CN111045076A - Multi-mode Rayleigh wave frequency dispersion curve parallel joint inversion method - Google Patents

Multi-mode Rayleigh wave frequency dispersion curve parallel joint inversion method Download PDF

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CN111045076A
CN111045076A CN201911259895.XA CN201911259895A CN111045076A CN 111045076 A CN111045076 A CN 111045076A CN 201911259895 A CN201911259895 A CN 201911259895A CN 111045076 A CN111045076 A CN 111045076A
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dispersion curve
inversion
order
formula
rayleigh wave
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雷宇航
乔宝平
黄昱丞
曹成寅
潘自强
黄伟传
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Beijing Research Institute of Uranium Geology
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    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
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    • G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
    • G01V1/30—Analysis
    • G01V1/306—Analysis for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles
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Abstract

The invention belongs to the technical field of near-surface seismic surface wave exploration, and particularly relates to a Rayleigh wave multi-mode dispersion curve parallel inversion method. The invention comprises the following steps: step one, performing two-dimensional Fourier transform on the actually acquired seismic record to obtain an actually measured Rayleigh wave frequency dispersion curve f-vo Rij(ii) a Step two, proving the relation between the dispersion curve and the comprehensive sensitivity of each order, wherein the dispersion curve corresponds to the highest value of the comprehensive sensitivity of each order; step three, based on the conclusion of the step two, the actually measured Rayleigh wave frequency dispersion curve f-v obtained in the step one is subjected too RijDesigning an inversion individual target function phi; performing iterative optimization by using a damped least square method based on the inversion individual target function in the step three, and updating a model x; and step five, repeating the step three and the step four based on the new model generated in the step four until the preset iteration number T is reached, and outputting a stratum model inversion result x. The invention can be seenThe inversion convergence efficiency and the parameter precision of the stratum model are obviously improved.

Description

Multi-mode Rayleigh wave frequency dispersion curve parallel joint inversion method
Technical Field
The invention belongs to the technical field of near-surface seismic surface wave exploration, and particularly relates to a Rayleigh wave multi-mode dispersion curve parallel inversion method.
Background
The multi-channel transient surface wave method utilizes the dispersion characteristic of Rayleigh waves propagating in elastic media (soil, rocks and subgrades), and constructs a near-surface S-wave velocity structure model by extracting and inverting dispersion curves, has the advantages of rapidness, convenience, non-invasiveness, high shallow resolution and the like, and is widely applied to exploration research of underground water, engineering geology, environment and the like. The rayleigh wave propagates forward in an inverted elliptical form from left to right in a depth range of about 0.5 wavelength near the interface of the medium, the energy thereof is unevenly distributed to each mode, and the dispersion of different modes may dominate in each frequency band. Research shows that high-mode Rayleigh waves have larger detection depth and inversion sensitivity, conventional single-mode inversion is limited by limited sensitive frequency bands, parameters of a model cannot be effectively and synchronously converged towards real parameters, and in order to further restrict formation parameters, the technology of a method for performing joint inversion by using a plurality of geophysical detection means such as Rayleigh wave combined body waves, electrical methods, gravity and even Leffer waves is infinite, and multi-mode frequency dispersion joint inversion is a more effective and more economic detection method.
The traditional combined inversion which gradually progresses from a fundamental order to a high order has slow convergence speed, and when actual measurement dispersion with large local variation gradient is processed, the inversion of the dispersion of each order is difficult to be mutually restricted so as to reach a balanced state, so that a real geophysical model and an inversion model cannot be completely matched.
Disclosure of Invention
The technical problems solved by the invention are as follows:
the invention provides a Rayleigh wave multi-mode dispersion curve parallel inversion method, which defines a dispersion curve comprehensive sensitivity function, further proves the corresponding relation between the dispersion curve comprehensive sensitivity function and a video dispersion curve in a spectrogram, defines a multi-mode dispersion curve parallel inversion target function based on the dispersion curve comprehensive sensitivity function, and can obviously improve inversion convergence efficiency and formation model parameter precision by carrying out multi-mode dispersion cross gradient constraint on an inversion formation model.
In order to solve the technical problem, the invention provides a Rayleigh wave multi-mode dispersion curve parallel inversion method, which comprises the following steps:
step one, performing two-dimensional Fourier transform on an actually acquired seismic record, and converting the seismic record from an x-t domain to an f-k domain; and then generating an f-v frequency spectrum energy graph according to the k-f/v, identifying the energy peak value of the f-v frequency spectrum energy graph, and obtaining an actually measured Rayleigh wave frequency dispersion curve f-vo Rij，vo RijIs a measured dispersion curve, where i is 1,2, … N, N is the number of measured phase velocities, j is 1,2, … M, M is the order of the picked rayleigh wave dispersion curve;
step two, proving the relation between the dispersion curve and the comprehensive sensitivity of each order, wherein the dispersion curve corresponds to the highest value of the comprehensive sensitivity of each order;
step three, based on the conclusion of the step two, the actually measured Rayleigh wave frequency dispersion curve f-v obtained in the step one is subjected too RijDesigning an inversion individual target function phi;
and step four, performing iterative optimization by using a damped least square method based on the step three-inversion individual target function, recording the iteration time T as 1, and solving a parameter correction formula as follows:
Figure BDA0002311336280000021
where I is the identity matrix, x0The parameters of an inversion initial model, mu is a damping factor, the initial value is set to be 1 in the embodiment, A is a Jacobian matrix, and the parameters are obtained through a sensitivity formula in the second step;
based on the obtained parameter correction quantity delta x, obtaining an optimal parameter correction step length lambda by using a steepest descent method; after the optimal correction step length lambda is obtained, the model x is updated according to the formula,
the currently selected individual parameter is x ═ x0+ λ Δ x, and let T ═ T + 1;
and step five, repeating the step three and the step four based on the new model generated in the step four until the preset iteration number T is reached, and outputting a stratum model inversion result x.
In the first step, the solving formula for converting the x-t domain into the f-k domain is as follows:
Figure BDA0002311336280000031
wherein f is frequency and u (x, t) is an x-t domain seismic record;
Figure BDA0002311336280000032
where k is the wavenumber and U (f, k) is the f-k domain seismic record.
The concrete steps of the second step are that,
calculating each layer transverse wave velocity v of stratum modelSkSensitivity to some j-order dispersion curve;
defining a comprehensive sensitivity function, i.e. for the same order SvSk(f, j) summing;
and comparing the comprehensive sensitivity curve of each order of frequency dispersion calculated according to the formula with a spectrum energy diagram, and proving that the frequency dispersion curve corresponds to the highest value of the comprehensive sensitivity of each order.
In the second step, the sensitivity calculation formula is as follows:
Figure BDA0002311336280000033
wherein SvSk(f, j) is the k-th layer transverse wave velocity vSkThe jth order dispersion sensitivity calculated at frequency f, c (f, j) is the jth order rayleigh wave phase velocity calculated at frequency f, α is the difference quotient factor.
The same order SvSk(f, j) is summed by the formula
Figure BDA0002311336280000034
Where k is 1,2, … L, and L is the number of layers in the formation model.
The solving formula in the third step is as follows:
Figure BDA0002311336280000035
wherein v iso RijIs the measured Rayleigh wave phase velocity vc RijIs the theoretical phase velocity value of the inversion.
The formula for finding the optimal correction step length lambda of the parameter in the fourth step is as follows:
Figure BDA0002311336280000041
in the formula, gi＝(ATA+μI)Δxi。
The invention has the beneficial technical effects that:
(1) according to the Rayleigh wave multi-mode dispersion curve parallel inversion method provided by the invention, the added high-order Rayleigh wave dispersion curve information enhances the constraint effect on the formation parameters, and the correction based on the multi-mode dispersion cross gradient enables each inversion parameter to be effectively and synchronously converged towards a real model in the whole frequency band range;
(2) the Rayleigh wave multi-mode dispersion curve parallel inversion method provided by the invention reduces the dependence degree of the damped least square method on the inversion initial model to a certain extent, greatly improves the inversion efficiency and the inversion precision,
(3) the Rayleigh wave multi-mode dispersion curve parallel inversion method provided by the invention has practical significance for detecting a multi-channel transient surface wave near-surface fine structure.
Drawings
FIG. 1 is a Rayleigh wave seismic record of actual acquisition;
FIG. 2 is a graph of seismic record dispersion energy and extracted multiple-order Rayleigh wave dispersion curves;
FIG. 3 is a frequency dispersion energy diagram and comprehensive sensitivity values of each order of frequency dispersion;
FIG. 4 is a final result of iterative inversion of the formation model according to the method.
Detailed Description
The method for performing parallel inversion on a rayleigh wave multi-mode dispersion curve provided by the invention is further described in detail with reference to the accompanying drawings and the implementation examples.
The invention relates to a Rayleigh wave multi-mode dispersion curve parallel inversion method, which specifically comprises the following steps:
step one, performing two-dimensional Fourier transform on the actually acquired seismic record shown in the figure 1, and converting the seismic record from an x-t domain to an f-k domain, wherein the solving formula is as follows:
Figure BDA0002311336280000051
wherein f is frequency and u (x, t) is an x-t domain seismic record;
Figure BDA0002311336280000052
where k is the wavenumber and U (f, k) is the f-k domain seismic record.
Then, an f-v frequency spectrum energy graph as shown in fig. 2 is generated according to k ═ f/v, the energy peak value is identified, and an actually measured Rayleigh wave frequency dispersion curve f-v is obtainedo Rij，vo RijIs the measured dispersion curve, where i is 1,2, … N, N is the number of measured phase velocities, j is 1,2, … M, and M is the order of the picked rayleigh wave dispersion curve.
Step two, calculating the transverse wave velocity v of each layer of the stratum modelSkFor the sensitivity of a certain j-order dispersion curve, the formula is obtained as follows:
Figure BDA0002311336280000053
wherein SvSk(f, j) is the k-th layer transverse wave velocity vSkThe calculated jth order dispersion sensitivity at the frequency f, c (f, j) is the calculated jth order rayleigh wave phase velocity at the frequency f, α is a difference quotient factor, and the embodiment takes 1.2.
For comprehensive analysis of inversion parametersNumber vSSensitivity value Sv for each order of frequency dispersionSjThis embodiment defines the integrated sensitivity function, i.e. for the same order SvSk(f, j) summing:
Figure BDA0002311336280000054
where k is 1,2, … L, L is the number of layers of the formation model, and fig. 3 is a comparison between the comprehensive sensitivity curve of each order of dispersion (dotted line, corresponding to the right ordinate) calculated according to the above formula and the spectrum energy diagram (the energy peak is the dispersion curve of each order, corresponding to the left ordinate), so that it can be seen that the dispersion curve (referred to as the video dispersion curve) appearing in the spectrum diagram corresponds to the highest value of the comprehensive sensitivity of each order.
Step three, based on the conclusion of the step two, the actually measured Rayleigh wave frequency dispersion curve f-v obtained in the step one is subjected too RijDesigning an inversion individual target function phi, wherein the solving formula is as follows:
Figure BDA0002311336280000061
wherein v iso RijIs the measured Rayleigh wave phase velocity vc RijIs the inverse theoretical phase velocity value;
and step four, performing iterative optimization by using a damped least square method based on the step three-inversion individual target function, recording the iteration time T as 1, and solving a parameter correction formula as follows:
Figure BDA0002311336280000062
where I is the identity matrix, x0The parameters of an inversion initial model, mu is a damping factor, the initial value is set to be 1 in the embodiment, A is a Jacobian matrix, and the parameters are obtained through a sensitivity formula in the second step;
based on the obtained parameter correction quantity delta x, a parameter optimal correction step length lambda is obtained by using the steepest descent method, and the obtaining formula is as follows:
Figure BDA0002311336280000063
in the formula, gi＝(ATA+μI)Δxi. After the optimal correction step length lambda is obtained, the model x is updated according to the formula, and the currently selected individual parameter is x ═ x0+ λ Δ x, and let T ═ T + 1;
and step five, repeating the step three and the step four based on the new model generated in the step four until the preset iteration times T is reached, and outputting a stratum model inversion result x as shown in the figure 4.
FIG. 4 shows that 38.735s is consumed by the method, the fitting error of the objective function of the formation model after 12 times of iterative optimization is 4.48e-14km/s, and it can be seen that although the initial model error is large and structural information of the formation is not reflected, under the constraint of the cross gradient of each mode, each parameter rapidly converges to the real formation, and the inversion result completely coincides with the real model, which illustrates the effectiveness and accuracy of the method.

Claims (7)

1. A Rayleigh wave multi-mode dispersion curve parallel inversion method is characterized by comprising the following steps: the method comprises the following steps:
step one, performing two-dimensional Fourier transform on an actually acquired seismic record, and converting the seismic record from an x-t domain to an f-k domain; and then generating an f-v frequency spectrum energy graph according to the k-f/v, identifying the energy peak value of the f-v frequency spectrum energy graph, and obtaining an actually measured Rayleigh wave frequency dispersion curve f-vo Rij，vo RijIs a measured dispersion curve, where i is 1,2, … N, N is the number of measured phase velocities, j is 1,2, … M, M is the order of the picked rayleigh wave dispersion curve;
step two, proving the relation between the dispersion curve and the comprehensive sensitivity of each order, wherein the dispersion curve corresponds to the highest value of the comprehensive sensitivity of each order;
step three, based on the conclusion of the step two, the actually measured Rayleigh wave frequency dispersion curve f-v obtained in the step one is subjected too RijDesigning an inversion individual target function phi;
and step four, performing iterative optimization by using a damped least square method based on the step three-inversion individual target function, recording the iteration time T as 1, and solving a parameter correction formula as follows:
Figure FDA0002311336270000011
where I is the identity matrix, x0The parameters of an inversion initial model, mu is a damping factor, the initial value is set to be 1 in the embodiment, A is a Jacobian matrix, and the parameters are obtained through a sensitivity formula in the second step;
based on the obtained parameter correction quantity delta x, obtaining an optimal parameter correction step length lambda by using a steepest descent method; after the optimal correction step length lambda is obtained, the model x is updated according to the formula,
the currently selected individual parameter is x ═ x0+ λ Δ x, and let T ═ T + 1;
and step five, repeating the step three and the step four based on the new model generated in the step four until the preset iteration number T is reached, and outputting a stratum model inversion result x.
2. The method according to claim 1, wherein the method comprises: in the first step, the solving formula for converting the x-t domain into the f-k domain is as follows:
Figure FDA0002311336270000021
wherein f is frequency and u (x, t) is an x-t domain seismic record;
Figure FDA0002311336270000022
where k is the wavenumber and U (f, k) is the f-k domain seismic record.
3. The method according to claim 2, wherein the method comprises: the concrete steps of the second step are that,
computing groundEach layer transverse wave velocity v of layer modelSkSensitivity to some j-order dispersion curve;
defining a comprehensive sensitivity function, i.e. for the same order SvSk(f, j) summing;
and comparing the comprehensive sensitivity curve of each order of frequency dispersion calculated according to the formula with a spectrum energy diagram, and proving that the frequency dispersion curve corresponds to the highest value of the comprehensive sensitivity of each order.
4. The method of claim 3, wherein the method comprises: in the second step, the sensitivity calculation formula is as follows:
Figure FDA0002311336270000023
wherein SvSk(f, j) is the k-th layer transverse wave velocity vSkThe jth order dispersion sensitivity calculated at frequency f, c (f, j) is the jth order rayleigh wave phase velocity calculated at frequency f, α is the difference quotient factor.
5. The method of claim 4, wherein the method comprises: the same order SvSk(f, j) is summed by the formula
Figure FDA0002311336270000024
Where k is 1,2, … L, and L is the number of layers in the formation model.
6. The method of claim 5, wherein the method comprises: the solving formula in the third step is as follows:
Figure FDA0002311336270000031
wherein v iso RijIs the measured Rayleigh wave phase velocity vc RijIs the theoretical phase velocity value of the inversion.
7. The method of claim 6, wherein the method comprises: the formula for finding the optimal correction step length lambda of the parameter in the fourth step is as follows:
Figure FDA0002311336270000032
in the formula, gi＝(ATA+μI)Δxi。
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CN112765774A (en) * 2020-12-25 2021-05-07 青岛黄海学院 Railway seismic source Rayleigh surface wave mechanical model and numerical simulation method thereof
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CN113945975A (en) * 2021-10-09 2022-01-18 中国船舶重工集团公司第七六0研究所 Method for jointly inverting stratum layered structure based on love waves and Rayleigh waves
CN114185093A (en) * 2021-12-07 2022-03-15 中国石油大学(北京) Near-surface velocity model building method and device based on Rayleigh surface wave inversion
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