SUMMARY

Structural joint inversion of several data sets on an irregular mesh requires appropriate coupling operators. To date, joint inversion algorithms are primarily designed for the use on regular rectilinear grids and impose structural similarity in the direct neighbourhood of a cell only. We introduce a novel scheme for calculating cross-gradient operators based on a correlation model that allows to define the operator size by imposing physical length scales. We demonstrate that the proposed cross-gradient operators are largely decoupled from the discretization of the modelling domain, which is particularly important for irregular meshes where cell sizes vary. Our structural joint inversion algorithm is applied to a synthetic electrical resistivity tomography and ground penetrating radar 3-D cross-well experiment aiming at imaging two anomalous bodies and extracting the parameter distribution of the geostatistical background models. For both tasks, joint inversion produced superior results compared with individual inversions of the two data sets. Finally, we applied structural joint inversion to two field data sets recorded over a karstified limestone area. By including geological a priori information via the correlation-based operators into the joint inversion, we find P-wave velocity and electrical resistivity tomograms that are in accordance with the expected subsurface geology.

中文翻译：

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不规则网格上的结构联合反演

概要

不规则网格上几个数据集的结构联合反演需要适当的耦合算子。迄今为止，联合反演算法主要设计用于规则的直线网格，并且仅在单元的直接邻域中施加结构相似性。我们介绍了一种基于相关模型来计算交叉梯度算子的新颖方案，该模型允许通过施加物理长度尺度来定义算子大小。我们证明了所提出的交叉梯度算子与建模域的离散化在很大程度上脱钩，这对于像元大小变化的不规则网格特别重要。我们的结构联合反演算法应用于合成电阻率层析成像和探地雷达3-D井间实验，旨在对两个异常物体进行成像并提取地统计背景模型的参数分布。对于这两个任务，联合反转比两个数据集的单独反转产生了更好的结果。最后，我们将结构联合反演应用于在喀斯特石灰岩地区记录的两个现场数据集。通过基于相关性的算子将地质先验信息包括到联合反演中，我们发现与期望的地下地质一致的P波速度和电阻率层析X射线照片。与两个数据集的单独反演相比，联合反演产生了更好的结果。最后，我们将结构联合反演应用于在喀斯特石灰岩地区记录的两个现场数据集。通过基于相关性的算子将地质先验信息包括到联合反演中，我们发现与期望的地下地质一致的P波速度和电阻率层析X射线照片。与两个数据集的单独反演相比，联合反演产生了更好的结果。最后，我们将结构联合反演应用于在喀斯特石灰岩地区记录的两个现场数据集。通过基于相关性的算子将地质先验信息包括到联合反演中，我们发现与期望的地下地质一致的P波速度和电阻率层析X射线照片。