CN105549079A - Method and device for establishing full-waveform inversion model for geophysics parameters - Google Patents

Abstract

The invention provides a method and device for establishing a full-waveform inversion model for geophysics parameters. The method comprises following steps: residual values of real wave-fields and initial model observation wave-fields are calculated; by use of the residual values, gradients of an objective function to model parameters are calculated through an adjoint state method; A Hessian matrix is calculated by use of variations of the model parameters and variations of the gradients By use of the gradients and the Hessian matrix, trust region sub-problems are established through performing second-order expansion calculation to the objective function according to Taylor's formula; the trust region sub-problems are solved through a conjugate gradient method to obtain solutions, namely the probe step length of the next iteration, of the trust region sub-problems; updates of the model parameters and trust region radii are performed on the basis of the trust region algorithm to obtain the full-waveform inversion model of geophysics parameters. By use of the method and device, a high fidelity velocity model is obtained.

Description

Method and device for establishing full waveform inversion model of geophysical parameters

Technical Field

The invention relates to the technical field of modeling of seismic exploration of coal, petroleum and the like, in particular to a method and a device for establishing a full waveform inversion model of geophysical parameters.

Background

The seismic model technology is to properly simplify the actual complex earth medium and the propagation rule of seismic waves, then to study the characteristics of the seismic waves propagated in a specific simplified model by a mathematical or physical method, to simulate the seismic wave field under the condition of real geological structure, and to guide the actual exploitation and theoretical study of coal, petroleum and other mineral resources; in the whole seismic exploration process, accurately calculating the propagation velocity of seismic waves in a subsurface medium is one of the core problems of the seismic exploration.

In the prior art, geophysical analysis mainly adopts a method of combining forward modeling and inversion, a geological model is known, and measured data of the geological model is solved as forward modeling; the measured data is known, and a geological model is reversely solved as inversion; in the analysis technology adopting the inversion method, gradient calculation is a core part and represents the updating direction of a model, and the prior art has a gradient calculation method based on an adjoint state method, namely, a data residual error of a forward wave field and a backward wave field is used as a new seismic source to carry out forward modeling so as to calculate the gradient of a target function to the model; in the prior art, a solving formula of a steepest descent method in FWI of a time domain 2D acoustic wave equation speed parameter is adopted, and an updating direction is constructed by utilizing negative gradient information to realize updating of a model; moreover, the inversion of longitudinal and transverse wave speeds and density is realized by using a conjugate gradient method, and the updating direction is constructed by using the information of two gradients; furthermore, the L-BFGS method is used for inverting the longitudinal and transverse wave velocity parameters of the 2D elastic wave equation, and the problems of large sea-sen matrix storage capacity and complex calculation in the quasi-Newton algorithm are solved.

However, the gradient algorithm and the newton algorithm of the velocity modeling in the prior art are prone to fall into local extrema due to the limitations of the algorithms themselves, and further updating and iteration cannot be performed, so that the calculation efficiency is low, and finally, it is difficult to obtain a high-fidelity velocity model.

Disclosure of Invention

The invention aims to provide a method and a device for establishing a full waveform inversion model of geophysical parameters, and aims to improve speed modeling precision and inversion efficiency and obtain a high-fidelity speed model.

In order to achieve the above object, an embodiment of the present invention provides a method for establishing a full waveform inversion model of geophysical parameters, and the technical solution is as follows:

a method for establishing a full waveform inversion model of geophysical parameters comprises the following steps:

based on a two-dimensional time domain constant density acoustic wave equation, carrying out forward modeling by a finite difference method to obtain an actual wave field and an initial model observation wave field;

establishing an objective function according to the obtained actual wave field and the observed wave field of the initial model;

calculating a residual value of the actual wavefield and the initial model observed wavefield;

applying the residual value, and calculating the gradient of the objective function to the model parameter by an adjoint state method;

calculating a hessian matrix using the variation of the model parameter and the variation of the gradient;

applying the gradient and the Hessian matrix, and performing second-order expansion operation on the target function according to a Taylor formula to establish a trust domain subproblem;

solving the sub-problem of the trust domain by a conjugate gradient method to obtain a solution of the sub-problem of the trust domain, and taking the solution of the sub-problem of the trust domain as a trial step length of the next iteration;

and updating the model parameters and the trust domain radius based on the trust domain algorithm and the heuristic step length to obtain a full waveform inversion model of the geophysical parameters.

Preferably, the obtaining of the actual wave field and the initial model observation wave field by forward modeling based on the two-dimensional time domain constant density acoustic wave equation through the finite difference method includes:

the acoustic wave equation is:

$\frac{1}{v^2}\frac{{\∂}^{2}p}{\∂t^2}=\frac{{\∂}^{2}p}{\∂x^2}+\frac{{\∂}^{2}p}{\∂z^2};$

where P denotes a sound pressure and v denotes an acoustic velocity.

Establishing an objective function according to the obtained actual wave field and the initial model observation wave field, wherein the method comprises the following steps:

the objective function is:

$E\left(m\right)=\frac{1}{2}\[{\left(f\right(m)-d_{obs})}^T\]\[\left(f\right(m)-d_{obs})\];$

wherein E (m) is an objective function, m is a model parameter, d_obsFor the actual wavefield, f (m) for the observed wavefield, f characterizes the seismic wavefield positive propagation process for the model parameter m.

Preferably, the sub-problem of establishing a trusted domain includes:

the trust domain sub-problem is:

wherein,is a model function obtained by performing a second order expansion of the objective function E (m) according to Taylor's formula ξ_kFor the solution of the sub-problem of the trust domain to be solved, g_kGradient of model parameters for the objective function, B_kIs a Hessian matrix, Δ_kRepresenting the confidence domain radius for the kth iteration.

Preferably, the updating of the model parameters and the confidence domain radius based on the confidence domain algorithm to obtain the full waveform inversion model of the geophysical parameters includes:

calculating the measurement value R of the approximation degree of the target function and the model function through forward modeling according to the solution of the sub-problem in the trust domain_kBased on said metric value R_kThe velocity model and confidence domain radius are updated.

The measure of dependence R_kUpdating the velocity model and trust domain radius, including:

let the solution of the trust domain sub-problem be ξ_k，

Will solve ξ_kSolving the subproblem brought into the trust domain to obtain the value Q of the model function_K；

Obtaining a first mesh according to the sound wave equationValue of standard function P_k；

Solving ξ the trust domain sub-problem_kIndependent variable v from the current velocity model_kAdding to obtain new argument value v_k+ξ_kCarrying out forward simulation on the new independent variable value through a sound wave equation, and calculating to obtain a second objective function value P_k+1；

By the first objective function P_kA second objective function value P_k+1And the value Q of the model function_KThe measurement value R is calculated according to the following formula_k：

$R_k=\frac{P_k-P_{k+1}}{-Q_K}.$

Preferably, the method further comprises the step of calculating a metric value R_kUpdating a velocity model, comprising:

the update of the velocity model follows the following rules:

$v_{k+1}=\left\{\begin{array}{cc}{v}_k+{\mathrm{\ξ}}_k,& R_k>0\\ v_k,& R_k\≤0\end{array}\right..$

according to the metric value R_kUpdating the confidence domain radius, including;

the update of the trust domain radius is determined according to the following equation:

${\mathrm{\&Delta;}}_{k+1}=\left\{\begin{array}{cc}min(r_2{\mathrm{\&Delta;}}_k,{\mathrm{\&Delta;}}_{max}),& R_k>{\mathrm{\&eta;}}_2\\ {\mathrm{\&Delta;}}_k,& {\mathrm{\&eta;}}_1\&le;R_k\&le;{\mathrm{\&eta;}}_2\\ r_1{\mathrm{\&Delta;}}_k,& R_k<{\mathrm{\&eta;}}_1\end{array}\right.;$

wherein r is₁<1，r₂>1，0<η₁<η₂<1, are all constants, Δ_maxIs the preset maximum trust domain radius allowed for the current iteration.

Preferably, the updating the model parameters and the radius of the confidence domain based on the confidence domain algorithm to obtain the full waveform inversion model of the geophysical parameters includes:

judging whether the iteration termination condition is met, if not, continuing to solve the sub-problem of the trust domain according to the updated model parameter and the trust domain radius;

and if the iteration termination condition is met, ending the iteration to obtain a final speed model.

Preferably, the judging whether the iteration termination condition is met includes:

the iteration termination condition is met when the iteration times reach the preset upper limit value,

and/or the presence of a gas in the gas,

and when the gradient of the target function reaches a preset minimum value, the iteration termination condition is met.

The embodiment of the invention also provides a device for establishing the full waveform inversion model of the geophysical parameters, which comprises the following steps:

the data acquisition module is used for carrying out forward modeling through a finite difference method based on a two-dimensional time domain constant density acoustic wave equation to obtain an actual wave field and an initial model observation wave field;

the objective function establishing module is used for establishing an objective function according to the obtained actual wave field and the observed wave field of the initial model;

a residual value calculation module for calculating a residual value of the actual wave field and the initial model observed wave field;

the gradient calculation module is used for calculating the gradient of the target function to the model parameters by using the residual value through an adjoint state method;

the hessian matrix calculation module is used for calculating a hessian matrix by using the variation of the model parameters and the variation of the gradient;

the confidence domain subproblem establishing module is used for applying the gradient and the Hessian matrix and establishing a confidence domain subproblem by performing second-order expansion operation on the target function according to a Taylor formula;

a tentative step length determining module, configured to solve the sub-problem in the trust domain by a conjugate gradient method, obtain a solution of the sub-problem in the trust domain, and use the solution of the sub-problem in the trust domain as a tentative step length of a next iteration;

and the inversion model determining module is used for updating the model parameters and the trust domain radius based on the trust domain algorithm and the heuristic step length to obtain a full waveform inversion model of the geophysical parameters.

According to the method and the device for establishing the full waveform inversion model of the geophysical parameters, provided by the embodiment of the invention, the problem of a trust domain is introduced, the trust domain problem can be understood as the trust of an approximate model in one neighborhood, namely, the full waveform inversion based on the trust domain algorithm is provided, the method has global convergence, the defect that a local extremum is easy to fall into in the traditional method is avoided, the inversion accuracy and the inversion efficiency of a velocity model are improved, and the positive effect of obtaining a high-fidelity velocity model is achieved.

In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.

FIG. 1 is a flow chart illustrating a method for building a full waveform inversion model of geophysical parameters according to one embodiment of the present invention;

FIG. 2 shows a forward fault model diagram of a real model;

FIG. 3 shows a normal fault model diagram obtained by applying the model building method provided by the embodiment of the invention;

FIG. 4 shows an inverse fault model diagram of a real model;

FIG. 5 is a diagram illustrating an inverse fault model obtained by applying the model building method provided by the embodiment of the invention;

fig. 6 is a schematic structural diagram of an apparatus for building a full waveform inverse model of geophysical parameters according to an embodiment of the present invention.

Detailed Description

It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.

In order to make the technical solutions of the present invention better understood, 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. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.

The basic idea of the trust domain algorithm is: and (2) providing a trust domain in each iteration, wherein the trust domain is generally a small neighborhood of the current iteration point, then solving a trust domain subproblem in the domain to obtain a solution of the trust domain subproblem, wherein the solution of the trust domain subproblem is a trial step size, then using a certain evaluation rule to determine whether to accept the trial step size and determine the trust domain of the next iteration, and repeating the steps to finally obtain an optimized result.

With the continuous deepening of coal and oil gas seismic exploration, people put higher requirements on high-precision seismic imaging, reservoir description and seismic geological interpretation and promote the continuous progress of an inversion imaging technology. The inversion is that a geological model is obtained from seismic data, a full waveform inversion method for storage and oil reservoir research is an inversion technology based on full waveforms, the full or partial seismic record waveforms are utilized, the information including amplitude, travel time, phase and the like is included, the two-way characteristics of kinematics and dynamics are extracted, and the method has the capability of revealing construction details and lithology under a complex geological background, so that a reliable basis is provided for seismic imaging and velocity modeling.

The inversion needs to give an initial model, here, a final model is obtained after repeated iteration on the basis of the initial model, and the basis is provided for seismic geological imaging and result explanation and coal and oil gas seismic exploration according to the final model.

As shown in fig. 1, the method for building a full waveform inversion model of geophysical parameters provided in the embodiment of the present invention includes the following steps:

s110, performing forward modeling by using a finite difference method based on a two-dimensional time domain constant density acoustic wave equation to obtain an actual wave field and an initial model observation wave field;

wherein, the acoustic wave equation is selected as shown in the following formula:

$\frac{1}{v^2}\frac{{\&part;}^{2}p}{\&part;t^2}=\frac{{\&part;}^{2}p}{\&part;x^2}+\frac{{\&part;}^{2}p}{\&part;z^2};$

wherein P represents a sound pressure, and v represents a sound wave velocity;

the finite difference method is a method for solving numerical solutions of partial differential (or ordinary differential) equations and equation sets definite solutions, and is called a difference method for short, and the finite difference method is a common calculation method in the field of mathematics and is not described herein again.

S120, establishing a target function according to the obtained actual wave field and the observed wave field of the initial model;

wherein the objective function is shown as follows:

$E\left(m\right)=\frac{1}{2}\&lsqb;{\left(f\right(m)-d_{obs})}^T\&rsqb;\&lsqb;\left(f\right(m)-d_{obs})\&rsqb;;$

where E (m) is the objective function, m is the model parameter, d_obsFor the actual wavefield, f (m) for the observed wavefield, f characterizing the seismic wavefield positive propagation process dependent on the model parameter m;

s130, calculating a residual error value of the actual wave field and the initial model observation wave field;

s140, calculating the gradient of the objective function to the model parameter by using the residual value through an adjoint state method;

s150, calculating to obtain a Hessian matrix by using the variable quantity of the model parameters and the variable quantity of the gradient;

the hessian matrix is obtained by calculating the second derivative of the model parameters by the objective function, the calculation process is complex, and the calculation difficulty is high, so that the BFGS algorithm is used for calculating the second derivative of the model parameters by the variation of the model parameters and the variation of the gradient to approximate the second derivative of the objective function.

S160, establishing a confidence domain subproblem by applying the gradient and the Hessian matrix and carrying out second-order expansion operation on the objective function according to a Taylor formula to obtain an equation;

the above trust domain sub-problem is:

in the formula (I), wherein,is a model function obtained by performing a second order expansion of the objective function E (m) according to Taylor's formula ξ_kFor the solution of the sub-problem of the trust domain to be solved, g_kGradient of model parameters for the objective function, B_kIs a Hessian matrix, Δ_kRepresenting the confidence domain radius for the kth iteration.

S170, solving the sub-problem of the trust domain by a conjugate gradient method to obtain a solution of the sub-problem of the trust domain, and taking the solution of the sub-problem of the trust domain as a trial step length of next iteration;

s180, updating the model parameters and the trust domain radius based on the trust domain algorithm and the heuristic step length to obtain a full waveform inversion model of the geophysical parameters; here, the method further includes: before obtaining a full waveform inversion model of the geophysical parameters, judging whether iteration termination conditions are met, if not, continuing to solve the sub-problem of the trust domain according to the updated model parameters and the radius of the trust domain; and if the iteration termination condition is met, ending the iteration to obtain a final speed model.

Further, whether the above-mentioned judgment meets the iteration termination condition or not may adopt any one of the following two ways:

judging whether the iteration times reach a preset upper limit value or not, and judging whether the gradient of the target function reaches a preset minimum value or not;

if the iteration times reach a preset upper limit value or the gradient of the target function reaches a preset minimum value, terminating the iteration; obtaining a final speed model after terminating iteration; the preset upper limit value and the preset minimum value are set in advance by a worker according to specific practical conditions.

In the step S180, the model parameters and the confidence domain radius are updated based on the confidence domain algorithm by using the solution of the confidence domain subproblem, which includes the following steps: calculating the measurement value R of the approximation degree of the target function and the model function through forward modeling according to the solution of the sub-problem in the trust domain_kBased on said metric value R_kThe velocity model and confidence domain radius are updated.

Further, the above is based on the metric value R_kUpdating the velocity model and trust domain radius, including:

let the solution of the trust domain sub-problem be ξ_k，

Will solve ξ_kSolving the subproblem brought into the trust domain to obtain the value Q of the model function_K；

Obtaining a first objective function value P according to the sound wave equation_k；

Solving ξ the trust domain sub-problem_kIndependent variable v from the current velocity model_kAdding to obtain new argument value v_k+ξ_kCarrying out forward simulation on the new independent variable value through a sound wave equation, and calculating to obtain a second objective function value P_k+1；

By the first objective function P_kA second objective function value P_k+1And the value Q of the model function_kThe measurement value R is calculated according to the following formula_k：

$R_K=\frac{P_k-P_{K+1}}{-Q_K}.$

Obtaining a metric value R_kThen according to the metric value R_kAnd updating the speed model, wherein the updating of the speed model conforms to the following rules:

$v_{k+1}=\left\{\begin{array}{cc}{v}_k+{\mathrm{\&xi;}}_k,& R_k>0\\ v_k,& R_k\&le;0\end{array}\right.;$

when R is obtained_kWhen greater than 0, v_k+1Is equal to v_k+ξ_k(ii) a When R is obtained_kWhen v is less than 0 or equal to 0, v is selected_k+1Is equal to v_k。

Obtaining a metric value R_kThen, according to the metric value R_kUpdatingA trust domain radius whose update is determined according to the following equation:

${\mathrm{\&Delta;}}_{k+1}=\left\{\begin{array}{cc}min(r_2{\mathrm{\&Delta;}}_k,{\mathrm{\&Delta;}}_{max}),& R_k>{\mathrm{\&eta;}}_2\\ {\mathrm{\&Delta;}}_k,& {\mathrm{\&eta;}}_1\&le;R_k\&le;{\mathrm{\&eta;}}_2\\ r_1{\mathrm{\&Delta;}}_k,& R_k<{\mathrm{\&eta;}}_1\end{array}\right.;$

wherein r is₁<1，r₂>1，0<η₁<η₂<1, are all constants, Δ_maxAnd presetting the maximum radius of the trust domain allowed by the current iteration according to the actual situation for the staff.

The above-mentioned metric R_kIn the process of solving R, the first solution of R is carried out₁Firstly, the value P of the objective function under the initial model is calculated₁(ii) a Bringing the solution of the current trust domain sub-problem into the trust domain sub-problem solution model parameter Q₁。

Adding the solution of the sub-problem in the trust domain and the current independent variable to obtain a new independent variable value, substituting the new variable value into the acoustic wave equation, performing forward modeling, and calculating a new objective function P₂According to P₁、P₂And Q₁Obtaining a metric value R₁Value of measurement R₁Satisfy the formula $R_1=\frac{P1-P2}{-Q1}.$

Then, the velocity model and the confidence domain radius are updated according to the rule to which the velocity model is updated and the confidence domain radius update formula.

The steps may be adjusted according to actual needs, and the order of the steps is not limited herein.

It can be seen that in the process of establishing the inversion model, an initial model and a real model should be given in advance, on the basis, forward modeling is performed through a finite difference method based on a two-dimensional time domain constant density acoustic wave equation to obtain an observed wave field and an actual wave field of the initial model, then the initial model is continuously updated according to a trust domain algorithm, so that a target function, namely a wave field residual error, is continuously reduced until an iteration termination condition is met, and the inversion model which is closer to the real model is obtained. In the whole process, the above-mentioned continuously updating the initial model means that the model obtained after each iteration is used as the initial model of the next iteration, and the model obtained by each iteration in this embodiment is determined according to the trust domain algorithm.

Obtaining a first objective function value P according to the sound wave equation_kHere P_kThe method is obtained by calculating the wave field residual error of an initial model and a real model through an objective function.

The initial model and the real model given in advance in the embodiment, and the inversion model to be finally obtained are velocity models.

The method for establishing the full waveform inversion model of the geophysical parameters introduces the problem of trust domain, can be understood as relying on an approximate model in one neighborhood, namely provides full waveform inversion based on the trust domain algorithm.

The invention provides a full waveform inversion technology based on a trust domain algorithm, wherein the trust domain algorithm is an algorithm for solving an unconstrained optimization problem, and the algorithm forcibly requires that the distance between a new iteration point and a current iteration point does not exceed a certain control quantity during each iteration. Heuristic step sizes are introduced because conventional line search methods often result in algorithm failures due to too large a step size, especially when the problem is ill-conditioned. The control step is substantially equivalent to extremizing a simple model approximating the original problem in a neighborhood centered on the current iteration point, and the skill can be understood as relying on the approximate model only in a neighborhood, so that the neighborhood is called a trust domain; the trust domain algorithm has global convergence, and avoids the defect that the traditional method is easily limited to local extremum.

FIG. 2 shows a forward fault model diagram of a real model; FIG. 3 shows a normal fault model diagram obtained by applying the model building method provided by the invention.

FIG. 4 shows an inverse fault model diagram of a real model; FIG. 5 shows a reverse fault model diagram obtained by applying the model building method provided by the present invention.

From the comparison between fig. 2 and fig. 3 and the comparison between fig. 4 and fig. 5, it can be clearly seen that the method for establishing the full waveform inversion model of geophysical parameters, provided by the embodiment of the present invention, can obtain a vivid and high-precision velocity model, and has the beneficial effects of improving modeling precision and inversion efficiency and obtaining a high-fidelity velocity model.

In an embodiment shown in fig. 6, an apparatus for building a full waveform inversion model of geophysical parameters includes:

the data acquisition module 210 is configured to perform forward modeling by using a finite difference method based on a two-dimensional time domain constant density acoustic wave equation to obtain an actual wave field and an initial model observation wave field;

an objective function establishing module 220, configured to establish an objective function according to the obtained actual wave field and the observed wave field of the initial model;

a residual value calculating module 230 for calculating a residual value of the actual wave field and the initial model observation wave field;

a gradient calculation module 240, configured to apply the residual value and calculate a gradient of the objective function to the model parameter by using an adjoint state method;

a hessian matrix calculation module 250, configured to calculate a hessian matrix using the variation of the model parameter and the variation of the gradient;

the Hessian matrix uses a BFGS algorithm, is obtained by the variable quantity and the gradient variable quantity of the model parameters and is used for approximately calculating the second derivative of the objective function to the model parameters;

a confidence domain subproblem establishing module 260, configured to apply the gradient and the hessian matrix, and perform a second-order expansion operation on the objective function according to a taylor formula to establish a confidence domain subproblem;

a tentative step size determining module 270, configured to solve the sub-problem in the trust domain by a conjugate gradient method, obtain a solution of the sub-problem in the trust domain, and use the solution of the sub-problem in the trust domain as a tentative step size of a next iteration;

an inversion model determining module 280 for updating the model parameters and the trust domain radius based on the trust domain algorithm and the heuristic step size to obtain a full waveform inversion model of geophysical parameters; here, the method further includes: before obtaining a full waveform inversion model of the geophysical parameters, judging whether iteration termination conditions are met, if not, continuing to solve the sub-problem of the trust domain according to the updated model parameters and the radius of the trust domain; and if the iteration termination condition is met, ending the iteration to obtain a final speed model.

The device provided by the embodiment is used for performing two-dimensional time domain acoustic wave equation full-waveform inversion based on a trust domain algorithm to finally obtain a velocity model, is used for solving the velocity modeling problem in coal petroleum seismic exploration, and has high inversion accuracy and resolution.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A method for establishing a full waveform inversion model of geophysical parameters is characterized by comprising the following steps:

based on a two-dimensional time domain constant density acoustic wave equation, carrying out forward modeling by a finite difference method to obtain an actual wave field and an initial model observation wave field;

establishing an objective function according to the obtained actual wave field and the observed wave field of the initial model;

calculating a residual value of the actual wavefield and the initial model observed wavefield;

applying the residual value, and calculating the gradient of the objective function to the model parameter by an adjoint state method;

calculating a hessian matrix using the variation of the model parameter and the variation of the gradient;

applying the gradient and the Hessian matrix, and performing second-order expansion operation on the target function according to a Taylor formula to establish a trust domain subproblem;

solving the sub-problem of the trust domain by a conjugate gradient method to obtain a solution of the sub-problem of the trust domain, and taking the solution of the sub-problem of the trust domain as a trial step length of the next iteration;

and updating the model parameters and the trust domain radius based on the trust domain algorithm and the heuristic step length to obtain a full waveform inversion model of the geophysical parameters.

2. The method for building the full waveform inversion model of geophysical parameters according to claim 1, wherein the forward modeling is performed by finite difference method based on the two-dimensional time domain constant density acoustic wave equation to obtain the actual wavefield and the initial model observation wavefield, and the method comprises:

the acoustic wave equation is:

$\frac{1}{v^2}\frac{{\&part;}^{2}p}{\&part;t^2}=\frac{{\&part;}^{2}p}{\&part;x^2}+\frac{{\&part;}^{2}p}{\&part;z^2};$

wherein P represents a sound pressure, v represents a sound wave velocity;

establishing an objective function according to the obtained actual wave field and the initial model observation wave field, wherein the method comprises the following steps:

the objective function is:

$E\left(m\right)=\frac{1}{2}\&lsqb;{\left(f\right(m)-d_{obs})}^T\&rsqb;\&lsqb;\left(f\right(m)-d_{obs})\&rsqb;;$

wherein E (m) is an objective function, m is a model parameter, d_obsFor the actual wavefield, f (m) for the observed wavefield, f characterizes the seismic wavefield positive propagation process that depends on the model parameter m.

3. The method of building a full waveform inverse model of geophysical parameters according to claim 2 wherein said building a trust domain sub-problem comprises:

the trust domain sub-problem is:

s.t.||ξ_k||₂≤Δ_k；

wherein,is a model function obtained by performing a second order expansion of the objective function E (m) according to Taylor's formula ξ_kFor the solution of the sub-problem of the trust domain to be solved, g_kGradient of model parameters for the objective function, B_kIs a Hessian matrix, Δ_kRepresenting the confidence domain radius for the kth iteration.

4. The method of building a full waveform inverse model of geophysical parameters according to claim 3 wherein said updating of said model parameters and said trust domain radii based on a trust domain algorithm to obtain a full waveform inverse model of geophysical parameters comprises:

calculating the measurement value R of the approximation degree of the target function and the model function through forward modeling according to the solution of the sub-problem in the trust domain_kBased on said metric value R_kThe velocity model and confidence domain radius are updated.

5. The method of building a full waveform inverse model of geophysical parameters according to claim 4 wherein said metric R_kUpdating the velocity model and trust domain radius, including:

let the solution of the trust domain sub-problem be ξ_k，

Will solve ξ_kSolving the subproblem brought into the trust domain to obtain the value Q of the model function_K；

Obtaining a first objective function value P according to the sound wave equation_k；

Solving ξ the trust domain sub-problem_kIndependent variable v from the current velocity model_kAddingObtaining new argument values v_k+ξ_kCarrying out forward simulation on the new independent variable value through a sound wave equation, and calculating to obtain a second objective function value P_k+1；

By the first objective function P_kA second objective function value P_k+1And the value Q of the model function_kThe metric value R is calculated according to the following formula_k：

$R_K=\frac{P_k-P_{K+1}}{-Q_K}.$

6. The method of building a full waveform inverse model of geophysical parameters according to claim 5 wherein said model is based on said metric R_kUpdating a velocity model, comprising:

the update of the velocity model follows the following rules:

$v_{k+1}=\left\{\begin{array}{cc}{v}_k+{\mathrm{\&xi;}}_k,& R_k>0\\ v_k,& R_k\&le;0\end{array}\right..$

7. the method of building a full waveform inverse model of geophysical parameters according to claim 6 wherein said model is based on said metric R_kUpdating the confidence domain radius, including:

the update of the trust domain radius is determined according to the following equation:

${\mathrm{\&Delta;}}_{k+1}=\left\{\begin{array}{cc}min(r_2{\mathrm{\&Delta;}}_k,{\mathrm{\&Delta;}}_{max}),& R_k>{\mathrm{\&eta;}}_2\\ {\mathrm{\&Delta;}}_k,& {\mathrm{\&eta;}}_1\&le;R_k\&le;{\mathrm{\&eta;}}_2\\ r_1{\mathrm{\&Delta;}}_k,& R_k<{\mathrm{\&eta;}}_1\end{array}\right.;$

wherein r is₁<1，r₂>1，0<η₁<η₂<1, are all constants, Δ_maxIs the preset maximum trust domain radius allowed for the current iteration.

8. The method of building a full waveform inverse model of geophysical parameters according to claim 1, wherein said confidence domain based algorithm performing radius updates of said model parameters and said confidence domain to obtain a full waveform inverse model of geophysical parameters comprises:

judging whether the iteration termination condition is met, if not, continuing to solve the sub-problem of the trust domain according to the updated model parameter and the trust domain radius;

and if the iteration termination condition is met, ending the iteration to obtain a final speed model.

9. The method of building a full waveform inverse model of geophysical parameters according to claim 8, wherein said determining if an iteration termination condition is met comprises:

the iteration termination condition is met when the iteration times reach the preset upper limit value,

and/or the presence of a gas in the gas,

and when the gradient of the target function reaches a preset minimum value, the iteration termination condition is met.

10. An apparatus for building a full waveform inverse model of geophysical parameters, comprising:

the data acquisition module is used for carrying out forward modeling through a finite difference method based on a two-dimensional time domain constant density acoustic wave equation to obtain an actual wave field and an initial model observation wave field;

the objective function establishing module is used for establishing an objective function according to the obtained actual wave field and the observed wave field of the initial model;

a residual value calculation module for calculating a residual value of the actual wave field and the initial model observed wave field;

the gradient calculation module is used for calculating the gradient of the target function to the model parameters by using the residual value through an adjoint state method;

the hessian matrix calculation module is used for calculating a hessian matrix by using the variation of the model parameters and the variation of the gradient;

the confidence domain subproblem establishing module is used for applying the gradient and the Hessian matrix and establishing a confidence domain subproblem by performing second-order expansion operation on the target function according to a Taylor formula;

a tentative step length determining module, configured to solve the sub-problem in the trust domain by a conjugate gradient method, obtain a solution of the sub-problem in the trust domain, and use the solution of the sub-problem in the trust domain as a tentative step length of a next iteration;

and the inversion model determining module is used for updating the model parameters and the trust domain radius based on the trust domain algorithm and the heuristic step length to obtain a full waveform inversion model of the geophysical parameters.