基于有限差分法的2.5D频谱激电法正演模拟

Research on 2.5-Dimensional Forward Modeling of Spectral Induced Polarization Based on Finite Difference Method

摘要: 随着地球物理勘探技术的不断进步，电法勘查作为一种对地下介质进行识别的重要手段而广泛应用于资源勘查、环境监测和工程勘察等领域。谱激电法作为电法勘查中的常用方法，由于其在探测地下低阻异常体和复杂地质体方面的独特优势，逐渐成为地球物理勘探中的核心技术之一。在谱激电法的正演模拟中，有限差分法能够通过网格剖分精确地求解地下介质各处的电位值，处理各种介质和几何结构，提供高度精确的模拟结果。该研究旨在结合激发极化法与有限差分法，深入探讨基于有限差分法的谱激电2.5维正演模拟的实现与应用。文章推导了有限差分法的相关公式，得到网格各节点所对应的边界条件与差分方程，并用Fortran90进行编程实现。通过建立不同的地电模型并对其进行正演模拟，通过得到的数据绘制等值线断面图，通过观察均可较好的模拟出所设置的地电模型形态特点。在此基础上修改对应参数，揭示了各电性参数对模拟结果的影响，为实际电法勘探和数据解释提供理论依据和技术支持。

Abstract: With the continuous advancement of geophysical exploration technology, electrical exploration, as an important means of identifying underground media, is widely used in fields such as resource exploration, environmental monitoring, and engineering exploration. Spectral induced polarization method, as a commonly used method in electrical exploration, has gradually become one of the core technologies in geophysical exploration due to its unique advantages in detecting underground low resistance anomalous bodies and complex geological bodies. In the forward simulation of spectral induced polarization method, the finite difference method can accurately solve the potential values of underground media at various locations through grid meshing, handle various media and geometric structures, and provide highly accurate simulation results. This study aims to explore in depth the implementation and application of 2.5-dimensional forward simulation of spectral induced polarization based on the finite difference method, by combining the induced polarization method and the finite difference method. This article derives the relevant formulas of the finite difference method, obtains the boundary conditions and difference equations corresponding to each node of the grid, and implements them using Fortran90 programming. By establishing different geoelectric models and conducting forward simulations, contour section maps can be drawn based on the obtained data, and the morphological characteristics of the geoelectric model can be well simulated through observation. On this basis, the corresponding parameters were modified to reveal the influence of various electrical parameters on the simulation results, providing theoretical basis and technical support for practical electrical exploration and data interpretation.