A probabilistic full waveform inversion of surface waves

IF 1.8 3区 地球科学 Q3 GEOCHEMISTRY & GEOPHYSICS
Sean Berti, Mattia Aleardi, Eusebio Stucchi
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引用次数: 0

Abstract

Over the past decades, surface wave methods have been routinely employed to retrieve the physical characteristics of the first tens of meters of the subsurface, particularly the shear wave velocity profiles. Traditional methods rely on the application of the multichannel analysis of surface waves to invert the fundamental and higher modes of Rayleigh waves. However, the limitations affecting this approach, such as the 1D model assumption and the high degree of subjectivity when extracting the dispersion curve, motivate us to apply the elastic full-waveform inversion, which, despite its higher computational cost, enables leveraging the complete information embedded in the recorded seismograms. Standard approaches solve the full-waveform inversion using gradient-based algorithms minimizing an error function, commonly measuring the misfit between observed and predicted waveforms. However, these deterministic approaches lack proper uncertainty quantification and are susceptible to get trapped in some local minima of the error function. An alternative lies in a probabilistic framework, but, in this case, we need to deal with the huge computational effort characterizing the Bayesian approach when applied to non-linear problems associated with expensive forward modelling and large model spaces. In this work, we present a gradient-based Markov chain Monte Carlo full-waveform inversion where we accelerate the sampling of the posterior distribution by compressing data and model spaces through the discrete cosine transform. Additionally, a proposal is defined as a local, Gaussian approximation of the target density, constructed using the local Hessian and gradient information of the log posterior. We first validate our method through a synthetic test where the velocity model features lateral and vertical velocity variations. Then we invert a real dataset from the InterPACIFIC project. The obtained results prove the efficiency of our proposed algorithm, which demonstrates to be robust against cycle-skipping issues and able to provide reasonable uncertainty evaluations with an affordable computational cost.

面波的概率全波形反演
在过去的几十年里,人们经常使用面波方法来检索地下前几十米的物理特征,特别是剪切波速度剖面。传统方法依赖于应用面波的多通道分析来反演瑞利波的基模和高模。然而,这种方法存在局限性,例如一维模型假设和提取频散曲线时的高度主观性,这促使我们应用弹性全波形反演,尽管计算成本较高,但能充分利用记录的地震图中蕴含的完整信息。标准方法使用基于梯度的算法解决全波形反演问题,最小化误差函数,通常测量观测波形和预测波形之间的不匹配度。然而,这些确定性方法缺乏适当的不确定性量化,容易陷入误差函数的某些局部极小值。另一种替代方法是概率框架,但在这种情况下,我们需要处理贝叶斯方法在应用于与昂贵的前向建模和大型模型空间相关的非线性问题时的巨大计算量。在这项工作中,我们提出了一种基于梯度的马尔可夫链蒙特卡洛全波形反演方法,通过离散余弦变换压缩数据和模型空间,加速后验分布的采样。此外,提案被定义为目标密度的局部高斯近似值,利用对数后验的局部黑森和梯度信息构建。我们首先通过速度模型具有横向和纵向速度变化的合成测试来验证我们的方法。然后,我们对 InterPACIFIC 项目的真实数据集进行反演。获得的结果证明了我们提出的算法的效率,该算法对周期跳跃问题具有很强的鲁棒性,能够以可承受的计算成本提供合理的不确定性评估。
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来源期刊
Geophysical Prospecting
Geophysical Prospecting 地学-地球化学与地球物理
CiteScore
4.90
自引率
11.50%
发文量
118
审稿时长
4.5 months
期刊介绍: Geophysical Prospecting publishes the best in primary research on the science of geophysics as it applies to the exploration, evaluation and extraction of earth resources. Drawing heavily on contributions from researchers in the oil and mineral exploration industries, the journal has a very practical slant. Although the journal provides a valuable forum for communication among workers in these fields, it is also ideally suited to researchers in academic geophysics.
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