任意三维密度分布地质体重力场及重力梯度张量快速正演方法研究

Three-dimensional inversion and human-computer interactive modeling for gravity anomaly and gravity gradient tensor is now the key research content in gravity prospecting. Efficient and accurate forward modeling algorithm is foundation for three-dimensional inversion and interactive modeling. According to the requirement of three-dimensional inversion and interactive modeling, this project is aimed at resolving the problem of fast computation of gravity and gravity gradient tensor with arbitrary density distribution. Based on the previous work, this project will further study fast computing method for three-dimensional discrete convolution, computation of gravity on the boundary and parallel computing algorithm design. The goal of this project is to put forward to a new methodology for forward modeling and give an efficient and accurate algorithm that resolves the forward modeling problem in the condition of arbitrary density distribution. The anticipated achievement will be valuable both in theory and application.

重力异常和重力梯度张量三维物性反演、人机交互建模是目前重力勘探领域研究的重点。高效、高精度正演算法是实现三维物性反演和人机交互建模的基础。本课题针对三维物性反演和人机交互建模对正演计算的需求，研究任意三维密度分布条件下重力场和重力梯度张量正演问题。在前期工作基础上，重点研究空间域三维离散卷积快速计算新方法、边界处场的计算方法和正演算法并行化。课题预期研究目标是形成一套新的正演计算方法体系，研发出高效、高精度正演算法，解决任意三维密度分布条件下重力场和重力梯度张量快速正演问题。预期研究成果具有重要的理论价值和应用价值。

为满足大规模重力测量数据三维密度反演、人机交互解释建模对正演计算速度和计算精度的需求，本项目重点研究了任意密度分布条件下复杂地质体重力场及其梯度张量快速、高精度正演方法，提出了一套系统地数值求解卷积积分的空间域快速、高精度算法，成功应用于任意密度分布情况下复杂地质体重力场和重力梯度张量的正演计算。数值模型算例验证了新算法的计算精度和计算速度。本项目提出的卷积积分空间域快速、高精度算法具有通用性，可用于解决地球物理中其它卷积积分的数值计算问题，具有重要的理论价值和应用前景。