A Fast and High-precision Forward Modeling Method for Gravity Field in Spherical Coordinate System

Abstract

The invention provides a rapid high-precision gravity field forward-modeling method in the spherical coordinate system. An underground field source is divided into ruled unit bodies at equal interval,whether one unit body is dissected into a proper size is determined by determining relation between the distance from an observation point to the central point of the unit body and lengths of the unit body in the radial, broadwise and warpwise directions, gravity response of each unit body in the observation point P beyond the field source body is calculated, the gravity potential V, the gravityacceleration galpha and the gravity gradient tensor galphabeta are represented in a matrix multiplying form, a calculation process can be simplified by utilizing the equivalence of a kernel matrix, kernel matrix elements can be obtained rapidly from one kernel matrix element, the gravity response of the multiple unit bodies is accumulated according to the superposition performance of the gravity field, and a gravity field generated in the point P by all substances underground is obtained. Thus, less fewer is occupied by introducing a kernel matrix equivalence strategy and an adaptive fine-dissection strategy, and the calculation efficiency and forward-modeling precision are improved greatly.

Description

technical field [0001] The invention relates to the technical field of geophysics, in particular to a fast and high-precision forward modeling method for gravity field in a large-scale spherical coordinate system; the method improves the calculation efficiency by two orders of magnitude by introducing the kernel matrix equivalence strategy, and at the same time greatly reduces the The method also reduces the relative error during calculation by introducing an adaptive subdivision strategy, which greatly improves the accuracy of forward modeling. Background technique [0002] Gravity exploration, as the most basic geophysical method, has been widely used in technical fields such as terrain correction, hydrogeological survey, geoid survey, solid mineral resource exploration, lithosphere crust and mantle structure research, etc. Since the gravity field data obtained through measurement are closely related to subsurface density anomalies, the data can be directly used to invert ...

AI Technical Summary

Problems solved by technology

The existing three-dimensional gravity field forward modeling methods in the spherical coordinate system include two-dimensional Gauss-Legendre algorithm, three-dimensional Gauss-Legendre algorithm, Taylor series expansion method, etc.; the above-mentioned methods all have the disadvantages of low forward modeling efficiency and poor calculation accuracy , seriously restricting the widespread use of large-scale gravity field inversion

[0005] For example, the traditional three-dimensional Gaussian Legendre algorithm is very time-consuming, especially when the numerical accuracy is improved by adding Gaussian nodes, or when the number of grids and observation points is large, the calculation time will increase exponentially, affecting positive In addition, when the observation point is too close to the underground field source, the size of many tesseroid units and the distance from the center point to the observation point do not meet the proportional requirements, resulting in low forward modeling accuracy

[0006] Under the background that the current computer hardware conditions are difficult to produce a leap forward, in order to solve the above problems, we can only seek new forward modeling methods

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