CN112817044B - Method and system for optimizing difference coefficient of frequency domain acoustic wave equation - Google Patents
Method and system for optimizing difference coefficient of frequency domain acoustic wave equationDownload PDFInfo
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Abstract
Description
Translated fromChinese技术领域Technical Field
本发明涉及正演模拟计算技术领域，具体是频率域声波方程的差分系数优化方法、系统。The invention relates to the technical field of forward simulation calculation, and in particular to a differential coefficient optimization method and system for a frequency domain acoustic wave equation.
背景技术Background Art
频率域全波形反演充分利用全波场的振幅、相位以及频率信息，采用较少的频率便能反演得到精度很高的速度模型。Frequency domain full waveform inversion makes full use of the amplitude, phase and frequency information of the full wave field, and can invert a high-precision velocity model using fewer frequencies.
频率域正演是频率域全波形反演的基础，在地震波数值模拟中占有十分重要的地位，相比时间域正演，频率域正演具有适合多炮并行运算，无时间频散，频带选取灵活、误差小等优点。学者们为提高频率域正演精度提出了许多种形式的有限差分网格，其中以旋转坐标系25点有限差分格式为最常用，但是该方法只适合于纵横采样间隔相等的情况，而对于纵横采样间隔不等的情况无法适用。Frequency domain forward modeling is the basis of frequency domain full waveform inversion and plays a very important role in numerical simulation of seismic waves. Compared with time domain forward modeling, frequency domain forward modeling has the advantages of being suitable for multi-shot parallel operation, no time dispersion, flexible frequency band selection, and small error. Scholars have proposed many forms of finite difference grids to improve the accuracy of frequency domain forward modeling, among which the 25-point finite difference format in the rotating coordinate system is the most commonly used. However, this method is only suitable for the case where the vertical and horizontal sampling intervals are equal, and cannot be applied to the case where the vertical and horizontal sampling intervals are unequal.
因此，现有技术仍需要改进。Therefore, the prior art still needs to be improved.
发明内容Summary of the invention
为解决上述技术问题，本发明的目的是提供一种频率域声波方程的差分系数优化方法、系统、机器可读存储介质。In order to solve the above technical problems, the purpose of the present invention is to provide a differential coefficient optimization method, system and machine-readable storage medium for frequency domain acoustic wave equations.
为了实现上述目的，在本申请第一方面，提供一种频率域声波方程的差分系数优化方法，适用于有限差分网格纵横采样间隔不等的情况，所述差分系数优化方法包括：确定所述频率域声波方程的有限差分网格；将所述有限差分网格对所述频率域声波方程进行差分近似，并建立有限差分格式；根据有限差分格式构建优化目标函数；并根据优化函数求解所述优化目标函数的优化差分系数。In order to achieve the above-mentioned purpose, in the first aspect of the present application, a method for optimizing differential coefficients of a frequency domain acoustic wave equation is provided, which is applicable to the situation where the vertical and horizontal sampling intervals of a finite difference grid are unequal, and the method for optimizing differential coefficients comprises: determining a finite difference grid of the frequency domain acoustic wave equation; performing differential approximation on the frequency domain acoustic wave equation by using the finite difference grid, and establishing a finite difference format; constructing an optimization objective function according to the finite difference format; and solving the optimized differential coefficients of the optimization objective function according to the optimization function.
在本申请实施例中，所述将所述有限差分网格对频率域声波方程进行差分近似得到有限差分格式包括：将所述有限差分网格对频率域声波方程中的二阶偏导数项进行差分近似得到第一差分模型；将所述有限差分网格对频率域声波方程中的质量加速度项进行差分近似得到第二差分模型；根据所述第一差分模型、第二差分模型得到所述有限差分格式。In an embodiment of the present application, the method of performing differential approximation on the frequency domain acoustic wave equation using the finite difference grid to obtain a finite difference format includes: performing differential approximation on the second-order partial derivative terms in the frequency domain acoustic wave equation using the finite difference grid to obtain a first differential model; performing differential approximation on the mass acceleration terms in the frequency domain acoustic wave equation using the finite difference grid to obtain a second differential model; and obtaining the finite difference format based on the first differential model and the second differential model.
在本申请实施例中，所述根据有限差分格式构建优化目标函数；并根据优化函数求解所述优化目标函数的优化差分系数包括：利用相速度频散方程基于所述有限差分格式构建优化目标函数；根据最优化函数得到所述目标函数求取最优化系数；根据所述最优化系数得到归一化相速度频散曲线，以验证所述目标函数的可靠性。In an embodiment of the present application, constructing an optimization objective function according to a finite difference format; and solving the optimization differential coefficients of the optimization objective function according to the optimization function include: constructing an optimization objective function based on the finite difference format using a phase velocity dispersion equation; obtaining the optimization coefficients of the objective function according to the optimization function; and obtaining a normalized phase velocity dispersion curve according to the optimization coefficients to verify the reliability of the objective function.
在本申请实施例中，所述有限差分网格为25点频率域有限差分网格。In the embodiment of the present application, the finite difference grid is a 25-point frequency domain finite difference grid.
在本申请实施例中，所述方法还包括：利用所述优化差分系数对所述频率域声波方程进行正演模拟。In an embodiment of the present application, the method further includes: performing forward modeling on the frequency domain acoustic wave equation using the optimized differential coefficients.
在本申请实施例中，所述利用所述优化差分系数对所述频率域声波方程进行正演模拟包括：利用完全匹配层吸收所述频率域声波方程的边界条件；通过预设的训练模型中的数值进行训练；根据训练结果，确定所述随机反演方法的可靠性。In an embodiment of the present application, the forward modeling of the frequency domain acoustic wave equation using the optimized differential coefficients includes: using a perfectly matched layer to absorb the boundary conditions of the frequency domain acoustic wave equation; training through numerical values in a preset training model; and determining the reliability of the random inversion method based on the training results.
在本申请实施例中，所述训练模型为层状介质、凹陷介质、Marmousi 模型的至少一种。In an embodiment of the present application, the training model is at least one of a layered medium, a concave medium, and a Marmousi model.
在本申请实施例中，所述根据训练结果包括：频率切片、波场快照和地震记录的至少一种。In the embodiment of the present application, the training results include: at least one of frequency slices, wave field snapshots and seismic records.
在本申请实施例的第二方面，还提供一种频率域声波方程的差分系数优化装置，包括确定模块，用于确定频率域声波方程的有限差分网格，计算模块，将所述有限差分网格对所述频率域声波方程进行差分近似，并建立有限差分格式；优化模块，用于根据所述有限差分格式构建优化目标函数，并根据优化函数求解优化目标函数的优化差分系数；模拟模块，用于利用优化差分系数对频率域声波方程进行正演模拟。In the second aspect of the embodiment of the present application, a device for optimizing differential coefficients of a frequency domain acoustic wave equation is also provided, including a determination module for determining a finite difference grid of the frequency domain acoustic wave equation, a calculation module for differentially approximating the frequency domain acoustic wave equation using the finite difference grid and establishing a finite difference format; an optimization module for constructing an optimization objective function according to the finite difference format and solving the optimized differential coefficients of the optimization objective function according to the optimization function; and a simulation module for forward modeling the frequency domain acoustic wave equation using the optimized differential coefficients.
另一方面，本申请实施例还提供一种计算机可读存储介质，该机器可读存储介质上存储有指令，该指令用于在被处理器执行时使得处理器能够执行根据权利要求的频率域声波方程的差分系数优化方法。On the other hand, an embodiment of the present application also provides a computer-readable storage medium, which stores instructions, and the instructions are used to enable the processor to execute the differential coefficient optimization method of the frequency domain acoustic wave equation according to the claim when executed by the processor.
通过上述技术方案，综上，本发明实施例通过有限差分网格对所述频率域声波方程进行差分近似，并建立有限差分格式，并利用有限差分格式构建优化目标函数；并根据优化函数求解所述优化目标函数的优化差分系数；从而解决了现有技术中频率域正演中有限差分法以传统的旋转坐标系25点有限差分网格，但是该网格只适合于纵横采样间隔相等的情况，从而导致应用范围窄的技术问题，达到了可靠、应用性广泛的技术效果。Through the above technical scheme, in summary, the embodiment of the present invention performs differential approximation on the frequency domain acoustic wave equation through a finite difference grid, establishes a finite difference format, and constructs an optimization objective function using the finite difference format; and solves the optimization differential coefficients of the optimization objective function according to the optimization function; thereby solving the problem in the prior art that the finite difference method in the frequency domain forward modeling uses a traditional rotating coordinate system 25-point finite difference grid, but the grid is only suitable for the situation where the vertical and horizontal sampling intervals are equal, which leads to a narrow application range of technical problems, and achieves a reliable and widely applicable technical effect.
本发明实施例的其它特征和优点将在随后的具体实施方式部分予以详细说明。Other features and advantages of the embodiments of the present invention will be described in detail in the subsequent detailed description.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
附图是用来提供对本发明实施例的进一步理解，并且构成说明书的一部分，与下面的具体实施方式一起用于解释本发明实施例，但并不构成对本发明实施例的限制。在附图中：The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the embodiments of the present invention, but do not constitute a limitation on the embodiments of the present invention. In the accompanying drawings:
图1是本发明实施例所提供的一种频率域声波方程的差分系数优化方法的流程图；FIG1 is a flow chart of a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图2是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中为演示传统差分网格的示意图；FIG2 is a schematic diagram for demonstrating a traditional differential grid in a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图3是本发明实施例所提供的一种频率域声波方程的差分系数优化方法的一种差分格式示意图；3 is a schematic diagram of a differential format of a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图4是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中步骤S102的流程图；FIG4 is a flow chart of step S102 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图5是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中步骤S103的流程图；FIG5 is a flow chart of step S103 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图6是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1033归一化相速度频散曲线的示意图；6 is a schematic diagram of a normalized phase velocity dispersion curve in step S1033 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图7是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中步骤S104的流程图；FIG7 is a flow chart of step S104 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图8a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1042对应模型为层状模型的示意图；FIG8a is a schematic diagram of a layered model corresponding to step S1042 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图8b是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1042对应模型为凹陷模型的示意图；FIG8b is a schematic diagram of a concave model corresponding to step S1042 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图8c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1042对应模型为Marmousi模型的示意图；FIG8c is a schematic diagram of a Marmousi model corresponding to step S1042 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
图9a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为层状介质，在30Hz频率切片下的正演结果示意图；9a is a schematic diagram of forward modeling results at a frequency slice of 30 Hz when the corresponding model of step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention is a layered medium;
图9b是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为层状介质，在层状介质0.25s波场快照下的正演结果示意图；9b is a schematic diagram of forward modeling results at a 0.25s wave field snapshot of a layered medium when the corresponding model of step S1043 in a frequency domain acoustic wave equation optimization method provided by an embodiment of the present invention is a layered medium;
图9c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为层状介质，在层状介质地震记录的正演结果示意图；9c is a schematic diagram of forward modeling results of seismic records in layered media when the corresponding model of step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention is a layered medium;
图10a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为凹陷介质，在30Hz频率切片下的正演结果示意图；10a is a schematic diagram of forward modeling results at a frequency slice of 30 Hz when the corresponding model of step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention is a concave medium;
图10b是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为凹陷介质，在0.25s波场快照下的正演结果示意图；10b is a schematic diagram of forward modeling results at a 0.25s wave field snapshot when the corresponding model of step S1043 in a frequency domain acoustic wave equation differential coefficient optimization method provided by an embodiment of the present invention is a concave medium;
图10c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为凹陷介质，在凹陷介质地震记录下的正演结果示意图；10c is a schematic diagram of forward modeling results under seismic records of a concave medium when the corresponding model of step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention is a concave medium;
图11a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为Marmousi模型，在30Hz频率切片下的部分正演结果示意图；11a is a schematic diagram of partial forward modeling results at a 30 Hz frequency slice when the corresponding model of step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention is a Marmousi model;
图11b是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为Marmousi模型，在0.25s波场快照下的部分正演结果示意图；FIG11b is a schematic diagram of partial forward modeling results at a 0.25s wave field snapshot when the corresponding model of step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention is a Marmousi model;
图11c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为Marmousi模型，在地震记录下的部分正演结果示意图；以及FIG11c is a schematic diagram of partial forward modeling results under seismic records when the corresponding model of step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention is a Marmousi model; and
图12是本发明实施例所提供的一种频率域声波方程的差分系数优化装置中的模块示意图。FIG. 12 is a schematic diagram of modules in a differential coefficient optimization device for a frequency domain acoustic wave equation provided by an embodiment of the present invention.
附图标号说明Description of Figure Numbers
100、差分系数优化装置；100. Differential coefficient optimization device;
10、确定模块； 20、计算模块；10. Determination module; 20. Calculation module;
30、优化模块； 40、模拟模块。30. Optimization module; 40. Simulation module.
具体实施方式DETAILED DESCRIPTION
以下描述中，为了说明而不是为了限定，提出了诸如特定系统结构、技术之类的具体细节，以便透彻理解本发明实施例。然而，本领域的技术人员应当清楚，在没有这些具体细节的其它实施例中也可以实现本发明。在其它情况中，省略对众所周知的系统、装置、电路及方法的详细说明，以免不必要的细节妨碍本发明的描述。In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present invention. However, it should be clear to those skilled in the art that the present invention may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present invention.
以下结合附图对本发明实施例的具体实施方式进行详细说明。应当理解的是，此处所描述的具体实施方式仅用于说明和解释本发明实施例，并不用于限制本发明实施例。The specific implementation of the embodiment of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the embodiment of the present invention, and is not used to limit the embodiment of the present invention.
发明人发现，在常规的频率域全波形反演方法中，有限差分网格通常是纵横采样间隔得到的，如旋转坐标系25点有限差分格式。这种方式具备精度高的特性，在低频段，频散误差接近于零，但是却无法适用于纵横采样间隔不等的去情况。为此，在本发明实施例中提出了一种频率域声波方程的差分系数优化方法来进行频率域声波正演模拟，本发明实施例基于旋转坐标系 25点方法进行改进，使用一种新的系数分布和求取格式，以相速度频散方程构建目标函数，最终求解出差分系数，带入频率域正演过程，试验结果证明了该方法的可靠性，以达到可适用纵横采样间隔不等时的差分系数的优化，从而增加非标领域的应用能力。The inventors found that in the conventional frequency domain full waveform inversion method, the finite difference grid is usually obtained by the vertical and horizontal sampling intervals, such as the 25-point finite difference format of the rotating coordinate system. This method has the characteristics of high precision. In the low frequency band, the dispersion error is close to zero, but it cannot be applied to the situation where the vertical and horizontal sampling intervals are unequal. To this end, in an embodiment of the present invention, a differential coefficient optimization method for the frequency domain acoustic wave equation is proposed to perform frequency domain acoustic wave forward simulation. The embodiment of the present invention is based on the 25-point method of the rotating coordinate system for improvement, using a new coefficient distribution and calculation format, and constructing the objective function with the phase velocity dispersion equation. Finally, the differential coefficient is solved and brought into the frequency domain forward process. The experimental results prove the reliability of the method, so as to achieve the optimization of the differential coefficient applicable to the unequal vertical and horizontal sampling intervals, thereby increasing the application capability in non-standard fields.
请参阅图1，图1是本发明实施例所提供的一种频率域声波方程的差分系数优化方法的流程图。本发明实施例主要提供用于频率域声波方程的正演方法，该方法旨在解决现有的方法无法适应于纵横采样间隔不等的情况，降低了正演的应用范围，从而导致达不到所预期的正演效果。Please refer to Figure 1, which is a flow chart of a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention. The embodiment of the present invention mainly provides a forward modeling method for a frequency domain acoustic wave equation, which aims to solve the problem that the existing method cannot adapt to the situation where the vertical and horizontal sampling intervals are unequal, which reduces the application scope of the forward modeling and thus fails to achieve the expected forward modeling effect.
在本发明实施例的一个方案中，该差分系数优化方法包括：In one solution of an embodiment of the present invention, the differential coefficient optimization method includes:
步骤S101、确定频率域声波方程的有限差分网格；Step S101, determining a finite difference grid of a frequency domain acoustic wave equation;
步骤S102、将有限差分网格对频率域声波方程进行差分近似，并建立有限差分格式；Step S102, performing differential approximation on the frequency domain acoustic wave equation using a finite difference grid, and establishing a finite difference format;
步骤S103、根据有限差分格式构建优化目标函数；并根据优化函数求解优化目标函数的优化差分系数。Step S103: construct an optimization objective function according to the finite difference format; and solve the optimization difference coefficients of the optimization objective function according to the optimization function.
为了更方便地阐述本发明实施例，且以使实施例清楚以，对以上步骤所涉及到的术语进行解释：In order to more conveniently explain the embodiments of the present invention and make the embodiments clear, the terms involved in the above steps are explained:
以上所提到的术语“频率域声波方程”即声波在频率域中的方程，具体地为通过声波随着频率变化的方程。可以表示为Laplacian(Laplacian：拉普拉斯)算子,质量加速项和震源项。The term "frequency domain acoustic wave equation" mentioned above refers to the equation of the acoustic wave in the frequency domain, specifically the equation of the acoustic wave changing with frequency. It can be expressed as the Laplacian operator, mass acceleration term and source term.
在本发明实施例中，首先需要分析旋转坐标系下25点频率域有限差分正演网格在纵横采样间隔不相等的情况下存在的无法适用的局限性；具体为下：In the embodiment of the present invention, it is first necessary to analyze the limitations of the 25-point frequency domain finite difference forward modeling grid in the rotating coordinate system when the vertical and horizontal sampling intervals are not equal; specifically, as follows:
在本发明实施例中，频率域二维声波方程(即频率域声波方程)可写为：In the embodiment of the present invention, the two-dimensional acoustic wave equation in the frequency domain (ie, the acoustic wave equation in the frequency domain) can be written as:
其中在公式1中，P为位移分量，ω为角频率，v为速度。In
请参阅图2，图2是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中为演示传统差分网格的示意图；在使用有限差分法正演时，传统四阶25点差分格式精度较高，其对应于1的差分格式如下公式2：Please refer to FIG. 2 , which is a schematic diagram for demonstrating a traditional differential grid in a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention; when using the finite difference method for forward modeling, the traditional fourth-order 25-point differential format has a higher accuracy, and its differential format corresponding to 1 is as follows: Formula 2:
在公式2中，pm，n为对应在网格m，n处的位移分量。a1～a6，以及b1～b6均为差分系数。In
可以理解，由于上述传统四阶25点差分格式为本领域技术人员常见技术手段，在本发明实施例中不予过多阐述。It can be understood that since the above-mentioned traditional fourth-order 25-point difference format is a common technical means for those skilled in the art, it will not be elaborated in detail in the embodiments of the present invention.
分析上述公式2，可知当Δx≠Δz时，拉普拉斯项的差分近似并不成立，此时混合25差分格式也将不适用。(混合差分格式：一种结合了中心差分格式和迎风格式的优点的混合格式)。Analyzing the
请参阅图3，图3是本发明实施例所提供的一种频率域声波方程的差分系数优化方法的一种差分格式示意图；通过上述，本发明实施例需要提供一种可适用于当Δx≠Δz时，即纵横采样间隔不相等的差分系数优化方法。首先需要确定纵横采样间隔，在旋转坐标系下25点频率域有限差分正演网格的差分系数优化方法作出改进，从而得到如图2所示的适应纵横采样间隔不等情况下的25点有限差分网格。可以理解的是，图2所提供的25点有限差分网格仅为优选性的示例作用，并不对该25点有限差分网格作出完全的限定，在图示上所作出非智力劳动上的简单改进，同样属于本发明申请所涵盖的保护范围内。Please refer to Figure 3, which is a differential format schematic diagram of a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention; through the above, an embodiment of the present invention needs to provide a differential coefficient optimization method that is applicable when Δx≠Δz, that is, the vertical and horizontal sampling intervals are unequal. First, it is necessary to determine the vertical and horizontal sampling intervals, and improve the differential coefficient optimization method of the 25-point frequency domain finite difference forward modeling grid in the rotating coordinate system, so as to obtain a 25-point finite difference grid that is adapted to the case of unequal vertical and horizontal sampling intervals as shown in Figure 2. It can be understood that the 25-point finite difference grid provided in Figure 2 is only an example of preference, and does not completely limit the 25-point finite difference grid. Simple improvements made on the diagram based on non-intellectual labor also fall within the scope of protection covered by the present invention application.
可以理解，纵横采样间隔相等的有限差分网格即为指的是对介质进行均匀剖分，所使用的所有网格大小相等，形态相同。It can be understood that a finite difference grid with equal vertical and horizontal sampling intervals means that the medium is uniformly divided, and all grids used are equal in size and shape.
可以理解，上述所提到的术语“有限差分网格”，是根据有限差分法 (FDM：FiniteDifferential Method，有限差分法)的基本步骤之一，通过时间步长和空间步长将所研究的时间和空间区域剖分为若干个网格，用未知函数在网格节点上所构成的差分近似代替所用偏微分方程中出现的各阶导数。而将所研究的声波弥散区域按照某种几何形状(如图示的矩形)剖分成网格系统，即称为本发明的有限差分网格。It can be understood that the term "finite difference grid" mentioned above is one of the basic steps of the finite difference method (FDM), which divides the time and space area under study into several grids by time step and space step, and uses the difference formed by the unknown function on the grid nodes to approximate the derivatives of various orders appearing in the partial differential equation used. The sound wave diffusion area under study is divided into a grid system according to a certain geometric shape (such as the rectangle shown in the figure), which is called the finite difference grid of the present invention.
请参阅图4，图4是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中步骤S102的流程图；在本发明实施例中，步骤S102中将有限差分网格对频率域声波方程进行差分近似，并建立有限差分格式的步骤可以包括：Please refer to FIG. 4 , which is a flow chart of step S102 in a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention; in the embodiment of the present invention, the step of performing differential approximation on the frequency domain acoustic wave equation using a finite difference grid and establishing a finite difference format in step S102 may include:
步骤S1021、将有限差分网格对频率域声波方程中的二阶偏导数项进行差分近似得到第一差分模型；Step S1021, performing differential approximation on the second-order partial derivative term in the frequency domain acoustic wave equation using a finite difference grid to obtain a first differential model;
步骤S1022、将有限差分网格对频率域声波方程中的质量加速度项进行差分近似得到第二差分模型；Step S1022, using a finite difference grid to perform differential approximation on the mass acceleration term in the frequency domain acoustic wave equation to obtain a second differential model;
步骤S1023、根据第一差分模型、第二差分模型得到有限差分格式。Step S1023: Obtain a finite difference format according to the first difference model and the second difference model.
在步骤S1021至步骤S1223中，首先执行步骤S1021，即利用适应非等间距纵横采样的25点有限差分网格对频率域声波方程中的二阶偏导数项进行有限差分近似从而得到以下公式3和公式4(即第一差分模型)。In steps S1021 to S1223, step S1021 is first executed, that is, a 25-point finite difference grid adapted to non-uniformly spaced vertical and horizontal sampling is used to perform finite difference approximation on the second-order partial derivative terms in the frequency domain acoustic wave equation to obtain the following
其中在公式3以及公式4中，差分系数满足：In
c0+2c1+2c2+4c3+2c4+2c5+4c6+4c7+4c8＝0 (公式5)c0 + 2c1 + 2c2 + 4c3 + 2c4 + 2c5 + 4c6 + 4c7 + 4c8 = 0 (Formula 5)
d0+2d1+2d2+4d3+2d4+2d5+4d6+4d7+4d8＝0 (公式6)d0 + 2d1 + 2d2 + 4d3 + 2d4 + 2d5 + 4d6 + 4d7 + 4d8 = 0 (Formula 6)
pm，n为对应在网格m，n处的位移分量。a1～a6，以及b1～b6均为差分系数pm,n is the displacement component corresponding to the grid m, n.a 1 ~ a6 and b1 ~ b6 are differential coefficients
随后执行步骤S1021，即利用适应非等间距纵横采样的25点有限差分网格对频率域声波方程中的质量加速度项进行有限差分近似；从而得到以下公式7(即第二差分模型)。Then, step S1021 is executed, i.e., a finite difference approximation is performed on the mass acceleration term in the frequency domain acoustic wave equation using a 25-point finite difference grid adapted to non-uniformly spaced vertical and horizontal sampling; thereby obtaining the following formula 7 (i.e., the second difference model).
其中系数满足：The coefficients satisfy:
b0+2b1+2b2+4b3+2b4+2b5+4b6+4b7+4b8＝1 (公式8)b0 +2b1 +2b2 +4b3 +2b4 +2b5 +4b6 +4b7 +4b8 =1 (Formula 8)
最后执行步骤S1023，即将以上两个有限差分近似公式，即公式3、公式 4，公式7带入频率域二维声波方程的原方程得到整个方程的适应非等间距纵横采样的25点有限差分格式(即以下公式9)：Finally, step S1023 is performed, that is, the above two finite difference approximation formulas, namely,
请参阅图5，图5是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中步骤S103的流程图；在步骤S103中根据有限差分格式构建优化目标函数；并根据优化函数求解优化目标函数的优化差分系数包括：Please refer to FIG. 5 , which is a flow chart of step S103 in a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention; in step S103 , an optimization objective function is constructed according to a finite difference format; and solving the optimization differential coefficient of the optimization objective function according to the optimization function includes:
步骤S1031、利用相速度频散方程基于有限差分格式构建优化目标函数；Step S1031, constructing an optimization objective function based on a finite difference format using a phase velocity dispersion equation;
步骤S1032、根据最优化函数得到目标函数求取最优化系数；Step S1032, obtaining an optimization coefficient by obtaining an objective function according to the optimization function;
步骤S1033、根据最优化系数得到归一化相速度频散曲线，以验证目标函数的可靠性。Step S1033: obtaining a normalized phase velocity dispersion curve according to the optimization coefficient to verify the reliability of the objective function.
可以理解，在步骤S1031至步骤S1033中，首先执行步骤S1031，即利用相速度频散方程构建适应非等间距纵横采样的25点有限差分系数优化目标函数。It can be understood that in step S1031 to step S1033, step S1031 is first performed, that is, the phase velocity dispersion equation is used to construct a 25-point finite difference coefficient optimization objective function that is suitable for non-uniformly spaced vertical and horizontal sampling.
在其中的一个示例中，目标函数可以如下：In one example, the objective function can be as follows:
其中，在上述公式10以及公式11中，Vph为相速度，G为波长，
可以看出，相速度频散方程定义为为波数
随后执行步骤S1032，即根据最优化函数得到目标函数求取最优化系数，具体地为：根据以上公式10至公式14，将积分改成求和，并使用多元函数最优化函数对上述目标函数求取最优化系数，如matlab函数指令中的fmincon，从而得到结果为：Then, step S1032 is executed, that is, the optimization coefficient of the objective function is obtained according to the optimization function. Specifically, according to the
a0＝-0.9765；a1＝0.0047；a2＝0.0049；a3＝0.0479；a4＝0.0871；a5＝0.0871；a6＝0.0474；a7＝0.0474；a8＝0.0095；a0=-0.9765; a1=0.0047; a2=0.0049; a3=0.0479; a4=0.0871; a5=0.0871; a6=0.0474; a7=0.0474; a8=0.0095;
b0＝0.2830；b1＝0.1098；b2＝0.1098；b3＝0.0547；b4＝0.0059；b5＝0.0059； b6＝0.0042；b7＝0.0042；b8＝0.0004；b0=0.2830; b1=0.1098; b2=0.1098; b3=0.0547; b4=0.0059; b5=0.0059; b6=0.0042; b7=0.0042; b8=0.0004;
c1＝0.0558；c2＝-0.0750；c3＝0.0365；c4＝0.0506；c5＝-0.0750；c6＝0.0263；c7＝0.0365；c8＝0.0263；c1=0.0558; c2=-0.0750; c3=0.0365; c4=0.0506; c5=-0.0750; c6=0.0263; c7=0.0365; c8=0.0263;
d1＝0.0599；d2-0.0750；d3＝0.0448；d4＝0.0511；d5＝-0.0750；d6＝0.0272； d7＝0.0448；d8＝0.0272；d1＝0.0599; d2-0.0750; d3＝0.0448; d4＝0.0511; d5＝-0.0750; d6＝0.0272; d7＝0.0448; d8＝0.0272;
可以理解，fmincon是用于求解非线性多元函数最小值的matlab函数。可以通过其他软件形式的其他指令实现相同的效果，对于本发明实施例所提供的仅为示例作用，可以通过更改指令，且对指令的语法格式不予限定，仅需满足相同的效果，均属于本发明所涵盖的保护范围内。It can be understood that fmincon is a MATLAB function for solving the minimum value of a nonlinear multivariate function. The same effect can be achieved by other instructions in other software forms. The embodiments of the present invention are only for illustrative purposes. The instructions can be changed, and the syntax format of the instructions is not limited. As long as the same effect is achieved, it belongs to the protection scope covered by the present invention.
请参阅图6，图6是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1033归一化相速度频散曲线的示意图；最后执行步骤S1033，利用得到的系数，即最优化系数并计算得到归一化相速度频散曲线，验证所求取的有限差分系数的可靠性。即通过对比有限差分系数和相速度频散曲线的吻合度，从而确定所求取的有限差分系数的可靠性。Please refer to Figure 6, which is a schematic diagram of a normalized phase velocity dispersion curve in step S1033 in a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention; finally, step S1033 is performed to use the obtained coefficients, i.e., the optimized coefficients, and calculate the normalized phase velocity dispersion curve to verify the reliability of the obtained finite difference coefficients. That is, by comparing the degree of agreement between the finite difference coefficients and the phase velocity dispersion curve, the reliability of the obtained finite difference coefficients is determined.
在本发明其中的一个实施例中，该基于统计特征参数的随机反演方法还包括：步骤S104、利用优化差分系数对频率域声波方程进行正演模拟以确定可靠性。In one embodiment of the present invention, the random inversion method based on statistical characteristic parameters further includes: step S104, performing forward simulation on the frequency domain acoustic wave equation using optimized differential coefficients to determine reliability.
在上述各个实施例中，上述步骤103利用优化后的有限差分系数(即优化差分系数)对频率域声波方程进行正演模拟，可以包括：将优化后的有限差分系数代入频率域二维声波方程以实现声波正演模拟。In each of the above embodiments, the above step 103 uses the optimized finite difference coefficients (i.e., optimized difference coefficients) to perform forward modeling on the frequency domain acoustic wave equation, which may include: substituting the optimized finite difference coefficients into the frequency domain two-dimensional acoustic wave equation to achieve acoustic wave forward modeling.
请参阅图7，图7是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中步骤S104的流程图；进一步地，步骤S104中利用优化差分系数对频率域声波方程进行正演模拟以确定可靠性可以包括：Please refer to FIG. 7 , which is a flow chart of step S104 in a differential coefficient optimization method for a frequency domain acoustic wave equation provided by an embodiment of the present invention; further, in step S104, forward modeling the frequency domain acoustic wave equation using the optimized differential coefficient to determine reliability may include:
步骤S1041、利用完全匹配层吸收频率域声波方程的边界条件；Step S1041, using a perfectly matched layer to absorb the boundary conditions of the frequency domain acoustic wave equation;
步骤S1042、通过预设的训练模型中的数值进行训练；Step S1042, training is performed using the values in the preset training model;
步骤S1043、根据训练结果，确定随机反演方法的可靠性。Step S1043: Determine the reliability of the random inversion method according to the training results.
在步骤S1041中，利用PML吸收边界条件减少或消除边界反射对数值试验模拟结果的干扰；添加边界条件的差分格式为：In step S1041, the PML absorbing boundary condition is used to reduce or eliminate the interference of boundary reflection on the numerical test simulation results; the difference format of adding boundary conditions is:
可以理解，在步骤S1041中，完全匹配层(PML)是通过在区域截断边界设置一种特殊的介质层，该层介质的波阻抗与相邻介质的波阻抗完全匹配，入射波将无反射地穿过分界面而进入PML。It can be understood that in step S1041, a perfectly matched layer (PML) is formed by setting a special dielectric layer at the regional cutoff boundary, the wave impedance of which is completely matched with the wave impedance of the adjacent medium, and the incident wave will pass through the interface without reflection and enter the PML.
在步骤S1042中，训练模型可以为编程简单模型的数值模拟试验；简单介质模型分别可以为：层状介质、凹陷介质、Marmousi模型。也即训练模型为层状介质、凹陷介质、Marmousi模型的至少一种。In step S1042, the training model may be a numerical simulation test of a simple programming model; the simple medium models may be: layered medium, concave medium, Marmousi model, that is, the training model is at least one of layered medium, concave medium, and Marmousi model.
在步骤S1043中根据训练结果，确定随机反演方法的可靠性，即对数值模拟试验结果图件进行对比分析，验证该系数优化方法的可靠性。In step S1043, the reliability of the random inversion method is determined according to the training results, that is, a comparative analysis is performed on the numerical simulation test result maps to verify the reliability of the coefficient optimization method.
其中训练结果包括：频率切片、波场快照和地震记录的至少一种。The training results include at least one of frequency slices, wave field snapshots and seismic records.
请参阅图8a，图8a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为层状模型的示意图；Please refer to FIG. 8 a , which is a schematic diagram of a layered model corresponding to step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention;
请参阅图8b，图8b是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为凹陷模型的示意图；以及Please refer to FIG. 8 b , which is a schematic diagram of a concave model corresponding to step S1043 in a method for optimizing differential coefficients of a frequency domain acoustic wave equation provided by an embodiment of the present invention; and
请参阅图8c，图8c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为Marmousi模型的示意图。Please refer to FIG. 8c, which is a schematic diagram of a Marmousi model corresponding to step S1043 in a method for optimizing differential coefficients of a frequency-domain acoustic wave equation provided by an embodiment of the present invention.
请参阅图9a至图9c，图9a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为层状介质，在30Hz频率切片下的正演结果示意图；图9b是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为层状介质，在层状介质 0.25s波场快照下的正演结果示意图；图9c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为层状介质，在层状介质地震记录的正演结果示意图；请参阅图10a至图10c，图10a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤 S1043对应模型为凹陷介质，在30Hz频率切片下的正演结果示意图；图10b 是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为凹陷介质，在0.25s波场快照下的正演结果示意图；图 10c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为凹陷介质，在凹陷介质地震记录下的正演结果示意图；请参阅图11a至图11c，图11a是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为Marmousi模型，在 30Hz频率切片下的部分正演结果示意图；图11b是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043对应模型为 Marmousi模型，在0.25s波场快照下的部分正演结果示意图；图11c是本发明实施例所提供的一种频率域声波方程的差分系数优化方法中执行步骤S1043 对应模型为Marmousi模型，在地震记录下的部分正演结果示意图。Please refer to Figures 9a to 9c. Figure 9a is a schematic diagram of the forward modeling results under a 30Hz frequency slice when the model corresponding to step S1043 is a layered medium in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention; Figure 9b is a schematic diagram of the forward modeling results under a 0.25s wave field snapshot of the layered medium when the model corresponding to step S1043 is a layered medium in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention; Figure 9c is a schematic diagram of the forward modeling results of a seismic record of the layered medium when the model corresponding to step S1043 is a layered medium in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention; Please refer to Figures 10a to 10c. Figure 10a is a schematic diagram of the forward modeling results under a 30Hz frequency slice when the model corresponding to step S1043 is a depression medium in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention; Figure 10b FIG10c is a schematic diagram of the forward modeling results under a 0.25s wave field snapshot when the corresponding model of step S1043 in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention is a concave medium; FIG10c is a schematic diagram of the forward modeling results under a 0.25s wave field snapshot when the corresponding model of step S1043 in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention is a concave medium; please refer to FIG11a to FIG11c, FIG11a is a schematic diagram of partial forward modeling results under a 30Hz frequency slice when the corresponding model of step S1043 in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention is a Marmousi model; FIG11b is a schematic diagram of partial forward modeling results under a 0.25s wave field snapshot when the corresponding model of step S1043 in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention is a Marmousi model; FIG11c is a schematic diagram of partial forward modeling results under a 0.25s wave field snapshot when step S1043 in the differential coefficient optimization method for a frequency domain acoustic wave equation provided in an embodiment of the present invention is a Marmousi model. The corresponding model is the Marmousi model, and a schematic diagram of some forward modeling results under seismic records.
从上述图示可知，从得到的频率切片、波场快照和地震记录结果可以看到该方法具有可行性和发展前景。As can be seen from the above diagrams, the obtained frequency slices, wave field snapshots and seismic recording results show that this method is feasible and has development prospects.
频率域正演是频率域全波形反演的基础，学者们为提高频率域正演精度提出了许多种形式的有限差分网格，其中以旋转坐标系25点有限差分格式为最常用，但是该方法只适合于纵横采样间隔相等的情况，而对于纵横采样间隔不等的情况无法适用。本发明基于旋转坐标系25点方法，使用一种新的系数分布和求取格式，以相速度频散方程构建目标函数，最终求解出差分系数，带入频率域正演过程，试验结果证明了该方法的可靠性。Frequency domain forward modeling is the basis of frequency domain full waveform inversion. Scholars have proposed many forms of finite difference grids to improve the accuracy of frequency domain forward modeling, among which the 25-point finite difference format in the rotating coordinate system is the most commonly used. However, this method is only suitable for the case where the vertical and horizontal sampling intervals are equal, and cannot be applied to the case where the vertical and horizontal sampling intervals are unequal. The present invention is based on the 25-point method in the rotating coordinate system, uses a new coefficient distribution and calculation format, constructs the objective function with the phase velocity dispersion equation, and finally solves the differential coefficient and brings it into the frequency domain forward modeling process. The experimental results prove the reliability of this method.
综上，本发明实施例通过有限差分网格对所述频率域声波方程进行差分近似，并建立有限差分格式，并利用有限差分格式构建优化目标函数；并根据优化函数求解所述优化目标函数的优化差分系数；从而解决了现有技术中频率域正演中有限差分法以传统的旋转坐标系25点有限差分网格，但是该网格只适合于纵横采样间隔相等的情况，而导致应用范围窄的技术问题，达到了可靠、应用性广泛的技术效果。In summary, the embodiment of the present invention performs differential approximation on the frequency domain acoustic wave equation through a finite difference grid, establishes a finite difference format, and constructs an optimization objective function using the finite difference format; and solves the optimization differential coefficients of the optimization objective function according to the optimization function; thereby solving the technical problem that the finite difference method in the frequency domain forward modeling in the prior art uses a traditional rotating coordinate system 25-point finite difference grid, but the grid is only suitable for the situation where the vertical and horizontal sampling intervals are equal, resulting in a narrow application range, and achieves a reliable and widely applicable technical effect.
请参阅图9，图9是本发明实施例所提供的一种频率域声波方程的差分系数优化装置中的模块示意图；本发明实施例还提供了一种频率域声波方程的差分系数优化装置100，包括：Please refer to FIG. 9 , which is a schematic diagram of modules in a differential coefficient optimization device for a frequency domain acoustic wave equation provided by an embodiment of the present invention; an embodiment of the present invention further provides a differential
确定模块10，用于确定频率域声波方程的有限差分网格，A
计算模块20，将有限差分网格对频率域声波方程进行差分近似，并建立有限差分格式；The
优化模块30，用于根据有限差分格式构建优化目标函数，并根据优化函数求解优化目标函数的优化差分系数；The
模拟模块40，用于利用优化差分系数对频率域声波方程进行正演模拟。The
可以理解，该装置100的各个模块可以通过执行上述方法实施例的部分方法或者全部方法，以解决了现有技术中频率域正演中有限差分法以传统的旋转坐标系25点有限差分网格，但是该网格只适合于纵横采样间隔相等的情况，而导致应用范围窄的技术问题，达到了可靠、应用性广泛的技术效果。对于本发明实施例所提供的装置具体执行的方式上述方法实施例已经予以阐述，此处不再重复。It can be understood that the various modules of the
本领域技术人员也应当理解，如果将本发明方法或者差分系数优化装置、经过简单变化、在其上述方法增添功能进行组合、或者在其装置上进行替换，如各组件进行型号材料上的替换、使用环境进行替换、各组件位置关系进行简单替换等；或者将其所构成的产品一体设置；或者可拆卸设计；凡组合后的组件可以组成具有特定功能的方法/设备/装置，用这样的方法/设备/装置替代本发明的方法和装置均同样落在本发明的保护范围内。Those skilled in the art should also understand that if the method or differential coefficient optimization device of the present invention is combined with the above-mentioned method after simple changes, or replaced on the device, such as the replacement of the model and material of each component, the replacement of the use environment, the simple replacement of the position relationship of each component, etc.; or the product constituted by it is set as an integral whole; or a detachable design; all the combined components can form a method/device/device with specific functions, and using such a method/device/device to replace the method and device of the present invention also falls within the protection scope of the present invention.
装置还包括存储器，上述频率域声波方程的差分系数优化方法可作为程序单元存储在存储器中，由处理器执行存储在存储器中的上述程序单元来实现相应的功能。The device also includes a memory, and the differential coefficient optimization method of the frequency domain acoustic wave equation can be stored in the memory as a program unit, and the processor executes the program unit stored in the memory to implement the corresponding function.
处理器中包含内核，由内核去存储器中调取相应的程序单元。内核可以设置一个或以上，通过调节内核参数来针对频率域声波方程的差分系数进行优化。The processor includes a kernel, which calls the corresponding program unit from the memory. One or more kernels can be set, and the differential coefficients of the frequency domain acoustic wave equation can be optimized by adjusting the kernel parameters.
存储器可能包括计算机可读介质中的非永久性存储器，随机存取存储器(RAM)和/或非易失性内存等形式，如只读存储器(ROM)或闪存(flashRAM)，存储器包括至少一个存储芯片。The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and/or non-volatile memory, such as read-only memory (ROM) or flash RAM, and the memory includes at least one memory chip.
本发明实施例提供了一种机器可读存储介质，其上存储有程序，该程序被处理器执行时实现频率域声波方程的差分系数优化方法。An embodiment of the present invention provides a machine-readable storage medium on which a program is stored. When the program is executed by a processor, a differential coefficient optimization method of a frequency domain acoustic wave equation is implemented.
本发明实施例提供了一种处理器，处理器用于运行程序，其中，程序运行时执行频率域声波方程的差分系数优化方法。An embodiment of the present invention provides a processor, which is used to run a program, wherein the program executes a differential coefficient optimization method of a frequency domain acoustic wave equation when running.
本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present application is described with reference to the flowchart and/or block diagram of the method, device (system) and computer program product according to the embodiment of the present application. It should be understood that each process and/or box in the flowchart and/or block diagram, and the combination of the process and/or box in the flowchart and/or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for implementing the function specified in one process or multiple processes in the flowchart and/or one box or multiple boxes in the block diagram.
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device that implements the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。These computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.
在一个典型的配置中，计算设备包括一个或多个处理器(CPU)、输入/输出接口、网络接口和内存。In a typical configuration, a computing device includes one or more processors (CPU), input/output interfaces, network interfaces, and memory.
存储器可能包括计算机可读介质中的非永久性存储器，随机存取存储器 (RAM)和/或非易失性内存等形式，如只读存储器(ROM)或闪存(flashRAM)。存储器是计算机可读介质的示例。The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and/or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.
计算机可读介质包括永久性和非永久性、可移动和非可移动媒体可以由任何方法或技术来实现信息存储。信息可以是计算机可读指令、数据结构、程序的模块或其他数据。计算机的存储介质的例子包括，但不限于相变内存 (PRAM)、静态随机存取存储器(SRAM)、动态随机存取存储器(DRAM)、其他类型的随机存取存储器(RAM)、只读存储器(ROM)、电可擦除可编程只读存储器(EEPROM)、快闪记忆体或其他内存技术、只读光盘只读存储器 (CD-ROM)、数字多功能光盘(DVD)或其他光学存储、磁盒式磁带，磁带磁磁盘存储或其他磁性存储设备或任何其他非传输介质，可用于存储可以被计算设备访问的信息。按照本文中的界定，计算机可读介质不包括暂存电脑可读媒体(transitorymedia)，如调制的数据信号和载波。Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.
还需要说明的是，术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含，从而使得包括一系列要素的过程、方法、商品或者设备不仅包括那些要素，而且还包括没有明确列出的其他要素，或者是还包括为这种过程、方法、商品或者设备所固有的要素。在没有更多限制的情况下，由语句“包括一个……”限定的要素，并不排除在包括要素的过程、方法、商品或者设备中还存在另外的相同要素。It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.
以上仅为本申请的实施例而已，并不用于限制本申请。对于本领域技术人员来说，本申请可以有各种更改和变化。凡在本申请的精神和原理之内所作的任何修改、等同替换、改进等，均应包含在本申请的权利要求范围之内。The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.
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