CN109598094B - Seismic vector wave field finite difference numerical simulation method, device and system - Google Patents
Seismic vector wave field finite difference numerical simulation method, device and system Download PDFInfo
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Abstract
The invention provides a finite difference numerical simulation method, a finite difference numerical simulation system, computer equipment and a computer readable storage medium for a seismic vector wave field, and relates to the technical field of seismic exploration. The method comprises the following steps: determining a mixed convolution optimization window function according to window functions of various different parameters and a cosine combination window function; truncating the space convolution sequence of the pseudo-spectrum method according to the mixed convolution optimization window function to obtain an optimized finite difference operator; and carrying out numerical simulation on the seismic vector wave field according to the optimized finite difference operator. The invention constructs a mixed convolution optimization window function based on least square combination, utilizes the window function to truncate a space convolution sequence of a pseudo-spectral method to obtain an optimized finite difference operator, and utilizes the finite difference operator to carry out seismic vector wave field numerical simulation, thereby improving the precision and the efficiency of the seismic vector wave field numerical simulation.
Description
Technical Field
The invention relates to the technical field of seismic exploration, in particular to a numerical simulation technology in the seismic field, and specifically relates to a finite difference numerical simulation method, a finite difference numerical simulation system, computer equipment and a computer readable storage medium for a seismic vector wave field.
Background
The seismic wave field numerical simulation is based on the wave theory, and the propagation process of seismic waves in the earth medium is simulated through numerical calculation. The wave field numerical simulation is the basis of geophysical inversion and imaging technology, a connection can be established between an elastic parameter and a seismic response by means of the seismic wave field numerical simulation, and what seismic response can be obtained under a known reservoir condition is known through the wave field numerical simulation. On the contrary, if a seismic response is assumed, the inversion algorithm can be applied to obtain elastic parameters, and with the elastic parameters, the inversion result can be interpreted based on a petrophysical model to obtain corresponding reservoir parameters. The differential equation method is based on the elastic dynamic principle of continuous medium differential volume elements, and commonly used differential equation methods comprise finite difference and finite element methods, and are an important tool and method for numerical simulation of seismic wave fields. Therefore, the finite difference algorithm with higher precision and efficiency is adopted, the seismic wave field numerical simulation result with higher precision can be obtained, and the requirements of imaging and inversion can be better met.
Finite difference algorithms approximate differential operators by using differential operators, and the approximation inevitably leads to the introduction of numerical dispersion, namely errors. Aiming at numerical dispersion, two methods are mainly used for optimizing a finite difference algorithm and improving the algorithm precision, wherein one method is an optimization method, and the other method is a window function method. The essence of both methods is to reduce the error limit on the premise of obtaining the maximum spectrum coverage, except that the optimization method improves the algorithm precision by searching the optimal solution, and the window function method improves the algorithm precision by interactively designing the optimal solution. In recent years, the geophysical field at home and abroad makes many research works aiming at the optimization of finite difference algorithm to improve the precision of numerical simulation of seismic wave fields, and obtains better effect.
The optimized finite difference coefficient obtained by the calculation of the optimization method is actually a problem of multi-parameter optimization, the optimization methods widely used for optimizing finite difference operators at present comprise a least square method, a simulated annealing method, a Remez algorithm and the like, and different objective functions are required to be used for different optimization methods. The optimal solution in the solution space is searched by the least square method and the Remez algorithm to meet the requirement of error limit, and the problems of slow convergence, and convergence failure to the global optimal solution or convergence failure are usually faced. The optimized finite difference operator is derived by adopting different window functions to truncate the space convolution sequence of the pseudo-spectral method through the preferred window function method.
Therefore, how to provide a new finite difference algorithm for the seismic vector wave field numerical simulation to realize the high-precision and high-efficiency numerical simulation of the seismic vector wave field is a technical problem to be solved in the field.
Disclosure of Invention
In view of this, embodiments of the present invention provide a seismic vector wave field finite difference numerical simulation method, a seismic vector wave field finite difference numerical simulation system, a seismic vector wave field finite difference numerical simulation computer equipment, and a computer readable storage medium, where the method includes performing mixed convolution on a plurality of window functions, performing optimized combination on the plurality of mixed convolution window functions after the mixed convolution and a cosine combination window function based on a least square method to obtain a mixed convolution optimized window function based on a least square combination, and finally truncating a spatial convolution sequence of a pseudo-spectral method by using the window function to obtain an optimized finite difference operator, and performing the seismic vector wave field numerical simulation by using the finite difference operator, thereby improving accuracy and efficiency of the seismic vector wave field numerical simulation.
One of the objectives of the present invention is to provide a finite difference numerical simulation method for seismic vector wavefields, comprising:
determining a mixed convolution optimization window function according to window functions of various different parameters and a cosine combination window;
truncating a space convolution sequence of the pseudo-spectrum method according to the mixed convolution optimization window function to obtain an optimized finite difference operator;
and carrying out numerical simulation on the seismic vector wave field according to the optimized finite difference operator.
Preferably, the determining a hybrid convolution optimization window function according to the window functions of the plurality of different parameters and the cosine combination window includes:
selecting a plurality of window functions;
performing mixed convolution on the window functions with various different parameters to obtain a plurality of mixed convolution window functions;
and optimally combining the plurality of mixed convolution window functions and the cosine combined window function to obtain a mixed convolution optimized window function.
Preferably, the window function is a cosine combining window and/or a rectangular window and/or a keiser window and/or a chebyshev window and/or a gaussian window.
Preferably, the selecting the plurality of window functions includes selecting the window functions according to the main lobe and the side lobe performance of the amplitude-frequency response of the window functions.
Preferably, the optimally combining the plurality of mixed convolution window functions and the cosine combined window function to obtain the mixed convolution optimized window function includes:
and carrying out optimization combination on the plurality of mixed convolution window functions and the cosine combination window function based on a least square method, wherein the error limit is passband ripple and stop band ripple, and the mixed convolution optimization window function is obtained.
One of the objects of the present invention is to provide a seismic vector wave field finite difference numerical simulation system, comprising:
the mixed convolution optimization window function construction module is used for determining a mixed convolution optimization window function according to window functions of various different parameters and a cosine combination window;
the truncation optimization module is used for truncating the space convolution sequence of the pseudo-spectrum method according to the mixed convolution optimization window function to obtain an optimized finite difference operator;
and the seismic vector wave field simulation module is used for carrying out numerical simulation on the seismic vector wave field according to the optimized finite difference operator.
Preferably, the hybrid convolution optimization window function construction module includes:
the window function selecting module is used for selecting various window functions;
the mixed convolution module is used for carrying out mixed convolution on the window functions with various different parameters to obtain a plurality of mixed convolution window functions;
and the optimization combination module is used for carrying out optimization combination on the multiple mixed convolution window functions and the cosine combination window function to obtain a mixed convolution optimization window function.
Preferably, the window function is a cosine combining window and/or a rectangular window and/or a keiser window and/or a chebyshev window and/or a gaussian window.
Preferably, the window function selecting module includes a window function obtaining module, configured to select a window function according to the main lobe and side lobe performance of the amplitude-frequency response of the window function
Preferably, the optimizing module comprises:
and the least square method optimization combination module is used for carrying out optimization combination on a plurality of mixed convolution window functions and cosine combination window functions based on a least square method, and obtaining the mixed convolution optimization window functions, wherein the error limit is passband ripple and stopband ripple.
One of the objects of the present invention is to provide a computer apparatus comprising: a processor adapted to implement instructions and a storage device storing instructions adapted to be loaded by the processor and to perform a seismic vector wavefield finite difference numerical simulation method.
It is an object of the present invention to provide a computer readable storage medium having stored thereon a computer program for executing a method for finite difference numerical simulation of seismic vector wavefields.
The invention has the beneficial effects that the invention provides a seismic vector wave field finite difference numerical simulation method, a system, computer equipment and a computer readable storage medium, firstly, a plurality of window functions are subjected to mixed convolution, secondly, a plurality of mixed convolution window functions after the mixed convolution and cosine combined window functions are subjected to optimized combination based on a least square method to obtain a mixed convolution optimized window function based on the least square combination, and finally, the window function is utilized to truncate a space convolution sequence of a pseudo-spectral method to obtain an optimized finite difference operator, and then the finite difference operator is utilized to carry out the seismic vector wave field numerical simulation, thereby improving the precision and the efficiency of the seismic vector wave field numerical simulation.
In order to make the aforementioned and other objects, features and advantages of the invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic structural diagram of a finite difference numerical simulation system for a seismic vector wavefield according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a hybrid convolution optimization window function constructing module in a seismic vector wave field finite difference numerical simulation system according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a window function selection module in a seismic vector wave field finite difference numerical simulation system according to an embodiment of the present invention;
FIG. 4 is a schematic structural diagram of an optimized combination module in a seismic vector wave field finite difference numerical simulation system according to an embodiment of the present invention;
FIG. 5 is a flow chart of a finite difference numerical simulation method for a seismic vector wavefield according to an embodiment of the present invention;
fig. 6 is a detailed flowchart of step S101 in fig. 5;
FIG. 7 is a schematic diagram of a dispersion curve of the order-1 derivative of a conventional grid optimized based on a least squares optimized hybrid convolution window function;
FIG. 8 is a schematic diagram of a precision error curve magnified 1000 times;
FIG. 9 is a wave field diagram of impulse response of a conventional interleaved mesh finite difference operator (using an 8 th order operator) in an embodiment provided by the present invention;
FIG. 10 is a wave field diagram of impulse response of a conventional interleaved mesh finite difference operator (using a 12 th order operator) in an embodiment provided by the present invention;
FIG. 11 is a wave field diagram of the impulse response of the least square combination-based hybrid convolution window function optimization finite difference operator (using an 8 th order operator) in the embodiment provided by the present invention;
FIG. 12 is a wave field diagram of the impulse response of the least square combination-based hybrid convolution window function optimization finite difference operator (using 12 th order operator) in the embodiment provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As will be appreciated by one skilled in the art, embodiments of the present invention may be embodied as a system, apparatus, method or computer program product. Accordingly, the present disclosure may be embodied in the form of: entirely hardware, entirely software (including firmware, resident software, micro-code, etc.), or a combination of hardware and software.
The principles and spirit of the present invention are explained in detail below with reference to several representative embodiments of the invention.
The essence of the window function method is the design of FIR (finite length) filter, because the finite difference method is the truncation of the pseudo-spectral spatial convolution sequence, different results can be obtained by using different windows to truncate, and for the finite difference optimization, the ideal truncated window function requires small passband cutoff frequency and large stopband attenuation, and simultaneously, passband ripple and stopband ripple are as small as possible. The optimized finite difference algorithm obtained by truncating the space convolution sequence of the pseudo-spectral method by the truncation window function has the largest spectrum coverage range and smaller precision error. The existing self-convolution combination window function optimization method adopts self-convolution on a certain window function and then combines the window function with another window function or several window functions to obtain the best optimization performance, but the self-convolution can increase the stopband attenuation but also increase the passband cut-off frequency, and in addition, the size control of passband ripple and stopband ripple does not have a more effective scheme.
The basic idea of the invention is to firstly carry out mixed convolution on a plurality of window functions, secondly carry out optimized combination based on a least square method on a plurality of mixed convolution window functions and cosine combined window functions after the mixed convolution to obtain a mixed convolution optimized window function based on the least square combination, finally use the window function to truncate a space convolution sequence of a pseudo-spectrum method to obtain an optimized finite difference operator, and then use the finite difference operator to carry out seismic vector wave field numerical simulation, thereby improving the precision and the efficiency of the seismic wave field numerical simulation.
Fig. 1 is a schematic structural diagram of a seismic vector wave field finite difference numerical simulation system according to an embodiment of the present invention, and referring to fig. 1, the seismic wave field numerical simulation system based on finite difference includes:
the hybrid convolution optimization window function constructing module 100 is configured to determine a hybrid convolution optimization window function according to window functions of a plurality of different parameters and a cosine combination window function.
A band-limited continuous signal f (x) can be sampled with a uniformly sampled signal fnAnd (3) interpolating and reconstructing through a sinc function:
where, Δ x is the sampling interval,
the cut-off wavenumber.
If the first derivative and the second derivative are respectively obtained for the left side and the right side of the formula (1), and the derivative value where x is 0 is taken, the formula (2) and the formula (3) can be obtained, if the formula (1) and the formula (3) are to be applied
Substituting into equation (1), equation (4) can be derived:
there is a window function with length N +1 point, N is even number, and formula (2) and formula (3) are truncated to obtain the conventional finite difference operator:
assuming that there is a window function with a length of N points, where N is an even number, the de-truncation equation (4) yields the interleaved mesh finite difference operator:
w (n) is a truncation window function. For the conventional finite difference operator, w (N) is a window function of N +1 points, and for the interleaved finite difference operator, w (N) is a window function of N points, with N being an even number.
Fig. 2 is a schematic structural diagram of the hybrid convolution optimization window function building module 100, please refer to fig. 2, in which the hybrid convolution optimization window function building module 100 includes:
a window function selecting module 201, configured to select multiple window functions.
Because the finite difference method is the truncation of the pseudo-spectral spatial convolution sequence, different results can be obtained by utilizing different windows to truncate, and for finite difference optimization, an ideal truncation window function requires that the passband cutoff frequency is as small as possible, the stopband attenuation is large, and simultaneously, passband ripple and stopband ripple are as small as possible. The optimized finite difference algorithm obtained by truncating the space convolution sequence of the pseudo-spectral method by the truncation window function has the largest spectrum coverage range and smaller precision error.
In order to design the target window function, firstly, a plurality of window functions are selected to carry out mixed convolution, in the invention, basic window functions generally comprise a cosine combination window, a rectangular window, a Kaiser window, a Chebyshev window, a Gaussian window and the like, only general expressions of the cosine combination window are listed, and expressions of other window functions are omitted:
wherein N is the window function length, L is the number of terms of the cosine combination window, alIs a coefficient, L and alDifferent values of (a) determine different cosine combination window functions. For example, when L is 1, it is a two-phase cosine window, when a0＝0.5,a10.5 is hanning window.
Fig. 3 is a schematic structural diagram of the window function selecting module 201, please refer to fig. 3, in which the window function selecting module 201 includes:
the window function obtaining module 2011 is configured to select a window function according to the main lobe and side lobe performance of the amplitude-frequency response of the window function.
Referring to fig. 2, the hybrid convolution optimization window function constructing module 100 further includes:
the hybrid convolution module 202 is configured to perform hybrid convolution on a plurality of window functions with different parameters to obtain a plurality of hybrid convolution window functions.
The mixed convolution between different types of window functions can increase the stopband attenuation and reduce the sidelobe, because the finite difference method is the truncation of the pseudo-spectrum spatial convolution sequence, the smaller the stopband attenuation of the window functions is, the less the leaked frequency spectrum components are, and therefore, the higher the precision of the approximate differential operator of the differential operator is. However, the convolution operation will bring about an increase in the width of the main lobe of the window function, and therefore a hybrid convolution scheme is selected, that is, different window functions with narrower main lobes are selected for convolution.
The mixed convolution can greatly reduce the attenuation of the stop band on the premise of not increasing the width of the main lobe greatly, so that the side lobe is reduced, and the precision of the approximate differential operator of the differential operator is improved.
And the optimization combination module 203 is configured to perform optimization combination on the multiple mixed convolution window functions and the cosine combination window function to obtain a mixed convolution optimized window function.
Fig. 4 is a schematic structural diagram of the optimal combination module 203, please refer to fig. 4, where the optimal combination module 203 includes:
the least square method optimization combination module 2031 is configured to perform an optimization combination based on a least square method on the multiple hybrid convolution window functions and the cosine combination window function, where the error limit is passband ripple and stopband ripple, and a hybrid convolution optimization window function is obtained.
In the invention, the influence brought by passband ripple and stopband ripple is also considered, the passband ripple and the stopband ripple can bring certain precision influence, in order to obtain a finite difference operator with higher precision and efficiency, a least square combination mode is adopted to set passband ripple and stopband ripple limits, and the best combination effect is obtained.
Referring to fig. 1, the seismic vector wave field finite difference numerical simulation system further includes:
and a truncation optimization module 200, configured to truncate the spatial convolution sequence of the pseudo-spectrum method according to the hybrid convolution optimization window function to obtain an optimized finite difference operator.
The mixed convolution optimization window function is applied to the solution of the finite difference coefficients, i.e. the objective function equations (9), (10), (11) are solved to obtain the optimized finite difference coefficients. The optimized finite difference coefficients may constitute a finite difference operator.
Conventional second derivative:
conventional first derivative:
and (3) interleaving grids:
and the seismic vector wave field simulation module 300 is used for carrying out numerical simulation on the seismic vector wave field according to the optimized finite difference operator. The optimized finite difference operator is used for carrying out seismic vector wave field numerical simulation, and the precision and the efficiency of the seismic vector wave field numerical simulation can be improved.
The seismic vector wave field finite difference numerical simulation system provided by the invention comprises the following steps of firstly carrying out mixed convolution on a plurality of window functions, secondly carrying out optimized combination on a plurality of mixed convolution window functions after the mixed convolution and a cosine combined window function based on a least square method to obtain a mixed convolution optimized window function based on the least square combination, and finally utilizing the window function to truncate a space convolution sequence of a pseudo-spectrum method to obtain an optimized finite difference operator, and then utilizing the finite difference operator to carry out seismic vector wave field numerical simulation, thereby improving the precision and the efficiency of the seismic vector wave field numerical simulation.
Furthermore, although in the above detailed description several unit modules of the system are mentioned, this division is not mandatory only. Indeed, the features and functions of two or more of the units described above may be embodied in one unit, according to embodiments of the invention. Also, the features and functions of one unit described above may be further divided into embodiments by a plurality of units. The terms "module" and "unit" used above may be software and/or hardware that realizes a predetermined function. While the modules described in the following embodiments are preferably implemented in software, implementations in hardware, or a combination of software and hardware are also possible and contemplated.
Having described the seismic vector wavefield finite difference numerical simulation system of an exemplary embodiment of the present invention, the method of an exemplary embodiment of the present invention will now be described with reference to the accompanying drawings. The implementation of the method can be referred to the above overall implementation, and repeated details are not repeated.
Fig. 5 is a schematic flow chart of a finite difference numerical simulation method for a seismic vector wavefield according to an embodiment of the present invention, please refer to fig. 5, in which the method includes:
s101: and determining a mixed convolution optimization window function according to the window functions of various different parameters and the cosine combination window function.
Fig. 6 is a detailed flowchart of step S101, please refer to fig. 6, wherein step S101 includes:
s201: a variety of window functions are selected.
Because the finite difference method is the truncation of the pseudo-spectral spatial convolution sequence, different results can be obtained by utilizing different windows to truncate, and for finite difference optimization, an ideal truncation window function requires that the passband cutoff frequency is as small as possible, the stopband attenuation is large, and simultaneously, passband ripple and stopband ripple are as small as possible. The optimized finite difference algorithm obtained by truncating the space convolution sequence of the pseudo-spectral method by the truncation window function has the largest spectrum coverage range and smaller precision error.
In order to design such a target window function, a plurality of window functions are selected to perform a hybrid convolution, and in the present invention, the basic window functions generally include a cosine combining window, a rectangular window, a kelvin window, a chebyshev window, a gaussian window, and the like.
In one embodiment of the present invention, step S201 may select a window function according to the main lobe and side lobe performance of the amplitude-frequency response of the window function.
Referring to fig. 6, step S102 further includes:
s202: and performing mixed convolution on the window functions with various different parameters to obtain a plurality of mixed convolution window functions.
The mixed convolution between different types of window functions can increase the stopband attenuation and reduce the sidelobe, because the finite difference method is the truncation of the pseudo-spectrum spatial convolution sequence, the smaller the stopband attenuation of the window functions is, the less the leaked frequency spectrum components are, and therefore, the higher the precision of the approximate differential operator of the differential operator is. However, the convolution operation will bring about an increase in the width of the main lobe of the window function, and therefore a hybrid convolution scheme is selected, that is, different window functions with narrower main lobes are selected for convolution.
The mixed convolution can greatly reduce the attenuation of the stop band on the premise of not increasing the width of the main lobe greatly, so that the side lobe is reduced, and the precision of the approximate differential operator of the differential operator is improved.
S203: and optimally combining the multiple mixed convolution window functions and the cosine combined window function to obtain a mixed convolution optimized window function.
In an embodiment of the present invention, in step S203, a least square method-based optimization combination may be performed on a plurality of hybrid convolution window functions and cosine combination window functions, and the error limit is the passband ripple and the stopband ripple to obtain the hybrid convolution optimization window function.
In the invention, the influence brought by passband ripple and stopband ripple is also considered, the passband ripple and the stopband ripple can bring certain precision influence, in order to obtain a finite difference operator with higher precision and efficiency, a least square combination mode is adopted to set passband ripple and stopband ripple limits, and the best combination effect is obtained.
Referring to fig. 5, the method further includes:
s102: and truncating the space convolution sequence of the pseudo-spectrum method according to the mixed convolution optimization window function to obtain an optimized finite difference operator.
The mixed convolution optimization window function is applied to the solution of the finite difference coefficients, i.e. the objective function equations (9), (10), (11) are solved to obtain the optimized finite difference coefficients.
In a preferred embodiment of the present invention, an improved window function is constructed, and the optimized finite difference algorithm obtained by truncating the spatial convolution sequence of the pseudo-spectral method by using the truncation window function has the largest spectrum coverage and smaller precision error. In this embodiment, the detailed steps of the algorithm are as follows:
(1) comparing the main lobe performance and the side lobe performance of the amplitude-frequency response of various window functions, and selecting the window function for performing mixed convolution;
(2) and changing parameters of the selected window function combination to be convolved, performing L-time mixed convolution, and selecting a result with optimal main lobe and side lobe performance.
(3) And (2) combining the mixed convolution window function and cosine combination window output in the step (1) and the mixed convolution result of the reorganized window function with different parameters based on a least square algorithm, wherein the error limit is passband ripple and stopband ripple.
(4) And (4) initially acquiring a window function with optimal truncation performance, and truncating and optimizing a finite difference operator.
(5) And (3) introducing an approximation error function by using the finite difference operator generated in the step (4), calculating and drawing an approximation error curve, observing the spectrum coverage range and the stability of approximation precision of the approximation error curve in a focused manner, and returning to the steps (1), (2) and (3) if the effect is not good, and restarting circulation until a satisfactory result is obtained.
S103: and carrying out numerical simulation on the seismic vector wave field according to the optimized finite difference operator. The optimized finite difference operator is used for carrying out seismic vector wave field numerical simulation, and the precision and the efficiency of the seismic vector wave field numerical simulation can be improved.
The seismic vector wave field finite difference numerical simulation method provided by the invention comprises the steps of firstly carrying out mixed convolution on a plurality of window functions, secondly carrying out optimized combination on a plurality of mixed convolution window functions after the mixed convolution and a cosine combined window function based on a least square method to obtain a mixed convolution optimized window function based on the least square combination, and finally utilizing the window function to truncate a space convolution sequence of a pseudo-spectrum method to obtain an optimized finite difference operator, and then utilizing the finite difference operator to carry out seismic vector wave field numerical simulation, thereby improving the precision and the efficiency of the seismic vector wave field numerical simulation.
The present invention also provides a computer device comprising: a processor adapted to implement instructions and a storage device storing instructions adapted to be loaded by the processor and to perform a seismic vector wavefield finite difference numerical simulation method.
The invention also provides a computer-readable storage medium storing a computer program for executing a method for finite difference numerical simulation of a seismic vector wavefield.
The technical solution of the present invention will be described in detail with reference to specific examples.
In the embodiment 1, a kaiser window and a chebyshev window are selected for mixed convolution, and the mixture convolution is combined with a kaiser window and a chebyshev window with different coefficients and a cosine combination window based on a least square algorithm to obtain an optimal truncation performance, and a finite difference operator is optimized, and a dispersion curve shows that the precision and the spectrum coverage range are higher. FIG. 7 is a plot of the dispersion of the conventional mesh finite difference operator (derivative of order 1) for the hybrid convolution window function optimization based on least squares optimization, with Nyquist wavenumber percentage on the abscissa and absolute error on the ordinate. Fig. 8 is a graph of accuracy error at 1000 x magnification, with nyquist wavenumber percentage on the abscissa and absolute error on the ordinate. It can be seen from fig. 7 that the precision of the optimized finite difference operator is much higher than that of the conventional operator, and the precision of the 12 th order operator is much higher than that of the conventional 16 th order operator, and it can be seen from fig. 8 that the fluctuation of the precision error is controlled in a lower range, and after long step lengths are accumulated, the stability is better, so that the algorithm provided by the present application is effective.
In this embodiment 1, a cheze window and a chebyshev window are selected for performing mixed convolution, and for a first-order conventional mesh, window function parameters participating in the mixed convolution are the chebyshev window (r ═ 45), and the cheze window (beta ═ 3.3); for a second-order conventional mesh, window function parameters participating in hybrid convolution are a chebyshev window (r is 53,51), and a keze window (beta is 3.3, 3.1); for the first-order interleaved mesh, the window function parameters involved in the hybrid convolution are the chebyshev window (r ═ 21) and the kesy window (beta ═ 4.2). After the mixed convolution, the combination based on the least square algorithm is performed, and a hanning window in a cosine combination window and the mixed convolution results of a cheque window and a cheque window with different coefficients are selected (the cheque window (r ═ 65) and the cheque window (beta ═ 3.3)). The combination coefficient is 0.568, 0.212 and 0.220.
Values for making an impulse response in example 2And (4) simulating, namely comparing the numerical simulation effect of the 8-order mixed convolution window function based on the least square combination to optimize the staggered grid finite difference operator and the conventional 8-order and 12-order staggered grid finite difference operator. A two-dimensional isotropic medium is defined, the grid size is 311 multiplied by 311, the grid spacing is 10m, and the longitudinal wave speed is 2000 m.s-1The transverse wave velocity is 1500 m.s-1，ρ＝1000kg·m-3. The point source is excited in the middle, a concentration source is adopted, the dominant frequency of Ricker wavelets is 30Hz, delta t is 1.5ms, and nt is 3000. Fig. 9-12, where the abscissa is distance in meters and the ordinate is depth in meters.
In summary, the present invention provides a seismic vector wave field finite difference numerical simulation method, a seismic vector wave field finite difference numerical simulation system, a seismic vector wave field finite difference numerical simulation computer equipment, and a computer readable storage medium, wherein the method comprises the steps of performing mixed convolution on a plurality of window functions, performing optimized combination on the plurality of mixed convolution window functions after the mixed convolution and a cosine combination window function based on a least square method to obtain a mixed convolution optimized window function based on the least square combination, and finally performing the seismic vector wave field numerical simulation by using the finite difference operator to truncate a space convolution sequence of a pseudo-spectral method.
Improvements to a technology can clearly be distinguished between hardware improvements (e.g. improvements to the circuit structure of diodes, transistors, switches, etc.) and software improvements (improvements to the process flow). However, as technology advances, many of today's process flow improvements have been seen as direct improvements in hardware circuit architecture. Designers almost always obtain the corresponding hardware circuit structure by programming an improved method flow into the hardware circuit. Thus, it cannot be said that an improvement in the process flow cannot be realized by hardware physical modules. For example, a Programmable Logic Device (PLD), such as a Field Programmable Gate Array (FPGA), is an integrated circuit whose Logic functions are determined by programming the Device by a user. A digital system is "integrated" on a PLD by the designer's own programming without requiring the chip manufacturer to design and fabricate application-specific integrated circuit chips. Furthermore, nowadays, instead of manually making an Integrated Circuit chip, such Programming is often implemented by "logic compiler" software, which is similar to a software compiler used in program development and writing, but the original code before compiling is also written by a specific Programming Language, which is called Hardware Description Language (HDL), and HDL is not only one but many, such as abel (advanced Boolean Expression Language), ahdl (alternate Language Description Language), traffic, pl (core unified Programming Language), HDCal, JHDL (Java Hardware Description Language), langue, Lola, HDL, laspam, hardbyscript Description Language (vhr Description Language), and the like, which are currently used by Hardware compiler-software (Hardware Description Language-software). It will also be apparent to those skilled in the art that hardware circuitry that implements the logical method flows can be readily obtained by merely slightly programming the method flows into an integrated circuit using the hardware description languages described above.
The controller may be implemented in any suitable manner, for example, the controller may take the form of, for example, a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro) processor, logic gates, switches, an Application Specific Integrated Circuit (ASIC), a programmable logic controller, and an embedded microcontroller, examples of which include, but are not limited to, the following microcontrollers: the ARC625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicone Labs C8051F320, the memory controller may also be implemented as part of the control logic for the memory.
Those skilled in the art will also appreciate that, in addition to implementing the controller as pure computer readable program code, the same functionality can be implemented by logically programming method steps such that the controller is in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Such a controller may thus be considered a hardware component, and the means included therein for performing the various functions may also be considered as a structure within the hardware component. Or even means for performing the functions may be regarded as being both a software module for performing the method and a structure within a hardware component.
The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions.
For convenience of description, the above devices are described as being divided into various units by function, and are described separately. Of course, the functionality of the units may be implemented in one or more software and/or hardware when implementing the present application.
From the above description of the embodiments, it is clear to those skilled in the art that the present application can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present application may be essentially or partially implemented in the form of software products, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and include instructions for causing a computer system (which may be a personal computer, a server, or a network system, etc.) to execute the methods described in the embodiments or some parts of the embodiments of the present application.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
The application is operational with numerous general purpose or special purpose computing system environments or configurations. For example: personal computers, server computers, hand-held or portable systems, tablet-type systems, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics systems, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or systems, and the like.
The application may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing systems that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage systems.
While the present application has been described with examples, those of ordinary skill in the art will appreciate that there are numerous variations and permutations of the present application without departing from the spirit of the application, and it is intended that the appended claims encompass such variations and permutations without departing from the spirit of the application.
Claims (10)
1. A method of finite difference numerical simulation of a seismic vector wavefield, the method comprising:
selecting a plurality of window functions;
performing mixed convolution on the window functions with various different parameters to obtain a plurality of mixed convolution window functions;
optimally combining the multiple mixed convolution window functions and the cosine combined window function to obtain a mixed convolution optimized window function;
truncating a space convolution sequence of the pseudo-spectrum method according to the mixed convolution optimization window function to obtain an optimized finite difference operator;
and carrying out numerical simulation on the seismic vector wave field according to the optimized finite difference operator.
2. Method according to claim 1, characterized in that the window function is a cosine combining window and/or a rectangular window and/or a Kernel window and/or a Chebyshev window and/or a Gaussian window.
3. The method of claim 1, wherein selecting the plurality of window functions comprises selecting the window functions based on main lobe and side lobe performance of amplitude-frequency response of the window functions.
4. The method of claim 1, wherein optimally combining the plurality of hybrid convolution window functions and the cosine combining window function to obtain a hybrid convolution optimized window function comprises:
and carrying out optimization combination on the plurality of mixed convolution window functions and the cosine combination window function based on a least square method, wherein the error limit is passband ripple and stop band ripple, and the mixed convolution optimization window function is obtained.
5. A seismic vector wavefield finite difference numerical simulation system, the system comprising:
the window function selecting module is used for selecting various window functions;
the mixed convolution module is used for carrying out mixed convolution on the window functions with various different parameters to obtain a plurality of mixed convolution window functions;
the optimization combination module is used for carrying out optimization combination on the multiple mixed convolution window functions and the cosine combination window function to obtain a mixed convolution optimization window function;
the truncation optimization module is used for truncating the space convolution sequence of the pseudo-spectrum method according to the mixed convolution optimization window function to obtain an optimized finite difference operator;
and the seismic vector wave field simulation module is used for carrying out numerical simulation on the seismic vector wave field according to the optimized finite difference operator.
6. System according to claim 5, characterized in that the window function is a cosine combining window and/or a rectangular window and/or a Kernel window and/or a Chebyshev window and/or a Gaussian window.
7. The system of claim 5, wherein the window function selecting module comprises a window function obtaining module configured to select the window function according to main lobe and side lobe performance of amplitude-frequency response of the window function.
8. The system of claim 5, wherein the optimized combining module comprises:
and the least square method optimization combination module is used for carrying out optimization combination on a plurality of mixed convolution window functions and cosine combination window functions based on a least square method, and obtaining the mixed convolution optimization window functions, wherein the error limit is passband ripple and stopband ripple.
9. A computer device, comprising: a processor adapted to implement instructions and a storage device storing instructions adapted to be loaded by the processor and to perform a method of finite difference numerical simulation of a seismic vector wavefield as claimed in any one of claims 1 to 4.
10. A computer-readable storage medium, in which a computer program is stored which is adapted to carry out a method of finite difference numerical simulation of a seismic vector wavefield as claimed in any one of claims 1 to 4.
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