CN111665550A - Underground medium density information inversion method - Google Patents

Underground medium density information inversion method Download PDF

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CN111665550A
CN111665550A CN201910172098.1A CN201910172098A CN111665550A CN 111665550 A CN111665550 A CN 111665550A CN 201910172098 A CN201910172098 A CN 201910172098A CN 111665550 A CN111665550 A CN 111665550A
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density
model
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王潇潇
雷霆
孙博文
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Zhongpu Baoxin Beijing Technology Co ltd
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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
    • G01V1/306—Analysis for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles
    • 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
    • G01V2210/62—Physical property of subsurface
    • G01V2210/622—Velocity, density or impedance
    • G01V2210/6224—Density

Abstract

The invention relates to an inversion method of density information of underground media, which comprises the following steps: acquiring a plurality of single-shot data of seismic source vibration in a detection area, wherein the single-shot data comprises single-shot single-channel data and single-shot multi-channel data; intercepting direct waves, shallow reflected waves and shallow refracted waves in the single shot data by using a time window to obtain observation data; acquiring an initial density model, and forward modeling a seismic source waveform based on the initial density model to obtain forward modeling data; calculating a wave field residual error according to the observation data and the forward modeling data, and constructing an error functional according to the wave field residual error; utilizing the wave field residual error to perform back propagation to the initial density model space to obtain residual error back propagation data; calculating the density updating gradient of the error functional according to a adjoint state method by utilizing the forward modeling data and the residual back propagation data; and updating the initial density model by using the density updating gradient of the error functional to obtain an accurate density model.

Description

Underground medium density information inversion method
Technical Field
The invention relates to the technical field of geophysical exploration, in particular to an underground medium density information retrieval method.
Background
In the field of exploration geophysical technology, shallow layer modeling technology is always a difficult point for modeling parameters of underground media. The method of first-arrival travel-time tomographic inversion based on ray is commonly used at present. The method is simple in calculation, does not require an accurate background model parameter field, and applies complex surface conditions, so that the method is a common method for solving parameter modeling of near-surface and shallow underground media. But this method is based on the shortest path principle of high frequency hypothesis, and in the case of low-speed body development, the technology has a modeled 'dead zone'. In addition, the ray method is sensitive to ray density, when the speed changes violently, even if the speed is a high-speed abnormal body, the ray density is seriously influenced due to the occurrence of the full-emission phenomenon, and then the inversion precision is reduced. In practical data application, the first arrival picking workload is huge, errors exist in manual picking, and the first arrival picking is difficult to be accurate under the condition that a local table is complex.
Another new method for solving the problems is a full waveform inversion method, which is based on the wave equation and can truly simulate the wave propagation wave field, so that the method is not influenced by ray density. However, the implementation of this new method has many limitations, such as an observation system requiring a large offset, lack of low-frequency information, and the like. The practical application of full waveform inversion has a long distance, especially the practical application of land data.
Therefore, a solution for inversion of density information of underground media in areas with drastic speed change or low-speed body development is lacking at present.
Disclosure of Invention
The invention aims to provide an underground medium density information inversion method aiming at the defects in the prior art.
In order to achieve the above object, in a first aspect, the present invention provides a method for inverting density information of a subsurface medium, including:
acquiring a plurality of single-shot data of seismic source vibration in a detection area, wherein the single-shot data comprises single-shot single-channel data and single-shot multi-channel data;
intercepting direct waves, shallow reflected waves and shallow refracted waves in the single shot data by using a time window to obtain observation data;
acquiring an initial density model, and forward modeling a seismic source waveform based on the initial density model to obtain forward modeling data;
calculating a wave field residual error according to the observation data and the forward modeling data, and constructing an error functional according to the wave field residual error;
utilizing the wave field residual error to perform back propagation to the initial density model space to obtain residual error back propagation data;
calculating the density updating gradient of the error functional according to a adjoint state method by utilizing the forward modeling data and the residual back propagation data;
and updating the initial density model by using the density updating gradient of the error functional to obtain an accurate density model.
Further, after the time window is used to intercept the direct wave, the shallow reflected wave, and the shallow refracted wave in the plurality of single shot data to obtain the observation data, the method further includes:
performing filtering processing on the observation data by utilizing wavelet transformation to obtain processed observation data;
and performing multiple suppression processing on the processed observation data.
Further, the forward modeling the seismic source waveform based on the initial density model to obtain forward modeling data specifically includes:
performing time domain dispersion on the wave equation of the seismic source waveform by using a staggered grid finite difference method to obtain a dispersed wave equation;
and determining the wave field value of the spatial distribution of the staggered grid at each moment according to the dispersed wave equation and the initial density model.
Further, the calculating a wave field residual according to the observation data and the forward modeling data specifically includes:
and subtracting the observation data and the forward modeling data to obtain the wave field residual error.
Further, the constructing an error functional according to the wave field residual specifically includes:
according to the formula
Figure BDA0001988396560000031
Calculating an error functional, wherein E (m) is the error functional, b (m) is a linear function representing the result data of the forward modeling, dobsFor observation data, b (m) -dobsAs wave field residual, CDAs a data covariance matrix, CMIs a covariance matrix of the model, m is a model parameter of the density initial model, mpriorIs a prior information model, and lambda is a prior information specific gravity parameter.
Further, the obtaining residual back propagation data by using the wave field residual back propagation to the initial density model space specifically includes:
and (3) acting a counter-propagation operator on the wave field residual error to obtain residual error counter-propagation data of the initial density model space.
Further, the calculating a density update gradient of the error functional according to an adjoint state method by using the forward modeling data and the residual back propagation data specifically includes:
according to the formula
Figure BDA0001988396560000032
Calculating a density update gradient;
wherein the content of the first and second substances,
Figure BDA0001988396560000033
k＝ρVp 2；Pffor forward modeling of data, PbResidual back propagation data, ω is frequency, ρ is density, k is modulus, E is error functional, VpIs the velocity.
Further, the method further comprises:
and determining the optimal iteration step size according to a fastest descent method, a conjugate gradient method and a quasi-Newton method LBFGS.
Further, the updating the initial density model by using the density update gradient of the error functional to obtain an accurate density model specifically includes:
updating the initial density model according to the density updating gradient of the error functional and the optimal iteration step length;
determining an iteration termination condition;
and when the initial density model meets the iteration termination condition, obtaining an accurate density model.
The invention provides an underground medium density information retrieval method, which comprises the steps of obtaining a plurality of single-shot data of seismic source vibration in a detection area, wherein the single-shot data comprise single-shot single-channel data and single-shot multi-channel data; intercepting direct waves, shallow reflected waves and shallow refracted waves in the single shot data by using a time window to obtain observation data; acquiring an initial density model, and forward modeling the seismic source waveform based on the initial density model to obtain forward modeling data; calculating a wave field residual error according to the observation data and the forward modeling data, and constructing an error functional according to the wave field residual error; utilizing wave field residual error back propagation to an initial density model space to obtain residual error back propagation data; calculating the density updating gradient of the error functional according to a adjoint state method by utilizing forward modeling data and residual back propagation data; and updating the initial density model by using the density updating gradient of the error functional to obtain an accurate density model. According to the method provided by the invention, waveform inversion is completed by using the kinematics and the dynamics characteristics of a wave field in a period of time after the first arrival according to the geological task requirements, and high-precision modeling of a shallow layer is realized.
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FIG. 1 is a flow chart of a method for inversion of density information of a subsurface medium according to an embodiment of the present invention;
FIG. 2 is a Gaussian function graph provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of a grid configuration of physical quantities and medium parameters of a two-dimensional sound wave according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a grid configuration of physical quantities and medium parameters of a three-dimensional acoustic wave according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the present invention will be described in further detail with reference to the accompanying drawings, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, 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.
Aiming at the difficulty of shallow layer modeling, particularly under the conditions of severe speed change and low-speed revolution body development, the method avoids the weakness based on the ray theory and comprehensively utilizes wave field information in a period of time after the first arrival to realize the high-precision shallow layer modeling. Particularly, the method solves the problem of low-speed body development areas such as mountain zones, loess tablelands, desert zones and the like, and provides reliable support for mid-deep layer modeling and offset imaging.
Fig. 1 is a flowchart of an inversion method of density information of a subsurface medium according to an embodiment of the present invention. As shown in fig. 1, the method specifically comprises the following steps:
101, acquiring a plurality of single shot data of seismic source vibration in a detection area;
the seismic prospecting instrument is arranged in a detection area, single-shot data of one shot are collected when each shot is placed, and the single-shot data comprises single-shot single-channel data and single-shot multi-channel data. And transmitting multiple guns to acquire multiple groups of single gun data according to specific conditions and construction requirements. The seismic exploration instrument is a 408ULS cable instrument and the like.
The single-shot data are shallow profile data, collected single-shot multi-channel data are processed into single-shot single-channel data by a Gaussian function, half of the Gaussian function is taken to cover the whole measuring line, then corresponding discrete points are used as weight coefficients, and the weight coefficients are normalized to enable the sum to be 1. And (4) sorting the single-shot multi-channel data into a super-channel set as shown in a formula (1), so that the single-shot multi-channel data is processed into single-shot single-channel data.
Figure BDA0001988396560000051
Where μ is the shot point, i is the demodulator probe, and σ is the Gaussian window factor.
And (3) selecting an x-axis positive half-axis part in a Gaussian function graph (shown in FIG. 2), wherein the abscissa corresponds to a demodulator probe, and the coefficient of each point is a Gaussian coefficient M, as shown in a formula (2).
Figure BDA0001988396560000052
Step 102, intercepting direct waves, shallow reflected waves and shallow refracted waves in single shot data by using a time window to obtain observation data;
specifically, the time window control is carried out in the process of sound wave propagation, and the waveform information of near offset distance propagating on the near-surface and the medium-shallow layer is obtained. And intercepting direct waves, shallow reflected waves and shallow refracted waves in the single shot data by using a moving time window with fixed time length or non-fixed time length to obtain observation data.
The intercepted wave field is not specific to a certain type of wave, and contains information of many waves, such as direct waves, first-cast waves, transmitted waves, refracted waves, and the like. The wave field intercepted by the dynamic time window is used for carrying out high-precision and high-density modeling on the low-speed body development area.
The method comprises the following steps of intercepting a direct wave, a shallow reflected wave and a shallow refracted wave in single shot data by using a time window to obtain observation data, and preprocessing the observation data, wherein the method specifically comprises the following steps: carrying out filtering processing on the observation data by utilizing wavelet transformation to obtain processed observation data; and performing multiple suppression processing on the processed observation data.
Specifically, the wavelet transformation is utilized to carry out frequency division and denoising on the observation data, the wavelet transformation can be infinitely subdivided and mutually orthogonal, the observation data containing coherent interference is subjected to frequency division, and denoising processing can be carried out only in a narrow frequency band, so that the loss of effective waves after denoising is reduced to the maximum extent, and the frequency leakage phenomenon of Fourier transformation does not exist.
And performing multiple suppression processing on the processed observation data by adopting a common central point superposition method. The common center point superposition method is to superpose the signals from different excitation points of the same underground reflection point received by different receiving points after dynamic correction according to the difference of residual time difference between primary wave and multiple wave after dynamic correction, and to suppress the multiple wave. The density of primary wave is used for actuating correction, the same phase axis of the primary wave is leveled, the multiple waves still have residual time difference, and the primary wave is enhanced and the multiple waves are weakened through superposition.
In addition, the multiple suppression can be carried out by adopting two-dimensional filtering methods such as dip filtering, density filtering, fan-shaped filtering and the like, and the multiple is filtered out and the primary wave is reserved.
103, acquiring an initial density model, and forward modeling the seismic source waveform based on the initial density model to obtain forward modeling data;
specifically, the underground is subjected to gridding subdivision, the size of the model is m × n, m represents the number of grid points in the horizontal direction, n represents the number of grid points in the longitudinal direction, the grid interval is h, the size of the initial density model is m × h meters in the horizontal direction, and n × h meters in the longitudinal direction. The matrix form of the initial density model is shown in equation (3):
Figure BDA0001988396560000071
the wave equation of the sound wave is shown in equation (4):
Figure BDA0001988396560000072
wherein p is a pressure field, vxAnd vzTransverse and longitudinal density fields, respectively; k is ρ v2；tsIs the seismic wave travel time.
In the field of seismic exploration, the idea of staggered grids of acoustic wave equations is to configure different wave field components and subsurface medium parameters on different grid nodes, and time stepping is also time staggered stepping. The grid configuration of each physical quantity and medium parameter of the two-dimensional sound wave adopted by the invention is shown in fig. 3, and the grid configuration of each physical quantity and medium parameter of the three-dimensional sound wave is shown in fig. 4.
Before the acoustic wave equation is dispersed, Taylor expansion method is firstly adopted to derive high-precision approximation of the spatial derivative of the seismic wave field in a regular grid and a staggered grid.
Assuming u (x) has a derivative of order 2N +1, the Taylor expansion of order 2N +1 at x0 +. DELTA.x and x 0-DELTA.x of u (x) is:
Figure BDA0001988396560000073
Figure BDA0001988396560000074
(5) and (6) obtaining a formula (7) by subtracting the two formulas:
Figure BDA0001988396560000075
the same principle is as follows:
Figure BDA0001988396560000081
Figure BDA0001988396560000082
Figure BDA0001988396560000083
then the calculation formula of any 2N order precision center finite difference coefficient is:
order to
Figure BDA0001988396560000084
Then there are:
Figure BDA0001988396560000085
simplifying to obtain:
Figure BDA0001988396560000086
Figure BDA0001988396560000087
Figure BDA0001988396560000091
and similarly, any 2N-order precision finite difference format and difference coefficient calculation formula of the staggered grid can be derived.
According to the Taylor expansion:
Figure BDA0001988396560000092
Figure BDA0001988396560000093
Figure BDA0001988396560000094
Figure BDA0001988396560000095
Figure BDA0001988396560000096
Figure BDA0001988396560000097
simplifying to obtain:
Figure BDA0001988396560000098
wherein, anIs a difference coefficient
Figure BDA0001988396560000099
Therefore, with the staggered grid finite difference, the three-dimensional first-order density-stress acoustic wave equation can be discretized into:
Figure BDA00019883965600000910
Figure BDA0001988396560000101
Figure BDA0001988396560000102
Figure BDA0001988396560000103
Figure BDA0001988396560000104
where Δ x, Δ y, Δ z, Δ t are the spatial and temporal sampling intervals, respectively, p is the stress wavefield at each time, v represents the displacement wavefield at each time, x, y, z represent different directions, respectively, ρ represents density, and f represents the source function.
When initial and edge conditions are given, the spatial distribution of the wavefield at each time instant can be recursively derived using the difference format described above.
In the forward modeling process of the finite difference wave equation, in order to avoid numerical noise and instability, the grid size and the time step length of the finite difference need to respectively satisfy the dispersion relation and the stability condition for a given frequency bandwidth. The technical scheme of the invention adopts the finite difference dispersion relation to meet the requirement that each minimum wavelength needs at least 5 grid points, namely the space sampling interval for avoiding grid dispersion needs to meet the formula (29):
Figure BDA0001988396560000105
where Δ x is the spatial grid size, λminIs the shortest wavelength of the light that is,
Figure BDA0001988396560000107
is the minimum longitudinal wave density, fmaxIs the maximum frequency.
After the spatial sampling grid size is determined, a proper time sampling size needs to be selected to satisfy the finite difference numerical stability condition:
Figure BDA0001988396560000106
where at is the time sampling interval,
Figure BDA0001988396560000112
is the maximum longitudinal wave density.
104, calculating a wave field residual error according to the observation data and the forward modeling data, and constructing an error functional according to the wave field residual error;
specifically, the observed data and the forward modeling data are subtracted to obtain a wave field residual error. And (3) subtracting data on corresponding points in the two-dimensional array by using the observation data and the forward modeling data which are both two-dimensional arrays to obtain wave field residual errors.
Constructing an error functional according to equation (31):
Figure BDA0001988396560000111
wherein E (m) is an error functional, b (m) is a linear function representing the result data of the forward modeling, dobsFor observation data, b (m) -dobsAs wave field residual, CDAs a data covariance matrix, CMIs a covariance matrix of the model, m is a model parameter of the density initial model, mpriorIs a prior information model, and lambda is a prior information specific gravity parameter and is used for adjusting the specific gravity of a model item and a prior information item.
105, reversely propagating the wave field residual error to an initial density model space to obtain residual error reverse propagation data;
and (4) acting the inverse transmission operator on the wave field residual error to obtain residual error inverse transmission data of the initial density model space.
And 104, obtaining wave field residual errors at the positions of the wave detection points, loading the wave field residual errors at the points into a time domain forward modeling process as a seismic source, and performing time reverse propagation to obtain residual reverse propagation data.
Step 106, calculating the density updating gradient of the error functional by using the forward modeling data and the residual back propagation data;
the gradient computation is a key part of parameter inversion and represents the updating direction of the model, and the gradient guiding inversion method searches the iterative updating direction through the derivative of the target functional to the model parameters so as to update the model. The method carries out gradient calculation based on an adjoint state method, and uses the data residual error of a forward wave field and a backward wave field as a new seismic source to carry out forward modeling so as to calculate the gradient of a target function to a model.
Calculating the density update gradient of the error functional for each single shot datum according to equation (32):
Figure BDA0001988396560000121
wherein m is the model parameter of the density initial model, u is the forward simulation broadcast field, B is the forward operator, Delta d is the wave field residual error, B is the model parameter of the density initial model-1tResidual back propagation data; and superposing the gradients of all the single shot data to obtain the global gradient of the density model space.
Specifically, the full waveform inversion of the characteristic wave based on the wave equation is researched by using the green function of the frequency domain acoustic wave equation, wherein the green function of the frequency domain acoustic wave equation is shown as a formula (33):
Figure BDA0001988396560000122
and selecting the density as a model parameterization mode, wherein the gradient of the conventional two-norm target functional about the density is as follows:
Figure BDA0001988396560000123
wherein
Figure BDA0001988396560000124
Figure BDA0001988396560000125
k＝ρVp 2(37)
Wherein, PfFor forward modeling of data, PbResidual back propagation data, ω is frequency, ρ is density, k is modulus, E is error functional, VpIs the velocity.
And step 107, updating the initial density model by using the density updating gradient of the error functional to obtain an accurate density model.
In particular, let the gradient function
Figure BDA0001988396560000126
And obtaining a disturbance model, wherein the final accurate density model is the sum of the initial density model and the disturbance model.
And determining the optimal iteration step size according to a fastest descent method, a conjugate gradient method and a quasi-Newton method LBFGS. Updating the initial density model according to the density updating gradient of the error functional and the optimal iteration step length; determining an iteration termination condition; and when the initial density model meets the iteration termination condition, obtaining an accurate density model.
Specifically, the model is updated using equation (39):
mupdate＝mbefore-αkdk(39)
wherein, αkFor the optimal iteration step size of step k, dkThe gradient of the model at step k.
The iteration termination condition is shown in equation (40):
Figure BDA0001988396560000131
equation (40) specifies an iterative convergence rule for the density ρ, and if the nth update is smaller than a certain proportion of n-1 iterations, e.g., 0.001, the iterations converge and the inversion terminates; otherwise, the updating result is used as input to carry out the next iteration.
The invention provides an underground medium density information retrieval method, which comprises the steps of obtaining a plurality of single-shot data of seismic source vibration in a detection area, wherein the single-shot data comprise single-shot single-channel data and single-shot multi-channel data; intercepting direct waves, shallow reflected waves and shallow refracted waves in the single shot data by using a time window to obtain observation data; acquiring an initial density model, and forward modeling the seismic source waveform based on the initial density model to obtain forward modeling data; calculating a wave field residual error according to the observation data and the forward modeling data, and constructing an error functional according to the wave field residual error; utilizing wave field residual error back propagation to an initial density model space to obtain residual error back propagation data; calculating the density updating gradient of the error functional according to a adjoint state method by utilizing forward modeling data and residual back propagation data; and updating the initial density model by using the density updating gradient of the error functional to obtain an accurate density model. According to the method provided by the invention, waveform inversion is completed by using the kinematics and the dynamics characteristics of a wave field in a period of time after the first arrival according to the geological task requirements, and high-precision modeling of a shallow layer is realized.
Those of skill would further appreciate that the various illustrative components and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, a software module executed by a processor, or a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A method for inversion of density information of a subsurface medium, the method comprising:
acquiring a plurality of single-shot data of seismic source vibration in a detection area, wherein the single-shot data comprises single-shot single-channel data and single-shot multi-channel data;
intercepting direct waves, shallow reflected waves and shallow refracted waves in the single shot data by using a time window to obtain observation data;
acquiring an initial density model, and forward modeling a seismic source waveform based on the initial density model to obtain forward modeling data;
calculating a wave field residual error according to the observation data and the forward modeling data, and constructing an error functional according to the wave field residual error;
utilizing the wave field residual error to perform back propagation to the initial density model space to obtain residual error back propagation data;
calculating the density updating gradient of the error functional according to a adjoint state method by utilizing the forward modeling data and the residual back propagation data;
and updating the initial density model by using the density updating gradient of the error functional to obtain an accurate density model.
2. The method of claim 1, wherein after the intercepting the direct wave, the shallow reflected wave, and the shallow refracted wave in the plurality of single shot data by using the time window to obtain the observation data, the method further comprises:
performing filtering processing on the observation data by utilizing wavelet transformation to obtain processed observation data;
and performing multiple suppression processing on the processed observation data.
3. The method of claim 1, wherein forward modeling the source waveform based on the initial density model to obtain forward modeling data comprises:
performing time domain dispersion on the wave equation of the seismic source waveform by using a staggered grid finite difference method to obtain a dispersed wave equation;
and determining the wave field value of the spatial distribution of the staggered grid at each moment according to the dispersed wave equation and the initial density model.
4. The method of claim 1, wherein said calculating a wavefield residual from said observation data and said forward modeling data specifically comprises:
and subtracting the observation data and the forward modeling data to obtain the wave field residual error.
5. The method according to claim 1, wherein said constructing an error functional from said wavefield residual specifically comprises:
according to the formula
Figure FDA0001988396550000021
Calculating an error functional, wherein E (m) is the error functional, b (m) is a linear function representing the result data of the forward modeling, dobsFor observation data, b (m) -dobsAs wave field residual, CDAs a data covariance matrix, CMIs a covariance matrix of the model, m is a model parameter of the density initial model, mpriorIs a prior information model, and lambda is a prior information specific gravity parameter.
6. The method according to claim 1, wherein said utilizing said wavefield residual back propagation to said initial density model space to obtain residual back propagation data specifically comprises:
and (3) acting a counter-propagation operator on the wave field residual error to obtain residual error counter-propagation data of the initial density model space.
7. The method according to claim 1, wherein said calculating a density update gradient of the error functional according to a adjoint state method using the forward modeling data and the residual back propagation data specifically comprises:
according to the formula
Figure FDA0001988396550000022
Calculating a density update gradient;
wherein the content of the first and second substances,
Figure FDA0001988396550000023
k＝ρVp 2；Pffor forward modeling of data, PbResidual back propagation data, ω is frequency, ρ is density, k is modulus, E is error functional, VpIs the velocity.
8. The method of claim 1, further comprising:
and determining the optimal iteration step size according to a fastest descent method, a conjugate gradient method and a quasi-Newton method LBFGS.
9. The method of claim 8, wherein updating the initial density model with the density update gradient of the error functional to obtain an accurate density model comprises:
updating the initial density model according to the density updating gradient of the error functional and the optimal iteration step length;
determining an iteration termination condition;
and when the initial density model meets the iteration termination condition, obtaining an accurate density model.
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