Abstract

The authors are developing a method for precision monitoring of the specific apparent electrical resistivities of individual layers of the Earth’s crust. This task is extremely difficult, since the apparent resistivities are actually observed, then it is necessary to solve an entire set of complex problems for their processing: noise removal, isolating the physically determined components, and, most importantly, solving the inverse problem of reconstructing the resistivity from the measured apparent resistivity values. The aim of the work is to improve the methodological foundations of precision monitoring to increase its accuracy. The data processing algorithm is divided into a sequence of elementary operations: data aggregation, time series smoothing, noise filtering, estimation of seasonal (exogenic) effects, and solving the inverse vertical electrical sounding (VES) problem. The solution to the inverse problem is an essentially nonlinear operation, and all others become nonlinear if there are data gaps in the signal, which is virtually inevitable during long-term observations. Therefore, the final result can significantly depend not only on the settings of individual operations (width and/or type of weight function of the aggregation/smoothing window, etc.), but also on the order in which these operations are performed. The study employs a numerical experiment with real data to estimate how strongly the sequence of the above operations affects the result. The calculations used unique long-term precision monitoring data by the VES method. It is shown that the smoothing operator can be applied to both the apparent and specific resistivities, which barely affects the result. Conversely, the order of seasonal filtering and solution of the inverse problem is important. It is shown that error estimates for calculating the specific resistivity based on the internal convergence of the algorithm for solving the inverse problem are unacceptable, since they differ from the real errors by two orders of magnitude. For reliable monitoring of temporary variations in resistivity in the deep layers of the studied structure under, it is necessary to increase the stability of the selection of resistivities according to a given VES curve, as well as to take other measures for optimizing the algorithm.

中文翻译：

---

使用Ves监视数据优化时间变化电阻率算法的算法，以提高结果的准确性和可靠性

摘要

作者正在开发一种方法，用于精确监视地壳各层的特定视在电阻率。由于实际上要观察到视在电阻率，因此此任务极为困难，因此有必要解决一整套复杂的处理问题：噪声消除，隔离物理确定的分量，最重要的是解决重建的逆问题根据测得的视在电阻率值得出电阻率。这项工作的目的是改善精密监测的方法基础，以提高其准确性。数据处理算法分为一系列基本操作：数据聚合，时间序列平滑，噪声过滤，季节性（外生）影响的估算，并解决了垂直电声反演问题。反问题的解决方案是从本质上讲是非线性操作，如果信号中存在数据间隙，则所有其他操作都会变为非线性，这在长期观察中实际上是不可避免的。因此，最终结果不仅可以极大地取决于各个操作的设置（聚合/平滑窗口的宽度和/或权重函数的类型等），而且还取决于这些操作的执行顺序。该研究采用具有真实数据的数值实验来估计上述操作的顺序对结果的影响程度。这些计算通过VES方法使用了独特的长期精度监控数据。结果表明，可以将平滑算子应用于视电阻率和比电阻率，这几乎不会影响结果。相反，季节性过滤的顺序和反问题的求解很重要。结果表明，基于解决反问题算法的内部收敛性来计算比电阻率的误差估计是不可接受的，因为它们与实际误差相差两个数量级。为了可靠地监视所研究结构深层中电阻率的临时变化，有必要根据给定的VES曲线增加电阻率选择的稳定性，并采取其他措施来优化算法。结果表明，基于解决反问题算法的内部收敛性来计算比电阻率的误差估计是不可接受的，因为它们与实际误差相差两个数量级。为了可靠地监视所研究结构深层中电阻率的临时变化，有必要根据给定的VES曲线增加电阻率选择的稳定性，并采取其他措施来优化算法。结果表明，基于解决反问题算法的内部收敛性来计算比电阻率的误差估计是不可接受的，因为它们与实际误差相差两个数量级。为了可靠地监视所研究结构深层中电阻率的临时变化，有必要根据给定的VES曲线增加电阻率选择的稳定性，并采取其他措施来优化算法。