Parameter inversion of the diffusive-viscous wave equation based on Gaussian process regression

IF 1.6 3区 地球科学 Q3 GEOCHEMISTRY & GEOPHYSICS
Zhaowei Bai, Haixia Zhao, Shaoru Wang
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引用次数: 0

Abstract

Abstract The diffusive-viscous wave (DVW) equation is used to characterize the relationship between frequency-dependent seismic responses and saturated fluids by incorporating the frictional dissipation and viscous damping to the scalar wave equation. Simultaneous inversion of three model parameters in DVW equation is essential for seismic interpretations. Traditional inversion methods require continuous forward modeling updates, resulting in low computational efficiency. Moreover, the traditional methods have limitations in simultaneously inverting multi-parameters of wave equations such as DVW equation, usually fixing one parameter to invert the other two parameters. Gaussian process regression (GPR) is a kernel-based non-parametric probabilistic model that introduces prior variables through Gaussian processes (GP). We present a method for the inversion of the three parameters (velocity, diffusive and viscous attenuation coefficients) of the DVW equation based on GPR. The procedure consists of initially implementing the central finite difference approximation to discretize the DVW equation in the time domain. Subsequently, a Gaussian prior is provided on two snapshots of the DVW equation to obtain the corresponding kernel functions. Furthermore, the hyperparameters in kernel functions and the three model parameters are simultaneously trained by minimizing the negative logarithmic marginal likelihood with few training samples while incorporating the underlying physics in terms of encoding the DVW equation into the kernel functions. It is worth noting that it is the first time to implement three-parameter simultaneous inversion based on DVW equation. The numerical examples in homogeneous, layered and heterogeneous media demonstrate the effectiveness of this method.
基于高斯过程回归的扩散-粘性波动方程参数反演
摘要通过将摩擦耗散和粘性阻尼加入标量波方程中,采用扩散-粘性波方程来表征频率相关地震响应与饱和流体的关系。DVW方程中三个模型参数的同时反演是地震解释的关键。传统的反演方法需要不断更新正演模型,计算效率较低。此外,传统方法在同时反演DVW方程等波动方程的多参数时存在局限性,通常固定一个参数来反演另外两个参数。高斯过程回归(GPR)是一种基于核函数的非参数概率模型,它通过高斯过程引入先验变量。提出了一种基于探地雷达反演DVW方程中速度、扩散和粘性衰减系数的方法。该过程包括初始实现中心有限差分逼近在时域离散化DVW方程。随后,对DVW方程的两个快照提供高斯先验以获得相应的核函数。此外,核函数中的超参数和三个模型参数通过最小化负对数边际似然来同时训练,同时结合底层物理,将DVW方程编码到核函数中。值得注意的是,这是首次实现基于DVW方程的三参数同时反演。在均质、层状和非均质介质中的数值算例表明了该方法的有效性。
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来源期刊
Journal of Geophysics and Engineering
Journal of Geophysics and Engineering 工程技术-地球化学与地球物理
CiteScore
2.50
自引率
21.40%
发文量
87
审稿时长
4 months
期刊介绍: Journal of Geophysics and Engineering aims to promote research and developments in geophysics and related areas of engineering. It has a predominantly applied science and engineering focus, but solicits and accepts high-quality contributions in all earth-physics disciplines, including geodynamics, natural and controlled-source seismology, oil, gas and mineral exploration, petrophysics and reservoir geophysics. The journal covers those aspects of engineering that are closely related to geophysics, or on the targets and problems that geophysics addresses. Typically, this is engineering focused on the subsurface, particularly petroleum engineering, rock mechanics, geophysical software engineering, drilling technology, remote sensing, instrumentation and sensor design.
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