CN113970789A - Full waveform inversion method, full waveform inversion device, storage medium and electronic equipment - Google Patents
Full waveform inversion method, full waveform inversion device, storage medium and electronic equipment Download PDFInfo
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Abstract
The application relates to the technical field of velocity modeling and seismic imaging of oil and gas exploration and development, in particular to a full waveform inversion method, a full waveform inversion device, a full waveform inversion storage medium and electronic equipment, and solves the problems of low resolution and insufficient precision when the full waveform inversion method is used for processing complex stratums. The method comprises the following steps: acquiring actual seismic data and an initial velocity model; acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization item according to actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional; processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional; solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula; and inputting the actual seismic data and the initial velocity model into a full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
Description
Technical Field
The application relates to the technical field of velocity modeling and seismic imaging in oil and gas exploration and development, in particular to a full waveform inversion method, a full waveform inversion device, a storage medium and electronic equipment.
Background
The conventional full waveform inversion method is to use an L2 norm (Euclidean norm) of an error between actual seismic data and simulated seismic data as a target functional and solve an inversion result by minimizing the target functional, but the conventional target functional only contains a data fitting item and does not contain regularization constraint, so that the inversion is easy to fall into a local extremum problem, an ideal high-resolution and high-precision inversion result cannot be obtained, and the regularization constraint needs to be carried out on the full waveform inversion.
While the regularization methods widely used in the related art include a Tikhonov regularization method and a total variation regularization method, the inversion result obtained by one method is still a smooth boundary and is difficult to meet the requirement of high resolution; the second method can improve inversion accuracy to some extent, but high-accuracy inversion results of boundary focusing are still difficult to obtain for other complex strata.
Disclosure of Invention
The application provides a full waveform inversion method, a full waveform inversion device, a storage medium and electronic equipment, aiming at the technical problems of low resolution and insufficient precision when the full waveform inversion method is used for processing complex stratums.
In a first aspect, the present application provides a method of full waveform inversion, the method comprising:
acquiring actual seismic data and an initial velocity model;
acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization item according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional;
processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional;
solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula;
and inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
According to an embodiment of the present application, optionally, in the full waveform inversion method, the introducing a high-order total variation regularization term according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional includes:
constructing a full-waveform inversion target functional according to the actual seismic data and the simulated seismic data;
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional;
wherein the full waveform inversion target functional comprises:
m represents a stratum medium model parameter;
g (m) represents a seismic wave forward modeling simulation wave field based on the stratum medium model parameter m;
d represents observed seismic data.
According to an embodiment of the present application, optionally, in the full waveform inversion method, the introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional includes:
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional, wherein the high-order total variation regularization target functional comprises:
wherein λ represents a regularization factor;
T(l)representing a high-order total variation regularization operator;
l represents a total variation regularization differential order;
λ||T(l)m||1a high order total variation regularization term is represented.
According to an embodiment of the present application, optionally, in the above full-waveform inversion method, the higher-order total variation regularization term λ | | T(l)m||1Including a norm penalty term for a sparse regularization operator.
According to an embodiment of the present application, optionally, in the full waveform inversion method, the processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional includes:
acquiring actual data and simulation data of a pre-stack seismic wave field;
matching the actual data with the simulated data through seismic wave forward modeling to obtain an inversion solution target functional;
the inversion solving of the target functional comprises the following steps:
wherein v represents the longitudinal wave velocity of the formation medium;
t represents the seismic wave propagation time;
xsrepresenting the coordinates of the shot point, xrRepresenting the coordinates of the demodulator probe;
u(t,xs,xr(ii) a v) representing the forward modeling wave field of the seismic waves;
dobs(t,xs,xr) Representing an observed seismic wavefield.
According to an embodiment of the present application, optionally, in the full waveform inversion method, the solving the inversion solution target functional to obtain a full waveform inversion iterative solution formula includes:
transforming the inversion solving target functional into an equivalent constraint form:
where eta is T(l)v；
Converting the target functional transformed into an equivalent constrained form into an unconstrained optimized form:
replacing the first two terms on the right side of an equation in the optimal form of the inversion solution target functional with preset variables, and updating the inversion solution target functional:
wherein J (v, η) is a predetermined variable;
and processing the updated inversion solving target functional through an iterative algorithm to obtain a full waveform inversion iteration solving formula.
According to an embodiment of the present application, optionally, in the full-waveform inversion method, the inputting the actual seismic data and the initial velocity model into the full-waveform inversion iterative solution formula to obtain a seismic wave full-waveform inversion velocity model includes:
inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula;
solving the full waveform inversion iteration solving formula to obtain a full waveform inversion velocity model of each iteration;
comparing the target spread function value of each iterative calculation with a preset threshold value, and obtaining a seismic wave full waveform inversion velocity model when the target spread function value is smaller than the preset threshold value;
wherein the iterative solution formula comprises:
k represents the number of iterations;
b represents the iterative solution introduction.
In a second aspect, the present application provides a full waveform inversion apparatus, the apparatus comprising:
the acquisition module is used for acquiring actual seismic data and an initial velocity model;
the construction module is used for acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization term according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional;
the conversion module is used for processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional;
the solving module is used for solving the inversion solving target functional to obtain a full waveform inversion iteration solving formula;
and the execution module is used for inputting the actual seismic data and the initial velocity model into the full waveform inversion solving formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a stratum velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
According to an embodiment of the present application, optionally, in the full-waveform inversion device, the introducing a high-order total variation regularization term according to the actual seismic data and the simulated seismic data to construct a high-order total variation regularization target functional includes:
constructing a full-waveform inversion target functional according to the actual seismic data and the simulated seismic data;
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional;
wherein the full waveform inversion target functional comprises:
m represents a stratum medium model parameter;
g (m) represents a seismic wave forward modeling simulation wave field based on the stratum medium model parameter m;
d represents observed seismic data.
According to an embodiment of the present application, optionally, in the above full-waveform inversion apparatus, the introducing a high-order total variation regularization term into the full-waveform inversion target functional to obtain a high-order total variation regularization target functional includes:
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional, wherein the high-order total variation regularization target functional comprises:
wherein λ represents a regularization factor;
T(l)representing a high-order total variation regularization operator;
l represents a total variation regularization differential order;
λ||T(l)m||1a high order total variation regularization term is represented.
According to an embodiment of the application, optionally, in the above full-waveform inversion apparatus, the higher-order total variation regularization term λ | | T(l)m||1Including a norm penalty term for a sparse regularization operator.
According to an embodiment of the present application, optionally, in the full-waveform inversion device, the processing the high-order total variation regularization target functional through forward modeling to obtain an inversion solution target functional includes:
acquiring actual data and simulation data of a pre-stack seismic wave field;
matching the actual data with the simulated data through seismic wave forward modeling to obtain an inversion solution target functional;
the inversion solving of the target functional comprises the following steps:
wherein v represents the longitudinal wave velocity of the formation medium;
t represents the seismic wave propagation time;
xsrepresenting the coordinates of the shot point, xrRepresenting the coordinates of the demodulator probe;
u(t,xs,xr(ii) a v) representing the forward modeling wave field of the seismic waves;
dobs(t,xs,xr) Representing an observed seismic wavefield.
According to an embodiment of the present application, optionally, in the full-waveform inversion apparatus, the solving the inversion solution target functional to obtain a full-waveform inversion iterative solution formula includes:
transforming the inversion solving target functional into an equivalent constraint form:
where eta is T(l)v；
Converting the target functional transformed into an equivalent constrained form into an unconstrained optimized form:
replacing the first two terms on the right side of an equation in the optimal form of the inversion solution target functional with preset variables, and updating the inversion solution target functional:
wherein J (v, η) is a predetermined variable;
and processing the updated inversion solving target functional through an iterative algorithm to obtain a full waveform inversion iteration solving formula.
According to an embodiment of the present application, optionally, in the full-waveform inversion apparatus, the inputting the actual seismic data and the initial velocity model into the full-waveform inversion iterative solution formula to obtain a seismic wave full-waveform inversion velocity model includes:
inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula;
solving the full waveform inversion iteration solving formula to obtain a full waveform inversion velocity model of each iteration;
comparing the target spread function value of each iterative calculation with a preset threshold value, and obtaining a seismic wave full waveform inversion velocity model when the target spread function value is smaller than the preset threshold value;
wherein the iterative solution formula comprises:
k represents the number of iterations and b represents the iterative solution lead-in variable.
In a third aspect, the present application provides a storage medium storing a computer program executable by one or more processors for implementing a full waveform inversion method as described above.
In a fourth aspect, the present application provides an electronic device comprising a memory and a processor, the memory having stored thereon a computer program, the memory and the processor being communicatively coupled to each other, the computer program, when executed by the processor, performing the full waveform inversion method as described above.
Compared with the prior art, the full waveform inversion method, the full waveform inversion device, the storage medium and the electronic equipment provided by the application have the beneficial effects that:
1. a high-order total variation regularization term is introduced in the full waveform inversion process, the sparsity of the model is improved by using a high-order total variation regularization operator, the sparsity of the inversion result is increased, the convergence speed of the full waveform inversion subjected to regularization constraint is higher, and the inversion efficiency is improved;
2. solving a target functional optimization solving problem through a high-efficiency target functional solving algorithm, and improving the depicting capability of the inversion result stratum boundary;
3. by the full waveform inversion method, a high-resolution and high-precision stratum velocity model with boundary focusing can be established.
Drawings
The present application will be described in more detail hereinafter on the basis of embodiments and with reference to the accompanying drawings:
FIG. 1 is an image of an unregulated full waveform inversion of formation velocity;
fig. 2 is a schematic flowchart of a full waveform inversion method according to an embodiment of the present application;
FIG. 3 is an image of formation velocity obtained from an initial velocity model provided by embodiments of the present application;
fig. 4 is a full waveform inversion image of the formation velocity obtained by a full waveform inversion method according to an embodiment of the present application;
fig. 5 is a connection block diagram of a full waveform inversion apparatus according to an embodiment of the present application.
In the drawings, like parts are designated with like reference numerals, and the drawings are not drawn to scale.
Detailed Description
The following detailed description will be provided with reference to the accompanying drawings and embodiments, so that how to apply the technical means to solve the technical problems and achieve the corresponding technical effects can be fully understood and implemented. The embodiments and various features in the embodiments of the present application can be combined with each other without conflict, and the formed technical solutions are all within the scope of protection of the present application.
The Full Waveform Inversion method (Full Waveform Inversion) is to use amplitude and phase information of seismic waves to obtain reliable model parameters by iteratively updating model parameters to minimize the difference between actual seismic records and synthetic records. The method has the characteristics of high resolution and high precision of inversion, can provide a high-precision velocity field for prestack time and depth migration, and provides reliable velocity data for lithology judgment and oil and gas reservoir identification, but the realization of a full waveform inversion method has a plurality of difficulties at present, such as instability of an inversion problem solution; strong non-linearity of the inverse problem; the immediacy of the processed data and the high complexity of the time space, etc. Therefore, improving the efficiency and the accuracy of the seismic wave full waveform inversion is work with great theoretical significance and practical value. Forward numerical simulation is an important theoretical basis for full waveform inversion, and the accuracy of the results affects the later work of seismic data processing.
Fig. 1 is an un-regularized earth velocity full waveform inversion image, and as shown in fig. 1, in the conventional full waveform inversion method, an L2 norm of an error between actual seismic data and simulated seismic data is used as a target functional, and an inversion result is solved by minimizing the target functional, but the conventional target functional only contains a data fitting item and does not contain regularization constraints, so that inversion is easy to fall into a local extremum problem, an ideal high-resolution high-precision inversion result cannot be obtained, and therefore regularization constraints need to be performed on full waveform inversion.
And the regularization methods widely used in the current-stage seismic inversion include a Tikhonov regularization method (gighong loff regularization method) and a total variation regularization method.
The Tikhonov regularization method cannot obtain a good inversion result due to smooth transition in constraint, because the regularization term is small for smooth parameters, but becomes large when the parameters are discontinuous or change greatly, and at the moment, the Tikhonov regularization method cannot obtain a good inversion result, and even cannot be stable. Therefore, the inversion result obtained by the Tikhonov regularization method is still a smooth boundary, and the requirement of high resolution is difficult to achieve.
And during seismic inversion, earth medium model parameters are usually discontinuous, such as a stratum velocity field, high velocity difference stratum may exist, the problem of velocity mutation may be solved by a total variation regularization method, however, the total variation regularization still has some limitations affecting the performance of the total variation regularization, the regularization penalty term utilizes the sparsity of the model, which is not applicable to non-block models, and the first-order difference of complex structure models is not sparse. Although the total variation regularization method can improve the inversion accuracy to a certain extent and has a good effect on solving the geologic body with high speed difference, the high-accuracy inversion result of boundary focusing is still difficult to obtain for other complex stratums.
The application provides a full waveform inversion method, a full waveform inversion device, a storage medium and electronic equipment, and solves the technical problems of low resolution and insufficient precision of the full waveform inversion method in the related art when complex formations are processed.
Example one
Fig. 2 is a schematic flow chart of a full waveform inversion method provided in an embodiment of the present application, and as shown in fig. 2, the method includes:
step S110: acquiring observation seismic data and an initial velocity model;
step S120: acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization item according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional;
step S130: processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional;
step S140: solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula;
step S150: and inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
Further, the introducing a high-order total variation regularization term according to the actual seismic data and the simulated seismic data to construct a high-order total variation regularization target functional includes:
constructing a full-waveform inversion target functional according to the actual seismic data and the simulated seismic data;
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional;
wherein the full waveform inversion target functional comprises:
m represents a stratum medium model parameter;
g (m) represents a seismic wave forward modeling simulation wave field based on the stratum medium model parameter m;
d represents observed seismic data.
Specifically, m represents a formation medium model parameter, which may be a formation medium velocity or other elastic parameters;
g (m) is a seismic wave forward modeling wave field based on the stratum medium model parameter m, and describes a seismic wave field propagation process.
The formation medium model is an existing model, and a modeling mode and related relevant parameters of the existing model are not specifically described in the embodiment.
Further, the introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional includes:
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional, wherein the high-order total variation regularization target functional comprises:
wherein λ represents a regularization factor;
T(l)representing a high-order total variation regularization operator;
l represents a total variation regularization differential order;
λ||T(l)m||1a high order total variation regularization term is represented.
Specifically, in
When the temperature of the water is higher than the set temperature,
expressing a Hamiltonian, and for m, not requiring the Hamiltonian to be continuous, but only requiring the Hamiltonian to meet bounded variation;
λ represents a regularization factor for controlling the balance between the data residual term and the high-order total variation term, which may be set to spatially varying such that the high-order total variation regularization term has different weights at different locations in the full waveform inversion model space.
Further, the higher-order total variation regularization term λ | | T(l)m||1Including norm penalties for sparse regularization operators, abbreviated as L1 regularization (L1 regularization or lasso).
Specifically, the high-order total variation regularization term can better utilize the sparsity of the full waveform inversion model, thereby constraining the inversion process.
According to the full waveform inversion method and the full waveform inversion device, the high-order total variation regularization item is introduced in the full waveform inversion process, and the sparsity of the high-order total variation regularization item to a full waveform inversion model is utilized, so that the sparsity of an inversion result is increased, the convergence speed of full waveform inversion is increased, and the inversion efficiency is improved.
Further, the processing the high-order total variation regularization target functional through forward seismic wave simulation to obtain an inversion solution target functional includes:
acquiring actual data and simulation data of a pre-stack seismic wave field;
matching the actual data with the simulated data through seismic wave forward modeling to obtain an inversion solution target functional;
the inversion solving of the target functional comprises the following steps:
wherein v represents the longitudinal wave velocity of the formation medium;
t represents the seismic wave propagation time;
xsrepresenting the coordinates of the shot point, xrRepresenting the coordinates of the demodulator probe;
u(t,xs,xr(ii) a v) representing the forward modeling wave field of the seismic waves;
dobs(t,xs,xr) Representing an observed seismic wavefield.
Matching the actual data with the simulation data through seismic wave forward modeling to obtain an inversion solution target functional, wherein the method comprises the following steps: and comparing the actual data with the simulated data through seismic wave forward modeling, and continuously correcting the high-order total variation regularization target functional to minimize the error between the actual data and the simulated data so as to enable the simulation result to be as close to the actual data as possible.
Specifically, a time domain wave equation is taken as an example. The time domain acoustic wave equation comprises:
wherein v represents the longitudinal wave velocity of the formation medium;
u represents the seismic wavefield;
t represents the seismic wave propagation time;
x and z represent sample point spatial locations;
s denotes the seismic source.
Acquiring actual data and simulation data of a pre-stack seismic wave field;
comparing the actual data with the simulation data through a forward modeling method to obtain an inversion solution target functional:
wherein x issRepresenting the coordinates of the shot point, xrRepresenting the coordinates of the demodulator probe;
u(t,xs,xr(ii) a v) representing the forward modeling wave field of the seismic waves;
dobsrepresenting an observed seismic wavefield.
Further, solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula, including:
transforming the inversion solving target functional into an equivalent constraint form:
where eta is T(l)v；
Converting the target functional transformed into an equivalent constrained form into an unconstrained optimized form:
replacing the first two terms on the right side of an equation in the optimal form of the inversion solution target functional with preset variables, and updating the inversion solution target functional:
wherein J (v, η) is a predetermined variable;
and processing the updated inversion solving target functional through an iterative algorithm to obtain a full waveform inversion iteration solving formula.
Specifically, η has no practical meaning and is an intermediate parameter, which facilitates expression of the formula.
Further, the inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model includes:
inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula;
solving the full waveform inversion iteration solving formula to obtain a full waveform inversion velocity model of each iteration;
comparing the target spread function value of each iterative calculation with a preset threshold value, and obtaining a seismic wave full waveform inversion velocity model when the target spread function value is smaller than the preset threshold value;
wherein the iterative solution formula comprises:
k represents the number of iterations and b represents the iterative solution lead-in variable.
Specifically, k is selected according to a simulation result of the full waveform inversion model;
the preset threshold value can be preset according to formation actual data and represents an inversion termination threshold value.
And comparing the target spread function value of each iteration calculation with a preset threshold, and when the iteration times reach a termination condition (namely the target spread function value is less than the preset threshold), obtaining an inversion result closest to an actual full waveform inversion velocity model, wherein the full waveform inversion velocity model of the iteration inversion result is a required seismic wave full waveform inversion velocity model.
According to the method and the device, the target functional solving algorithm is introduced in the full waveform inversion process to solve the target functional, so that the description capability of the stratum boundary of the inversion result is improved.
For example, obtaining actual seismic data and an initial velocity model, obtaining simulated seismic data according to the initial velocity model, and constructing a full-waveform inversion target functional according to the actual seismic data and the simulated seismic data:
introducing a high-order total variation regularization term lambda | T into a full waveform inversion target functional(l)m||1And obtaining a high-order total variation regularization target functional:
acquiring actual data and simulation data of a pre-stack seismic wave field, comparing the actual data with the simulation data through seismic wave forward modeling, and continuously correcting the high-order total variation regularization target functional to minimize the error of the actual data and the simulation data, so as to obtain an inversion solving target functional:
transforming the inversion solving target functional into an equivalent constraint form:
and then converting the inversion solution target functional transformed into the equivalent constraint form into an unconstrained finalized form:
replacing the first two terms on the right side of an equation in the optimal form of the inversion solution target functional with preset variables, and obtaining the result after updating the inversion solution target functional:
then obtaining an iterative solution formula through an iterative algorithm:
inputting the actual seismic data and the initial velocity model into the full waveform inversion iteration solving formula, and solving the full waveform inversion iteration solving formula to obtain a full waveform inversion velocity model of each iteration;
and comparing the target spread function value of each iterative calculation with a preset threshold value, determining a full waveform inversion velocity model with the target spread function value smaller than the preset threshold value as a required seismic wave full waveform inversion velocity model, and obtaining a stratum velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
The application provides a full waveform inversion method, which comprises the following steps: acquiring actual seismic data and an initial velocity model; acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization item according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional; processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional; solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula; and inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model to provide a reliable basis for formation lithology judgment and reservoir identification. According to the full waveform inversion method and device, a high-order total variation regularization term is introduced in the full waveform inversion process, the sparsity of a model is improved by using the high-order total variation regularization operator, the sparsity of an inversion result is increased, the full waveform inversion convergence speed for regularization constraint is higher, and the inversion efficiency is improved; and then solving a target functional optimization solving problem through a high-efficiency target functional solving algorithm, improving the description capacity of the inversion result stratum boundary, obtaining a seismic wave full waveform inversion image through a full waveform inversion model, and providing a reliable basis for lithology judgment and oil and gas reservoir identification.
Example two
This example uses an initial velocity model to test the full waveform inversion method of the present application.
The initial velocity model size includes: the transverse direction is 4km, the depth is 2.3km, and the transverse and longitudinal grid numbers respectively comprise: 201 in the transverse direction nx, 116 in the longitudinal direction nz, wherein the transverse grid interval and the longitudinal grid interval respectively comprise: the transverse direction dx is 20m, the longitudinal direction dz is 20m, and the speed range is 3364m/s to 7000 m/s.
Wherein, the seismic source and the detector are both positioned on the earth surface, 40 cannon data are provided in total, the cannon spacing is 100m, and the interval of the wave detection points is not 20 m. And (3) performing standard wave forward modeling by adopting a high-order finite difference method, wherein the theoretical wavelet is a Rake wavelet with a main frequency of 20Hz, the seismic recording time is 1.5s, and the time sampling interval is 0.001 s.
Fig. 3 is a formation velocity image obtained by an initial velocity model according to an embodiment of the present application, and as shown in fig. 3, when the full waveform inversion method of the present application is not used, the boundary of the full waveform inversion image of the seismic waves obtained by the initial velocity model is smooth and fuzzy, and has low resolution.
As shown in fig. 4, after the initial velocity model adopts the full waveform inversion method of the present application, the obtained formation velocity full waveform inversion image has clear formation boundary delineation, boundary focusing, high resolution and high precision.
In this embodiment, the specific embodiment process of the method steps of the initial velocity model test full waveform inversion method can be referred to as embodiment one, and this embodiment is not repeated here.
EXAMPLE III
Fig. 5 is a connection block diagram of a full waveform inversion apparatus 200 according to an embodiment of the present application, and as shown in fig. 5, the full waveform inversion apparatus 200 includes:
an obtaining module 201, configured to obtain actual seismic data and an initial velocity model;
the building module 202 is configured to obtain simulated seismic data according to the initial velocity model, introduce a high-order total variation regularization term according to the actual seismic data and the simulated seismic data, and build a high-order total variation regularization target functional;
the conversion module 203 is used for processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional;
a solving module 204, configured to solve the inversion solution target functional to obtain a full waveform inversion iteration solution formula;
the executing module 205 is configured to input the actual seismic data and the initial velocity model into the full waveform inversion solving formula to obtain a seismic wave full waveform inversion velocity model, and obtain a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
Further, the introducing a high-order total variation regularization term according to the actual seismic data and the simulated seismic data to construct a high-order total variation regularization target functional includes:
constructing a full-waveform inversion target functional according to the actual seismic data and the simulated seismic data;
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional;
wherein the full waveform inversion target functional comprises:
m represents a stratum medium model parameter;
g (m) represents a seismic wave forward modeling simulation wave field based on the stratum medium model parameter m;
d represents observed seismic data.
Further, the introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional includes:
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional, wherein the high-order total variation regularization target functional comprises:
wherein λ represents a regularization factor;
T(l)representing a high-order total variation regularization operator;
l represents a total variation regularization differential order;
λ||T(l)m||1a high order total variation regularization term is represented.
Further, the higher-order total variation regularization term λ | | T(l)m||1Including a norm penalty term for a sparse regularization operator.
Further, the processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional, including:
acquiring actual data and simulation data of a pre-stack seismic wave field;
matching the actual data with the simulated data through seismic wave forward modeling to obtain an inversion solution target functional;
the inversion solving of the target functional comprises the following steps:
wherein v represents the longitudinal wave velocity of the formation medium;
t represents the seismic wave propagation time;
xsrepresenting the coordinates of the shot point, xrRepresenting the coordinates of the demodulator probe;
u(t,xs,xr(ii) a v) representing the forward modeling wave field of the seismic waves;
dobs(t,xs,xr) Representing an observed seismic wavefield.
Further, solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula, including:
transforming the inversion solving target functional into an equivalent constraint form:
where eta is T(l)v；
To transform into equivalent constraint formThe standard functional is converted to an unconstrained optimization form:
replacing the first two terms on the right side of an equation in the optimal form of the inversion solution target functional with preset variables, and updating the inversion solution target functional:
wherein J (v, η) is a predetermined variable;
and processing the updated inversion solving target functional through an iterative algorithm to obtain a full waveform inversion iteration solving formula.
Further, the inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model includes:
inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula;
solving the full waveform inversion iteration solving formula to obtain a full waveform inversion velocity model of each iteration;
comparing the target spread function value of each iterative calculation with a preset threshold value, and obtaining a seismic wave full waveform inversion velocity model when the target spread function value is smaller than the preset threshold value;
wherein the iterative solution formula comprises:
k represents the number of iterations;
b represents the iterative solution induced variables.
In this embodiment, the specific implementation process of the method steps can be referred to as the first implementation process, and this embodiment is not repeated here.
Example four
The present embodiments also provide a computer-readable storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory (e.g., SD or DX memory, etc.), a Random Access Memory (RAM), a Static Random Access Memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, a server, an App application mall, etc., having stored thereon a computer program that, when executed by a processor, performs the method steps of the first embodiment.
The method executed by the processor comprises the following steps:
acquiring actual seismic data and an initial velocity model;
acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization item according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional;
processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional;
solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula;
and inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
Further, the introducing a high-order total variation regularization term according to the actual seismic data and the simulated seismic data to construct a high-order total variation regularization target functional includes:
constructing a full-waveform inversion target functional according to the actual seismic data and the simulated seismic data;
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional;
wherein the full waveform inversion target functional comprises:
m represents a stratum medium model parameter;
g (m) represents a seismic wave forward modeling simulation wave field based on the stratum medium model parameter m;
d represents observed seismic data.
Further, the introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional includes:
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional, wherein the high-order total variation regularization target functional comprises:
wherein λ represents a regularization factor;
T(l)representing a high-order total variation regularization operator;
l represents a total variation regularization differential order;
λ||T(l)m||1a high order total variation regularization term is represented.
Further, the higher-order total variation regularization term λ | | T(l)m||1Including a norm penalty term for a sparse regularization operator.
Further, the processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional, including:
acquiring actual data and simulation data of a pre-stack seismic wave field;
matching the actual data with the simulated data through seismic wave forward modeling to obtain an inversion solution target functional;
the inversion solving of the target functional comprises the following steps:
wherein v represents the longitudinal wave velocity of the formation medium;
t represents the seismic wave propagation time;
xsrepresenting the coordinates of the shot point, xrRepresenting the coordinates of the demodulator probe;
u(t,xs,xr(ii) a v) representing the forward modeling wave field of the seismic waves;
dobs(t,xs,xr) Representing an observed seismic wavefield.
Further, solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula, including:
transforming the inversion solving target functional into an equivalent constraint form:
where eta is T(l)v；
Converting the target functional transformed into an equivalent constrained form into an unconstrained optimized form:
replacing the first two terms on the right side of an equation in the optimal form of the inversion solution target functional with preset variables, and updating the inversion solution target functional:
wherein J (v, η) is a predetermined variable;
and processing the updated inversion solving target functional through an iterative algorithm to obtain a full waveform inversion iteration solving formula.
Further, the inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model includes:
inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula;
solving the full waveform inversion iteration solving formula to obtain a full waveform inversion velocity model of each iteration;
comparing the target spread function value of each iterative calculation with a preset threshold value, and obtaining a seismic wave full waveform inversion velocity model when the target spread function value is smaller than the preset threshold value;
wherein the iterative solution formula comprises:
k represents the number of iterations;
b represents the iterative solution induced variables.
In this embodiment, the specific implementation process of the method steps can be referred to as the first implementation process, and this embodiment is not repeated here.
EXAMPLE five
An electronic device provided in an embodiment of the present application may include: a processor and a memory, said memory having a computer program stored thereon, said memory and said processor being communicatively coupled to each other, said computer program, when executed by said processor, performing a full waveform inversion method as described in embodiment one.
The Processor may be an Application Specific Integrated Circuit (ASIC), a Digital Signal Processor (DSP), a Digital Signal Processing Device (DSPD), a Programmable Logic Device (PLD), a Field Programmable Gate Array (FPGA), a controller, a microcontroller, a microprocessor, or other electronic components, and is configured to execute the full waveform inversion method in the first embodiment.
The Memory may be implemented by any type of volatile or non-volatile Memory device or combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic Memory, flash Memory, magnetic disk or optical disk.
In summary, the present application provides a full waveform inversion method, apparatus, storage medium and electronic device, where the method includes: acquiring actual seismic data and an initial velocity model; acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization item according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional; processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional; solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula; and inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
According to the full waveform inversion method and device, a high-order total variation regularization term is introduced in the full waveform inversion process, the sparsity of a model is improved by using the high-order total variation regularization operator, the sparsity of an inversion result is increased, the full waveform inversion convergence speed for regularization constraint is higher, and the inversion efficiency is improved; then solving a target functional optimization solving problem through a high-efficiency target functional solving algorithm, and improving the depicting capability of the inversion result stratum boundary; according to the full waveform inversion method, a high-resolution and high-precision stratum velocity model with a focused boundary can be established, and a seismic wave full waveform inversion image is obtained through the full waveform inversion model, so that a reliable basis is provided for lithology judgment and oil-gas reservoir identification of the stratum.
In the embodiments provided in the present application, it should be understood that the disclosed method can be implemented in other ways. The above-described method embodiments are merely illustrative.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
Although the embodiments disclosed in the present application are described above, the above descriptions are only for the convenience of understanding the present application, and are not intended to limit the present application. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims.
Claims (10)
1. A method of full waveform inversion, the method comprising:
acquiring actual seismic data and an initial velocity model;
acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization item according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional;
processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional;
solving the inversion solution target functional to obtain a full waveform inversion iteration solution formula;
and inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
2. The method of claim 1, wherein said introducing a higher order total variation regularization term from said actual seismic data and said simulated seismic data to construct a higher order total variation regularization target functional comprises:
constructing a full-waveform inversion target functional according to the actual seismic data and the simulated seismic data;
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional;
wherein the full waveform inversion target functional comprises:
m represents stratum medium model parameters, G (m) represents a seismic wave forward modeling wave field based on the stratum medium model parameters m, and d represents observation seismic data.
3. The method according to claim 2, wherein the introducing a high-order total variation regularization term into the full-waveform inversion target functional to obtain a high-order total variation regularization target functional comprises:
introducing a high-order total variation regularization term into the full waveform inversion target functional to obtain a high-order total variation regularization target functional, wherein the high-order total variation regularization target functional comprises:
where λ represents the regularization factor, T(l)Representing a high-order total variation regularization operator, l representing a total variation regularization differential order, λ | | T(l)m||1A high order total variation regularization term is represented.
4. The method of claim 3, wherein the higher-order total variation regularization term λ | | T(l)m||1Including a norm penalty term for a sparse regularization operator.
5. The method of claim 3, wherein said processing said higher order total variation regularized target functional by seismic wave forward modeling to obtain an inverse solution target functional comprises:
acquiring actual data and simulation data of a pre-stack seismic wave field;
matching the actual data with the simulated data through seismic wave forward modeling to obtain an inversion solution target functional;
the inversion solving of the target functional comprises the following steps:
wherein v represents the longitudinal wave velocity of the stratum medium, t represents the seismic wave propagation time, and xsRepresenting the coordinates of the shot point, xrDenotes the coordinate of the demodulator probe, u (t, x)s,xr(ii) a v) representation of the forward simulated wavefield of seismic waves, dobs(t,xs,xr) Representing an observed seismic wavefield.
6. The method of claim 5, wherein solving the inversion solution target functional to obtain a full waveform inversion iterative solution formula comprises:
transforming the inversion solving target functional into an equivalent constraint form:
where eta is T(l)v；
Converting a target functional transformed into an equivalent constrained form to an unconstrained maximumAnd (3) optimizing the form:
replacing the first two terms on the right side of an equation in the optimal form of the inversion solution target functional with preset variables, and updating the inversion solution target functional:
wherein J (v, η) is a predetermined variable;
and processing the updated inversion solving target functional through an iterative algorithm to obtain a full waveform inversion iteration solving formula.
7. The method of claim 6, wherein said inputting said actual seismic data and said initial velocity model into said full waveform inversion iterative solution formula to obtain a seismic waveform full waveform inversion velocity model comprises:
inputting the actual seismic data and the initial velocity model into the full waveform inversion iterative solution formula;
solving the full waveform inversion iteration solving formula to obtain a full waveform inversion velocity model of each iteration;
comparing the target spread function value of each iterative calculation with a preset threshold value, and obtaining a seismic wave full waveform inversion velocity model when the target spread function value is smaller than the preset threshold value;
wherein the iterative solution formula comprises:
k represents the number of iterations and b represents the iterative solution lead-in variable.
8. A full waveform inversion apparatus, characterized in that the apparatus comprises:
the acquisition module is used for acquiring actual seismic data and an initial velocity model;
the construction module is used for acquiring simulated seismic data according to the initial velocity model, introducing a high-order total variation regularization term according to the actual seismic data and the simulated seismic data, and constructing a high-order total variation regularization target functional;
the conversion module is used for processing the high-order total variation regularization target functional through seismic wave forward modeling to obtain an inversion solution target functional;
the solving module is used for solving the inversion solving target functional to obtain a full waveform inversion iteration solving formula;
and the execution module is used for inputting the actual seismic data and the initial velocity model into the full waveform inversion solving formula to obtain a seismic wave full waveform inversion velocity model, and obtaining a formation velocity full waveform inversion image according to the seismic wave full waveform inversion velocity model.
9. A storage medium storing a computer program executable by one or more processors to perform a method of full waveform inversion according to any one of claims 1 to 7.
10. An electronic device comprising a memory and a processor, the memory having a computer program stored thereon, the memory and the processor being communicatively coupled to each other, the computer program when executed by the processor performing the full waveform inversion method of any of claims 1 to 7.
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