FIG. 4 or 5.
The absorption effect characterization module 402 is able to invoke
a single-mode wave absorption parameter estimation module 404 to
compute desired values, as discussed above. Both modules 402 and
404, which can be implemented in software, are executed on one or
more central processing units (CPUs) 406, which are connected to a
storage 408 (e.g., volatile memory or persistent storage). The
storage 408 can store measurement data 410, such as seismic
measurement data.
[0047] Data and instructions (of the software modules discussed
above) are stored in respective storage devices, which are
implemented as one or more computer-readable or computer-usable
storage media. The storage media include different forms of memory
including semiconductor memory devices such as dynamic or static
random access memories (DRAMs or SRAMs), erasable and programmable
read-only memories (EPROMs), electrically erasable and programmable
read-only memories (EEPROMs) and flash memories; magnetic disks
such as fixed, floppy and removable disks; other magnetic media
including tape; and optical media such as compact disks (CDs) or
digital video disks (DVDs).
[0048] While the invention has been disclosed with respect to a
limited number of embodiments, those skilled in the art will
appreciate numerous modifications and variations there from. It is
intended that the appended claims cover such modifications and
variations as fall within the true spirit and scope of the
invention.
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