CN115079254A - VSP up-down traveling wave separation method based on Radon domain AWT - Google Patents

VSP up-down traveling wave separation method based on Radon domain AWT Download PDF

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CN115079254A
CN115079254A CN202210554725.XA CN202210554725A CN115079254A CN 115079254 A CN115079254 A CN 115079254A CN 202210554725 A CN202210554725 A CN 202210554725A CN 115079254 A CN115079254 A CN 115079254A
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刘彦萍
杨飞龙
马征
唐炎敏
张英
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Abstract

The invention discloses a method for separating vertical traveling wave (VSP) from vertical traveling wave (VSP) based on Radon domain anisotropic wavelet transform, and relates to the field of seismic exploration. The invention comprises the following steps: reading VSP data by adopting Matlab software; transforming the VSP data from a time-space domain to a time intercept-slowness domain by adopting a linear Radon transform; performing anisotropic wavelet transform on a Radon domain to obtain a decomposition coefficient matrix, and realizing sparse representation of wave field information of upper and lower traveling waves in VSP data; and dividing and extracting the decomposition coefficient matrix, respectively reserving the coefficient matrixes representing the upgoing wave and the downgoing wave, respectively carrying out anisotropic wavelet transformation reconstruction on the coefficient matrixes representing the upgoing wave and the downgoing wave in a Radon domain, and then carrying out Radon inverse transformation to obtain the upgoing wave and the downgoing wave field. The method can more thoroughly separate the up-going wave field and the down-going wave field in the VSP data, and the in-phase axes in the wave field record are clearer and more coherent.

Description

VSP up-down traveling wave separation method based on Radon domain AWT
Technical Field
The invention relates to the field of seismic exploration, in particular to a VSP up-down traveling wave separation method based on Radon domain Anisotropic Wavelet Transform (AWT).
Background
Conventional Seismic exploration is a means for exciting Seismic waves on the ground and arranging detectors on the ground for receiving, but with the increase of the difficulty of oil field exploration and development, the accuracy of Seismic data obtained by the conventional Seismic exploration is far from meeting the exploration requirement, so that a Vertical Seismic Profiling (VSP) (vertical Seismic profiling) method is researched. The seismic detector is a refined seismic exploration technology, and adopts a method that the detector is vertically placed downwards along a well hole and receives seismic waves in a stratum. The seismic data acquired by the method has the obvious advantages of high signal-to-noise ratio, high resolution, rich wave field information and the like. In the VSP, because the detector is vertically arranged in the stratum downwards along a borehole, longitudinal waves, converted waves and even transverse waves can be received, the most direct corresponding relation between the underground structure and the ground parameter measurement can be provided, an accurate time-depth conversion and velocity model is provided for the ground seismic data processing and interpretation, the geological horizon of a seismic reflecting layer is reliably identified, and the obtained data is utilized to research the lithology of the stratum and the physical property of the reservoir stratum. Therefore, VSP technology is very important in both exploration and development.
In the original VSP data, wave field information is rich, and the situation is complex. Including both up-going and down-going waves, it is very difficult to directly interpret the formation with VSP data. Therefore, the VSP wave field is separated in a high fidelity mode to fully reflect the wave field characteristics of different waves, and therefore geological horizon calibration, lithology, reservoir physical property explanation and the like can be better conducted. Therefore, up-down traveling wave separation is a key in VSP data processing, and an up-down traveling wave separation method with a better research effect is an important subject. The existing VSP data up-down traveling wave separation method, such as a linear Radon transformation separation method and a Curvelet transformation separation method, has certain limitation, so that the separation effect is not good.
Disclosure of Invention
In view of the above, the invention provides a VSP up-down traveling wave separation method based on Radon domain AWT.
In order to achieve the purpose, the invention adopts the following technical scheme:
a VSP up-down traveling wave separation method based on Radon domain AWT comprises the following steps:
reading VSP data by adopting Matlab software;
transforming VSP data from a time-space t-z domain to a time intercept-slowness tau-p domain by adopting a linear Radon transform;
performing AWT on a Radon transform domain to obtain a decomposition coefficient matrix, and realizing sparse representation of up-and-down traveling wave field information in VSP data;
and dividing and extracting the Radon domain AWT decomposition coefficient matrix, reserving a coefficient representing the information of the upgoing wave field, performing AWT reconstruction on the reserved coefficient, and performing Radon inverse transformation to obtain the upgoing wave field.
Optionally, the method further includes dividing and extracting the decomposition coefficient matrix, reserving a coefficient representing the information of the downlink wave field, performing AWT reconstruction on the reserved coefficient, and then performing Radon inverse transformation to obtain the downlink wave field.
Optionally, a linear Radon transform is used to transform VSP data from the t-z domain to the τ -p domain, which is performed as follows:
let u (t, z) be the VSP raw data, where t is time and z is offset; u (tau, p) is tau-p domain data after Radon transformation, wherein tau-t-pz is a time intercept, and p-dt/dz is a ray parameter; the positive transformation equation of tau-p is:
Figure BDA0003651912930000021
optionally, the AWT formula is as follows:
Figure BDA0003651912930000022
wherein x is [ x ] 1 x 2 ] T Is a number on the x-axis of the plane rectangular coordinate, b ═ b 1 b 2 ] T Are respectively x 1 、x 2 The displacement of the direction, a being the scale factor,
Figure BDA0003651912930000031
is a twiddle factor; ε is the attenuation factor, φ ε Is an anisotropic two-dimensional wavelet basis function.
Optionally, an anisotropic two-dimensional wavelet basis function phi ε The mathematical expression of (a) is as follows:
Figure BDA0003651912930000032
where y represents a number on the y-axis of the planar rectangular coordinate.
Performing AWT on a tau-p domain obtained by Radon transformation, namely substituting tau-p domain data into a formula (3), namely substituting x and y in the formula (3) by tau and p; the resulting basis functions are then substituted into equation (2), and in this case f (x) in equation (2) is replaced by U (τ, p) and x is replaced by τ.
Optionally, the AWT reconstruction formula is as follows:
Figure BDA0003651912930000033
wherein the content of the first and second substances,
Figure BDA0003651912930000034
ω is a frequency variable.
Then, dividing the Radon domain AWT decomposition coefficient matrix, respectively extracting the coefficient matrixes corresponding to the up-going wave field information and the down-going wave field information, and respectively performing AWT reconstruction on the coefficients representing the up-going wave and the down-going wave according to a formula (4) to respectively obtain tau-p domain data of the up-going wave and the down-going wave;
the formula for the inverse Radon transform is as follows:
Figure BDA0003651912930000035
and then respectively carrying out Radon inverse transformation on tau-p domain data corresponding to the uplink wave and the downlink wave according to a formula (5) to obtain t-z domain data of the uplink wave and the downlink wave.
According to the technical scheme, compared with the prior art, the invention discloses the method for separating the up-going wave and the down-going wave of the VSP based on the Radon domain AWT. And then the method is applied to the separation processing of up-going and down-going waves of the actual VSP data, and compared with the separation result of the traditional linear Radon transformation method, the method is found to be superior to the traditional linear Radon transformation separation method, the up-going and down-going wave fields in the actual VSP data can be separated more thoroughly, and the in-phase axes in the wave fields are clearer and coherent.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a diagram of a model-VSP raw record of the present invention;
FIG. 3 is the up-going wave separated by a linear Radon transform method of the model of the present invention;
FIG. 4 is a diagram of the downgoing wave separated by a linear Radon transform method according to the model of the present invention;
FIG. 5 is the upgoing wave separated by the Curvelet transform method, a model of the present invention;
FIG. 6 is a diagram of the down-going wave separated by the Curvelet transform method, a model of the present invention;
FIG. 7 is a diagram of an upgoing wave separated based on Radon domain AWT method in a model I of the present invention;
FIG. 8 shows a model of the present invention, i.e., a down-going wave separated based on Radon domain AWT method;
FIG. 9 is a graph of the original record of model two VSP of the present invention;
FIG. 10 shows the up-going wave separated by the model two-linear Radon transform method of the present invention;
FIG. 11 shows the down-going wave separated by the model two-linear Radon transform method of the present invention;
FIG. 12 shows the upgoing wave separated by the model two Curvelet transform method according to the present invention;
FIG. 13 shows the downgoing wave separated by the model two Curvelet transform method according to the present invention;
FIG. 14 shows the upgoing wave separated by the Radon domain AWT method according to the second model of the present invention;
FIG. 15 shows a second model of the present invention based on a Radon domain AWT method to separate a downlink wave;
FIG. 16 is a graph of a model three VSP raw record of the present invention;
FIG. 17 is an up-going wave separated by the model trilinear Radon transform of the present invention;
FIG. 18 is the downgoing wave separated by the model trilinear Radon transform of the present invention;
FIG. 19 is the up-going wave separated by the model three Curvelet transform method of the present invention;
FIG. 20 shows the down-going wave separated by the model three Curvelet transform method of the present invention;
FIG. 21 shows the up-going wave separated by the Radon domain AWT method according to the third model of the present invention;
FIG. 22 shows a third model of the present invention, which is based on the down-going wave separated by Radon domain AWT method;
FIG. 23 is an original record of VSP actual data of the present invention;
FIG. 24 is a record of the up-going waves of VSP actual data processed by the linear Radon transform method according to the present invention;
FIG. 25 is a downlink recording of the present invention using a linear Radon transform to process VSP real data;
FIG. 26 is a graph of the present invention illustrating the upgoing wave recording of VSP actual data processed by the Radon domain AWT method;
FIG. 27 is a downlink recording of the present invention using the Radon domain AWT based method to process VSP real data.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a method for separating up and down traveling waves of a VSP (vertical seismic profiling) based on Radon domain AWT (active wavelet transform), which specifically comprises the following steps of:
step 1: reading VSP data by adopting Matlab software;
step 2: transforming the VSP data from a t-z domain to a tau-p domain by adopting a linear Radon transform;
let u (t, z) be the VSP raw data, where t is time and z is offset. U (τ, p) is τ -p domain data after Radon transform, where τ -t-pz is the time intercept, p-dt/dz is the ray parameter (or apparent slowness), which is the inverse of apparent velocity.
The positive transformation of τ -p is:
Figure BDA0003651912930000061
and step 3: performing Anisotropic Wavelet Transform (AWT) on a Radon domain to obtain a decomposition coefficient matrix, so as to realize sparse representation of up and down traveling wave field information in VSP data;
because: a continuous two-dimensional wavelet transform can be generally defined as
Figure BDA0003651912930000062
In the above formula, x ═ x 1 x 2 ] T Is a number on the x-axis of the plane rectangular coordinate, b ═ b 1 b 2 ] T Are respectively x 1 、x 2 The displacement of the direction, a being the scale factor,
Figure BDA0003651912930000063
is a twiddle factor; ε is the attenuation factor, φ ε Is an anisotropic two-dimensional wavelet basis function.
The attenuation factor epsilon can make the two-dimensional wavelet base protrude the dimension along any direction, thereby realizing the aim of anisotropy. The anisotropic two-dimensional wavelet basis functions are:
Figure BDA0003651912930000064
wherein y is a number on the y-axis of the planar rectangular coordinate.
In summary, the formula for AWT is:
Figure BDA0003651912930000065
performing AWT on a tau-p domain obtained by Radon transformation, namely substituting tau-p domain data into a formula (3), namely substituting x and y in the formula (3) by tau and p; the resulting basis functions are then substituted into equation (4), and in this case f (x) in equation (4) is replaced by U (τ, p) and x is replaced by τ.
And 4, step 4: and dividing and extracting the Radon domain AWT decomposition coefficient matrix, respectively retaining the coefficient matrixes corresponding to the up-going wave field information and the down-going wave field information, respectively carrying out AWT reconstruction on the coefficients representing the up-going wave and the down-going wave, and then carrying out Radon inverse transformation to respectively obtain the up-going wave field and the down-going wave field.
The AWT reconstruction formula is:
Figure BDA0003651912930000071
wherein the content of the first and second substances,
Figure BDA0003651912930000072
ω is a frequency variable.
Then, after the field coefficients of the upgoing wave and the downgoing wave are divided and extracted from the AWT decomposition coefficient matrix in the Radon domain, AWT reconstruction is respectively carried out on the coefficients representing the upgoing wave and the downgoing wave according to a formula (5), and tau-p domain data of the upgoing wave and the downgoing wave are obtained.
The formula for the inverse Radon transform is as follows:
Figure BDA0003651912930000073
and respectively carrying out Radon inverse transformation on the tau-p domain data of the up-going wave and the down-going wave according to a formula (6) to obtain t-z domain data of the up-going wave and the down-going wave.
With reference to fig. 2-27, it can be seen that a Radon domain AWT up-down traveling wave separation method is verified by applying VSP theoretical model experiments under different conditions such as horizontal strata, inclined strata, interwell earthquakes and the like, and compared with a linear Radon transformation method and a Curvelet transformation method in the conventional separation method, the result shows that tau-p domain energy is diverged due to the influence of spurious frequency and truncation effect, and up-down traveling wave energy and down-down traveling wave energy are mutually influenced, so that the VSP up-down traveling wave separation is not thorough, and the definition and continuity of the same phase axis are influenced; although the upper and lower traveling waves can be separated by adopting a Curvelet transformation method, compared with the original VSP record, the obtained wave field profile has fuzzy in-phase axis, the effective signal is subjected to frequency reduction, and the in-phase axis of the upper and lower traveling waves has a more serious distortion phenomenon; by adopting the Radon domain AWT method, the up-and-down traveling wave fields of the VSP can be separated more thoroughly, and the in-phase axis information is kept better, so that the in-phase axes of the up-and-down traveling waves are clear and coherent. Therefore, the method provided by the patent is superior to the traditional linear Radon transformation method and Curvelet transformation method in the separation effect of the up-going wave and the down-going wave. Finally, the method is applied to separation processing of up-going waves and down-going waves of actual VSP data, and compared with a separation result of a traditional linear Radon transformation method, the method is found to be superior to the traditional linear Radon transformation method, namely, up-going waves and down-going waves in the actual VSP data can be separated more thoroughly, wave field characteristics are obvious, and the up-going waves and the down-going waves are clear and coherent in phase axes. The advantages of the method in the aspect of VSP up-down traveling wave separation processing are verified through simulation data experiments and actual data processing.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant part can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (6)

1. A VSP up-down traveling wave separation method based on Radon domain AWT is characterized by comprising the following steps:
reading VSP data by adopting Matlab software;
transforming the VSP data from a time-space domain to a time intercept-slowness domain by adopting a linear Radon transform;
performing Anisotropic Wavelet Transform (AWT) on a Radon domain to obtain a decomposition coefficient matrix, and realizing sparse representation of up and down traveling wave field information in VSP data;
and dividing and extracting a coefficient matrix obtained by AWT decomposition in a Radon domain, reserving a coefficient representing the information of the upgoing wave field, performing AWT reconstruction on the reserved coefficient, and then performing Radon inverse transformation to obtain the upgoing wave field.
2. The VSP up-down traveling wave separation method based on Radon domain AWT as claimed in claim 1, further comprising dividing and extracting a decomposition coefficient matrix, retaining coefficients representing down-going wave field information, performing AWT reconstruction on the retained coefficients, and performing Radon inverse transformation to obtain a down-going wave field.
3. The VSP up-down traveling wave separation method based on Radon domain AWT as claimed in claim 1, wherein the VSP data is transformed from time-space domain to time intercept-slowness domain by linear Radon transform as follows:
let u (t, z) be the VSP raw data, where t is time and z is offset; u (tau, p) is tau-p domain data after Radon transformation, wherein tau-t-pz is a time intercept, and p-dt/dz is a ray parameter; the positive transformation equation of tau-p is:
Figure FDA0003651912920000011
4. the method of claim 1, wherein the AWT formula is as follows:
Figure FDA0003651912920000012
wherein x is [ x ] 1 x 2 ] T Is a number on the x-axis of the plane rectangular coordinate, b ═ b 1 b 2 ] T Are respectively x 1 、x 2 The displacement of the direction, a being the scale factor,
Figure FDA0003651912920000021
is a twiddle factor; ε is the attenuation factor, φ ε Is an anisotropic two-dimensional wavelet basis function.
5. The method of claim 4, wherein the anisotropic two-dimensional wavelet basis function phi is a two-dimensional wavelet basis function ε The mathematical expression of (a) is as follows:
Figure FDA0003651912920000022
AWT is carried out on a tau-p domain obtained by Radon transformation, namely tau-p domain data are substituted into a formula (3), namely x and y in the formula (3) are replaced by tau and p; the resulting basis functions are then substituted into equation (2), and in this case f (x) in equation (2) is replaced by U (τ, p) and x is replaced by τ.
6. The method of claim 1, wherein the AWT reconstruction formula is as follows:
Figure FDA0003651912920000023
wherein the content of the first and second substances,
Figure FDA0003651912920000024
ω is a frequency variable;
then, dividing the coefficient matrix obtained by AWT decomposition in the Radon domain, respectively extracting the coefficient matrixes corresponding to the wave field information of the uplink wave and the downlink wave, and respectively carrying out AWT reconstruction on the coefficients representing the uplink wave and the downlink wave according to a formula (4) to respectively obtain tau-p domain data of the uplink wave and the downlink wave;
the formula for the inverse Radon transform is as follows:
Figure FDA0003651912920000025
and then respectively carrying out Radon inverse transformation on tau-p domain data corresponding to the uplink wave and the downlink wave according to a formula (5) to obtain t-z domain data of the uplink wave and the downlink wave.
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CN116561481A (en) * 2023-05-10 2023-08-08 广东海洋大学 Speed analysis method for AVO effect

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116561481A (en) * 2023-05-10 2023-08-08 广东海洋大学 Speed analysis method for AVO effect
CN116561481B (en) * 2023-05-10 2023-12-19 广东海洋大学 Speed analysis method for AVO effect

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