CN113805225A - Phase-constrained high-resolution seismic inversion method and computer equipment - Google Patents

Phase-constrained high-resolution seismic inversion method and computer equipment Download PDF

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CN113805225A
CN113805225A CN202110924824.8A CN202110924824A CN113805225A CN 113805225 A CN113805225 A CN 113805225A CN 202110924824 A CN202110924824 A CN 202110924824A CN 113805225 A CN113805225 A CN 113805225A
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phase
seismic
inversion
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裴松
印兴耀
李坤
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China University of Petroleum East China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/282—Application of seismic models, synthetic seismograms
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/30—Analysis
    • G01V1/307—Analysis for determining seismic attributes, e.g. amplitude, instantaneous phase or frequency, reflection strength or polarity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/63—Seismic attributes, e.g. amplitude, polarity, instant phase

Abstract

The invention relates to the field of geophysical oil-gas exploration, and particularly discloses a phase-constrained high-resolution seismic inversion method and computer equipment. The method comprises the following steps: step 1, deducing a linear relation between an instantaneous seismic phase and a reflection coefficient; step 2, establishing a phase-constrained seismic inversion target functional; and 3, solving an inversion reflection coefficient and an inversion longitudinal wave impedance through a phase-constrained seismic inversion target functional. According to the method, the linear relation between the seismic instantaneous phase and the reflection coefficient is deduced, the seismic inversion target functional constrained by the instantaneous phase is established, the inversion result resolution can be effectively improved, more effective parameter prediction can be carried out on a weak reflection area, and effective data support is provided for the high-resolution inversion of the underground parameters.

Description

Phase-constrained high-resolution seismic inversion method and computer equipment
Technical Field
The invention relates to the field of geophysical oil and gas exploration, in particular to a high-resolution seismic inversion method with phase constraint.
Background
Seismic inversion is an important means for predicting subsurface parameters by using seismic data acquired by artificial earthquakes. However, the bandwidth of the frequency band of the seismic data is limited, which is reflected by the lack of high-frequency and low-frequency components in the seismic data, which results in the lack of high-frequency details in the parameter prediction results obtained by the conventional inversion method. Therefore, the underground parameters can be effectively predicted more accurately by improving the resolution of the seismic inversion result. Secondly, a weak reflection area often exists in a seismic section, and for a conventional method, the underground parameter prediction is more difficult due to the existence of the weak reflection area, so in recent years, high-resolution seismic inversion and the weak reflection area parameter prediction are always important points of interest in the industry.
In recent years, many scholars have studied and tried high-resolution inversion methods, such as frequency domain inversion, matching pursuit inversion, and markov chain monte carlo model inversion. However, how to effectively utilize the phase information to constrain seismic inversion still remains the focus of research in the field of seismic inversion. At present, the seismic high-resolution inversion method mainly focuses on seismic signal frequency information or solves a target functional of seismic inversion by using different algorithms. For a frequency domain seismic inversion method, the problems of limited inversion result resolution improvement effect, weak identification capability of weak reflection areas and the like exist. For iterative algorithms such as matching pursuit, random inversion and the like, the excessively high calculation cost is prohibitive.
Disclosure of Invention
Therefore, the invention develops a phase-constrained high-resolution seismic inversion method, and the instantaneous phase-constrained seismic inversion target functional is established by deducing the linear relation between the seismic instantaneous phase and the reflection coefficient, so that the parameter prediction of a weak reflection area is realized and the inversion resolution is improved.
In order to solve the technical problems, the invention adopts the technical scheme that:
a phase constrained high resolution seismic inversion method comprising the steps of:
step 1, deducing a linear relation between an instantaneous seismic phase and a reflection coefficient;
step 2, establishing a phase-constrained seismic inversion target functional;
and 3, solving an inversion reflection coefficient and an inversion longitudinal wave impedance through a phase-constrained seismic inversion target functional.
Preferably, the step 1 comprises:
and (3) setting a time domain seismic signal as S (t), a time domain seismic wavelet matrix as W (t), a time domain reflection coefficient as m (t) and time domain noise as N (t), and then expressing a time domain convolution model as:
S(t)＝W(t)m(t)+N(t) (1)，
on the basis of the time domain convolution model of the formula (1), the instantaneous phase formula of the seismic signals is expressed as follows:
P(t)＝tan-1(Im(H(W(t)m(t)))/Re(H(W(t)m(t)))) (2)，
in formula (2), p (t) is the instantaneous phase of the seismic signal, H (×) represents the hilbert transform, Im (×) is the imaginary part, Re (×) is the real part;
as is clear from the formula (1), Im (H (W (t) m (t))) in the formula (2) can be rewritten as:
Im(H(W(t)m(t)))＝Im(H(S(t))) (3)，
equation (3) is to perform 90 degree phase filtering on the seismic signals,
the hilbert transform of a seismic signal is considered to be the result of the convolution of a 90 ° filtered wavelet with the reflection coefficients, i.e.:
Im(H(W(t)*m(t)))＝Im(H(S(t)))＝Im(H(W(t)))*m(t) (4)，
in the formula (4), a value represents a convolution operator.
Let GHA matrix representing Im (H (W)) wavelets, with equation (2) rewritten as:
P(t)＝tan-1(GHm(t)/S(t)) (5)，
the formula (5) is simplified to obtain:
Figure BDA0003208879980000031
in formula (6), p (t) tan-1(GSHm (t) is a signal containing phase information, S (tn) is time domain seismic record, m (t) is time domain reflection coefficient, GSHFor the phase constrained kernel matrix, write:
Figure BDA0003208879980000032
equation (2) is written as:
tan(P(t))＝GSHm(t)＝DSH (7)，
in the formula (7), DSHThe resulting signal is the tangent of P (t).
Preferably, the step 2 comprises:
let the low frequency model constraint be expressed as:
Plow＝Cm(t) (8)，
the parameters in formula (8) are expressed as follows:
Figure BDA0003208879980000033
in the formula (9), C is an integration matrix, ZPmAnd ZP0In order to relatively and smoothly obtain longitudinal wave impedance information,
the seismic inversion target functional based on the phase constraint comprises three parts: time domain convolution model, phase constraint and low frequency model constraint:
Figure BDA0003208879980000034
solving equation (10) using the two-norm, the phase-constrained seismic inversion target functional j (m) is expressed as:
Figure BDA0003208879980000041
in the formula (11), α 1, α 2, and α 3 are weights of time domain seismic inversion, phase constraint, and low frequency model constraint, respectively.
Preferably, the step 3 comprises:
the inverse reflection coefficient solved according to equation (11) is:
m(t)＝(α1W(t)TW(t)+α2GSH TGSH+α3CTC)-1(α1W(t)TS(t)+α2GSH TDSH+α3CTPlow)
(12)，
the formula for obtaining the impedance of the inverted longitudinal wave from the inversion reflection coefficient is as follows:
P(t)＝exp(2Cm(t))*ZP0 (13)，
in the formula (13), p (t) is the inverse longitudinal wave impedance.
In order to solve the technical problem, the invention adopts another technical scheme that:
a computing device, the computing device comprising: a processor, a storage device, and a computer program; a computer program is stored on a storage device and is executable on a processor, the computer program when executed performs the steps of the phase constrained high resolution seismic inversion method described above.
The method can effectively improve the resolution of the inversion result, can obtain the inversion result of the high-resolution reflection coefficient, and can obtain the high-resolution longitudinal wave impedance by using the inversion result of the high-resolution reflection coefficient; the reflection coefficient obtained by the method has rich high-frequency information, can effectively identify underground thin layers and underground information of weak reflection areas, and can also carry out more effective parameter prediction on the weak reflection areas; model trial calculations and actual data testing both show the applicability and effectiveness of the method of the invention.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In order to more clearly illustrate the specific implementation or technical scheme of the invention, the attached drawings are as follows:
FIG. 1 is a comparative schematic of synthetic seismic records.
FIG. 2 is a schematic diagram of a model test performed on the method of the present invention.
FIG. 3 is a schematic diagram of a model with rich high frequency information tested using the method of the present invention and a conventional inversion method.
FIG. 4 is a schematic diagram of the spectral analysis of the inversion results calculated by the method of the present invention and the conventional inversion method.
FIG. 5 is a schematic diagram of the practical testing of the method of the present invention using actual seismic 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 invention relates to a phase-constrained high-resolution seismic inversion method, which comprises the following steps of:
step 1, deducing a linear relation between an instantaneous seismic phase and a reflection coefficient;
step 2, establishing a phase-constrained seismic inversion target functional;
and 3, solving an inversion reflection coefficient and an inversion longitudinal wave impedance through a phase-constrained seismic inversion target functional.
Step 1, deducing a linear relation between the instantaneous seismic phase and the reflection coefficient.
The seismic phase information contains rich high-frequency information, the seismic phase is sensitive to weak reflection, however, the strong nonlinearity of the seismic phase makes the seismic phase difficult to effectively play a role in seismic inversion, so the step 1 mainly solves the strong nonlinearity of the seismic phase, linearizes the seismic phase, and provides a theoretical basis for adding a target functional and acquiring high-resolution longitudinal wave impedance subsequently.
And (3) setting a time domain seismic signal as S (t), a time domain seismic wavelet matrix as W (t), a time domain reflection coefficient as m (t) and time domain noise as N (t), wherein the time domain convolution model can be expressed as:
S(t)＝W(t)m(t)+N(t) (1)
the time domain convolution model is given by equation (1), and on this basis, the instantaneous phase formula of the seismic signal is expressed as follows:
P(t)＝tan-1(Im(H(W(t)m(t)))/Re(H(W(t)m(t)))) (2)
in the formula (2), p (t) is an instantaneous phase of the seismic signal, H (×) represents hilbert transform, Im (×) is an imaginary part, and Re (×) is a real part.
The nonlinearity of the imaginary part (i.e., Im (H (w (t) m (t)))) in the equation (2) is a key to make it difficult to introduce the seismic phase into the target functional, and therefore, the linearization of this part is a key to introduce the seismic phase into the target functional to obtain high-resolution longitudinal wave impedance.
As is clear from the formula (1), Im (H (W (t) m (t))) in the formula (2) can be rewritten as:
Im(H(W(t)m(t)))＝Im(H(S(t))) (3)
to linearize this portion to introduce the target functional to obtain high resolution total impedance, the imaginary part in equation (3) needs to be linearized. The physical meaning of equation (3) is clear, i.e. 90 ° phase filtering is performed on the seismic signal, we can also consider the hilbert transform of the seismic signal as the result of convolution of the 90 ° filtered wavelet and the reflection coefficient, i.e.:
Im(H(W(t)*m(t)))＝Im(H(S(t)))＝Im(H(W(t)))*m(t) (4)
in the formula (4), a value represents a convolution operator.
In fig. 1, the black solid line is the calculation result of formula (1), the black dashed line is the calculation result of the left side of formula (4) (i.e., Im (H (w (t)) m (t))), and the gray solid line is the calculation result of the right side of formula (4) (i.e., Im (H (w (t)) m (t))), and it can be seen from fig. 1 that the black dashed line and the gray solid line are highly consistent, i.e., the accuracy of formula (4) is verified.
For convenience we will use G hereinafterHA matrix representing Im (H (W)) wavelets.
In this case, equation (2) can be rewritten as:
P(t)＝tan-1(GHm(t)/S(t)) (5)
by simplifying the formula (5), the following can be obtained:
Figure BDA0003208879980000071
in formula (6), p (t) tan-1(GSHm (t) is a signal containing phase information, S (tn) is time domain seismic record, m (t) is time domain reflection coefficient, GSHFor a phase constrained kernel matrix, we can write:
Figure BDA0003208879980000072
formula (2) can therefore be finally rewritten as follows:
tan(P(t))＝GSHm(t)＝DSH (7)
in the formula (7), DSHThe resulting signal is the tangent of P (t). The formula (7) overcomes the strong nonlinear characteristic of the seismic phase information, establishes the linear relation between the seismic phase information and the reflection coefficient, and can be easily introduced into a seismic inversion target functional. Due to the abundant high-frequency information of seismic phases and the high sensitivity of weak reflection signals, the inversion result with higher resolution can be obtained by introducing the formula (7) into a target functional, more accurate parameter prediction can be performed on a weak reflection area, and the obtained high-resolution headquarter impedance also provides powerful data support for extracting high-resolution underground parameters.
And 2, establishing a seismic inversion target functional of phase constraint.
In order to increase inversion result low-frequency information, relieve multiple solutions and enhance transverse continuity, a low-frequency model constraint needs to be added into a target functional, and the low-frequency model constraint can be expressed as follows:
Plow＝Cm(t) (8)
the parameters in formula (8) are expressed as follows:
Figure BDA0003208879980000073
in the formula (9), C is an integration matrix, ZPmAnd ZP0Is relative toAnd smoothing the longitudinal wave impedance information.
The seismic inversion target functional based on the phase constraint comprises three parts: the time domain convolution model, the phase constraint and the low-frequency model constraint are as follows:
Figure BDA0003208879980000081
the time domain convolution model in the formula (10) provides a stable solution for inversion, and since the phase has rich high-frequency information, the phase constraint term is added into the target functional to effectively improve the high-frequency information of the inversion result, namely, the inversion resolution is improved. In addition, the addition of the low-frequency model constraint can effectively relieve the problem of multiple solutions of inversion.
Solving equation (10) with a two-norm, the phase-constrained seismic inversion target functional j (m) can be expressed as:
Figure BDA0003208879980000082
in the formula (11), α 1, α 2, and α 3 are weights of time domain seismic inversion, phase constraint, and low frequency model constraint, respectively.
And 3, solving an inversion reflection coefficient and an inversion longitudinal wave impedance through a phase-constrained seismic inversion target functional.
The solution (i.e., the inverse reflection coefficient) of equation (11) is:
m(t)＝(α1W(t)TW(t)+α2GSH TGSH+α3CTC)-1(α1W(t)TS(t)+α2GSH TDSH+α3CTPlow)
(12)
the formula (12) is obtained by solving the phase constraint target functional, the high-resolution reflection coefficient inversion result can be effectively obtained by using the formula, and compared with the traditional inversion method, the reflection coefficient obtained by using the formula has abundant high-frequency information, and the underground information of an underground thin layer and a weak reflection area can be effectively identified.
In addition, the high-resolution longitudinal wave impedance can be obtained by utilizing the inversion result of the high-resolution reflection coefficient, and the method for obtaining the longitudinal wave impedance is as follows. The formula for obtaining the inverted longitudinal wave impedance from the inverted reflection coefficient can be written as:
P(t)＝exp(2Cm(t))*ZP0 (13)
in the formula (13), p (t) is the inverse longitudinal wave impedance.
Fig. 2 is a schematic diagram of model testing performed by the method of the present invention, in which fig. 2 (a) is a built synthetic seismic record, fig. 2 (b) is a reflection coefficient obtained by inverting a seismic record by using the method of the present invention, and fig. 2 (c) is a longitudinal wave impedance obtained by inverting a seismic record by using the method of the present invention.
In fig. 2, a black solid line, a gray broken line, and a gray solid line are a model value, an inverted value, and an initial model in this order.
From the inversion test result (fig. 2), it can be seen that the reflection coefficient and the inversion value and the model value of the longitudinal wave impedance are highly consistent, and the high and low frequency information is supplemented to a certain extent.
In order to more intuitively show the effectiveness of the method, a model (figure 3) with rich high-frequency information is tested by respectively utilizing the method and a conventional inversion method. As can be seen from the test results (FIG. 3), the inversion result obtained by the method of the present invention can be more accurately depicted in a high frequency range than the inversion result obtained by conventional inversion, and particularly in the area indicated by the black arrow, the high frequency information is improved to a certain extent.
FIG. 3 (a) model values of longitudinal wave impedance; FIG. 3 (b) the inversion result of longitudinal wave impedance by the conventional method; FIG. 3 (c) shows the inversion result of longitudinal wave impedance in the method of the present invention; wherein, the black solid line, the gray dotted line and the gray solid line are a model value, an inversion value of the method, an inversion result of the conventional method and an initial model in sequence.
In addition, as shown in fig. 4, the frequency band (gray dotted line) of the inversion result obtained by the method is expanded to a certain extent compared with the conventional method (black solid line), and particularly, the high-frequency information (70-100Hz) is rich, so that the effectiveness of the method is further verified. In fig. 4, the black solid line and the gray dashed line are frequency spectrums of the inversion result of the conventional method and the inversion result of the method of the present invention in sequence.
After the validity and reliability are verified by using the model, the practical seismic data is required to be used for carrying out the practicability test of the method. FIG. 5 is a result of actual data testing, FIG. 5 (a) seismic section; FIG. 5 (b) reflection coefficient inversion results of the conventional method; FIG. 5 (c) shows the reflection coefficient inversion result of the method of the present invention; FIG. 5 (d) the inversion result of longitudinal wave impedance by the conventional method; FIG. 5 (e) shows the inversion result of longitudinal wave impedance in the method of the present invention.
Compared with the conventional inversion method, the inversion result of the method has higher resolution no matter the reflection coefficient or the longitudinal wave impedance, and more accurate prediction can be carried out in a weak reflection area, so that the test also verifies the applicability and reliability of the method.
The invention also provides computer equipment. The computing device includes: a processor, a storage device, and a computer program.
The processor may be a Central Processing Unit (CPU), controller, microcontroller, microprocessor, or other data processing chip.
The storage device may be Random Access Memory (RAM), Read Only Memory (ROM), a hard disk, a magnetic disk, an optical disk, or other storage device.
The computer program is stored on the storage device and the processor runs the computer program, which when run performs the steps of the phase constrained high resolution seismic inversion method described above.
The above description and examples are intended to be illustrative only, and all equivalent changes and modifications made on the basis of the technical solutions of the present invention are intended to be included within the scope of the present invention.

Claims (5)

1. A phase-constrained high-resolution seismic inversion method is characterized by comprising the following steps:
step 1, deducing a linear relation between an instantaneous seismic phase and a reflection coefficient;
step 2, establishing a phase-constrained seismic inversion target functional;
and 3, solving an inversion reflection coefficient and an inversion longitudinal wave impedance through a phase-constrained seismic inversion target functional.
2. The phase constrained high resolution seismic inversion method of claim 1,
the step 1 comprises the following steps:
and (3) setting a time domain seismic signal as S (t), a time domain seismic wavelet matrix as W (t), a time domain reflection coefficient as m (t) and time domain noise as N (t), and then expressing a time domain convolution model as:
S(t)＝W(t)m(t)+N(t) (1)，
on the basis of the time domain convolution model of the formula (1), the instantaneous phase formula of the seismic signals is expressed as follows:
P(t)＝tan-1(Im(H(W(t)m(t)))/Re(H(W(t)m(t)))) (2)，
in formula (2), p (t) is the instantaneous phase of the seismic signal, H (×) represents the hilbert transform, Im (×) is the imaginary part, Re (×) is the real part;
according to formula (1), in formula (2), Im (H (W (t) m (t))) is partially rewritten as:
Im(H(W(t)m(t)))＝Im(H(S(t))) (3)，
equation (3) is to perform 90 degree phase filtering on the seismic signals,
the 90 ° phase filtering of seismic signals is considered to be the result of the convolution of the 90 ° filtered wavelet with the reflection coefficients, i.e.:
Im(H(W(t)*m(t)))＝Im(H(S(t)))＝Im(H(W(t)))*m(t) (4)，
in the formula (4), a convolution operator is represented,
let GHA matrix representing Im (H (W)) wavelets, with equation (2) rewritten as:
P(t)＝tan-1(GHm(t)/S(t)) (5)，
the formula (5) is simplified to obtain:
Figure FDA0003208879970000021
in formula (6), p (t) tan-1(GSHm (t) is a signal containing phase information, S (tn) is time domain seismic record, m (t) is time domain reflection coefficient, GSHFor the phase constrained kernel matrix, write:
Figure FDA0003208879970000022
equation (2) is written as:
tan(P(t))＝GSHm(t)＝DSH (7)，
in the formula (7), DSHThe resulting signal is the tangent of P (t).
3. The phase constrained high resolution seismic inversion method of claim 2,
the step 2 comprises the following steps:
let the low frequency model constraint be expressed as:
Plow＝Cm(t) (8)，
the parameters in formula (8) are expressed as follows:
Figure FDA0003208879970000023
in the formula (9), C is an integration matrix, ZPmAnd ZP0In order to relatively and smoothly obtain longitudinal wave impedance information,
the seismic inversion target functional based on the phase constraint comprises three parts: time domain convolution model, phase constraint and low frequency model constraint:
Figure FDA0003208879970000031
solving equation (10) using the two-norm, the phase-constrained seismic inversion target functional j (m) is expressed as:
Figure FDA0003208879970000032
in the formula (11), α 1, α 2, and α 3 are weights of time domain seismic inversion, phase constraint, and low frequency model constraint, respectively.
4. The phase constrained high resolution seismic inversion method of claim 3,
the step 3 comprises the following steps:
the inverse reflection coefficient solved according to equation (11) is:
m(t)＝(α1W(t)TW(t)+α2GSH TGSH+α3CTC)-1(α1W(t)TS(t)+α2GSH TDSH+α3CTPlow)
(12)，
the formula for obtaining the impedance of the inverted longitudinal wave from the inversion reflection coefficient is as follows:
P(t)＝exp(2Cm(t))*ZP0 (13)，
in the formula (13), p (t) is the inverse longitudinal wave impedance.
5. A computer device, comprising: a processor, a storage device, and a computer program;
stored on the memory and executable on the processor, the computer program when executed performing the steps of the phase constrained high resolution seismic inversion method of claims 1 to 4.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2974134A1 (en) * 2016-09-09 2018-03-09 China Petroleum & Chemical Corporation Method and system for seismic data processing
CN110618453A (en) * 2019-08-07 2019-12-27 成都理工大学 Wave impedance inversion method based on improved damping least square method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2974134A1 (en) * 2016-09-09 2018-03-09 China Petroleum & Chemical Corporation Method and system for seismic data processing
CN110618453A (en) * 2019-08-07 2019-12-27 成都理工大学 Wave impedance inversion method based on improved damping least square method

Non-Patent Citations (2)

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Title
P.C.H. VEEKEN 等: "Seismic inversion methods and some of their constraints", FIRST BREAK, vol. 22, pages 47 - 70, XP002498173 *
赵亮 等: "焉耆盆地高分辨率地震资料解释方法探讨", 河南石油, no. 03, pages 16 - 18 *

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