Abstract

Modern visualization can be formulated as inversion problems that aim to obtain structural information about a complex medium through wave excitations. However, without numerically efficient forward calculations, even state-of-the-art inversion procedures are too computationally intensive to implement. We adapt a method previously used to treat transport in electronic waveguides to describe acoustic wave motion in complex media with high gains in computational time. The method consists of describing the system as if it was made of disconnected parts that are patched together. By expressing the system in this manner, wave-propagation calculations that otherwise would involve a very large matrix can be done with considerably smaller matrices instead. In particular, by treating one of such patches as a target whose parameters are changeable, we are able to implement target-oriented optimization in which the model parameters can be continuously refined until the ideal result is reproduced. The so-called Patched Green's function (PGF) approach is mathematically exact and involves no approximations, thus improving the computational cost without compromising accuracy. Given the generality of our method, it can be applied to a wide variety of inversion problems. Here we apply it to the case of seismic modeling where acoustic waves are used to map the earth subsurface in order to identify and explore mineral resources. The technique is tested with realistic seismic models and compared to standard calculation methods. The reduction in computational complexity is remarkable and paves the way to treating larger systems with increasing accuracy levels.

中文翻译：

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修补格林函数方法应用于无序介质中声波传播的跨学科方法

摘要

现代可视化可以表述为反演问题，旨在通过波激励获得有关复杂介质的结构信息。但是，如果没有数值有效的前向计算，即使是最新的反演程序也需要大量的计算才能实现。我们采用了以前用于处理电子波导中的传输的方法来描述复杂介质中的声波运动，从而在计算时间上获得了很高的收益。该方法包括将系统描述为好像是由修补在一起的不连续部分组成的。通过以这种方式表示系统，可以用相当小的矩阵来完成否则会涉及非常大的矩阵的波传播计算。特别地，通过将​​这些补丁之一视为其参数可更改的目标，我们能够实现面向目标的优化，其中可以不断优化模型参数，直到再现理想的结果。所谓的修补格林函数（PGF）方法在数学上是精确的，并且不包含任何近似值，因此可以在不影响准确性的情况下提高计算成本。鉴于我们方法的一般性，它可以应用于各种各样的反演问题。在这里，我们将其应用于地震建模的情况，在该建模中，声波被用来绘制地球地下表面，以识别和勘探矿产资源。该技术已通过实际地震模型进行了测试，并与标准计算方法进行了比较。计算复杂度的降低非常显着，为以更高的精度水平处理大型系统铺平了道路。