Resolution analysis in full waveform inversion
Resolution analysis in full waveform inversion
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DOI：
10.1111/j.1365-246x.2011.05218.x
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发表时间：
2011-12-01
影响因子：
2.8
通讯作者：
Trampert, Jeannot
中科院分区：
文献类型：
--
作者：
Fichtner, Andreas;Trampert, Jeannot
我们提出了一种新的方法，在全地震波形反演的定量分辨率分析，克服了传统的合成反演的局限性，同时计算更有效，适用于任何失配措施。该方法依赖于（1）在最佳地球模型附近的失配泛函的局部二次近似，（2）根据父函数及其连续导数的Hessian的参数化和（3）通过Hessian的傅立叶变换计算空间相关参数，借助于伴随技术计算。在高斯近似的最简单的情况下，我们可以推断出严格定义的3-D分布的方向相关的分辨率长度和图像失真的层析成像方法。我们说明了这些概念与一个现实的全波形反演欧洲下的上地幔结构。作为一个推论的分辨率分析的方法，我们提出了几个改进的全波形反演技术。其中包括共轭梯度型优化方案的预条件，一个新的家庭牛顿式的方法，独立于射线理论的自适应参数化的方法和目标的功能设计，旨在最大限度地提高分辨率的战略。我们的方法的计算要求是小于一个典型的合成反演，但产生一个更完整的图片的分辨率和权衡。虽然本文中提出的例子是相当具体的，但其基本思想是非常普遍的。它允许根据问题对主题进行变化，并根据勘探情况和其他使用地质雷达或微波数据的基于波动方程的层析成像技术进行调整。
We propose a new method for the quantitative resolution analysis in full seismic waveform inversion that overcomes the limitations of classical synthetic inversions while being computationally more efficient and applicable to any misfit measure. The method rests on (1) the local quadratic approximation of the misfit functional in the vicinity of an optimal earth model, (2) the parametrization of the Hessian in terms of a parent function and its successive derivatives and (3) the computation of the space-dependent parameters via Fourier transforms of the Hessian, calculated with the help of adjoint techniques. In the simplest case of a Gaussian approximation, we can infer rigorously defined 3-D distributions of direction-dependent resolution lengths and the image distortion introduced by the tomographic method. We illustrate these concepts with a realistic full waveform inversion for upper-mantle structure beneath Europe. As a corollary to the method for resolution analysis, we propose several improvements to full waveform inversion techniques. These include a pre-conditioner for optimization schemes of the conjugate-gradient type, a new family of Newton-like methods, an approach to adaptive parametrization independent from ray theory and a strategy for objective functional design that aims at maximizing resolution. The computational requirements of our approach are less than for a typical synthetic inversion, but yield a much more complete picture of resolution and trade-offs. While the examples presented in this paper are rather specific, the underlying idea is very general. It allows for problem-dependent variations of the theme and for adaptations to exploration scenarios and other wave-equation-based tomography techniques that employ, for instance, georadar or microwave data.