ABSTRACT New developments in mobile resistivity meter instrumentation have made it possible to survey large areas with dense data coverage. The mobile system usually has a limited number of electrodes attached to a cable that is pulled along behind an operator so that a large area can be covered within a short time. Such surveys can produce three‐dimensional datasets with hundreds of thousands of electrodes positions and data points. Similarly, the inverse model used to interpret the data can have several hundred thousand cells. It is impractical to model such large datasets within a reasonable time on microcomputers used by many small companies employing standard inversion techniques. We describe a model segmentation technique that subdivides the finite‐element mesh used to calculate the apparent resistivity and Jacobian matrix values into a number of smaller meshes. A fast technique that optimizes the calculation of the Jacobian matrix values for multi‐channel systems was also developed. A one‐dimensional wavelet transform method was then used to compress the storage of the Jacobian matrix, in turn reducing the computer time and memory required to solve the least‐squares optimization equation to determine the inverse model resistivity values. The new techniques reduce the calculation time and memory required by more than 80% while producing models that differ by less than 1% from that obtained using the standard inversion technique with a single mesh. We present results using a synthetic model and a field dataset that illustrates the effectiveness of the proposed techniques.

中文翻译：

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边缘保留噪声衰减的变分模式分解

摘要 移动电阻率仪仪器的新发展使测量具有密集数据覆盖的大面积成为可能。移动系统通常将有限数量的电极连接到一根电缆上，该电缆在操作员身后被牵引，因此可以在短时间内覆盖大片区域。这样的调查可以产生具有数十万个电极位置和数据点的三维数据集。同样，用于解释数据的逆模型可能有几十万个单元格。在许多采用标准反演技术的小公司使用的微型计算机上，在合理的时间内对如此大的数据集进行建模是不切实际的。我们描述了一种模型分割技术，该技术将用于计算视电阻率和雅可比矩阵值的有限元网格细分为多个较小的网格。还开发了一种优化多通道系统雅可比矩阵值计算的快速技术。然后使用一维小波变换方法压缩雅可比矩阵的存储，从而减少求解最小二乘优化方程以确定逆模型电阻率值所需的计算机时间和内存。新技术将所需的计算时间和内存减少了 80% 以上，同时生成的模型与使用具有单个网格的标准反演技术获得的模型相差不到 1%。