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Gravitational field rapid forward modeling method and inversion method based on Toplite kernel matrix

A technology of kernel matrix and gravity field, applied in the field of fast forward modeling method and inversion of gravity field

Active Publication Date: 2020-07-10
CENT SOUTH UNIV
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  • Description
  • Claims
  • Application Information

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Problems solved by technology

The traditional gravity field forward and inversion method has been difficult to meet the basic requirements of massive high-resolution data, and it is urgent to develop a set of efficient and high-precision forward and inversion methods

Method used

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  • Gravitational field rapid forward modeling method and inversion method based on Toplite kernel matrix
  • Gravitational field rapid forward modeling method and inversion method based on Toplite kernel matrix
  • Gravitational field rapid forward modeling method and inversion method based on Toplite kernel matrix

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Embodiment 1

[0119] This embodiment uses a lunar spherical shell forward model to verify the correctness and efficiency of the method proposed by the present invention, because only the spherical shell model has an analytical solution. The thickness of the spherical shell is 100km, the initial range is 1638 to 1738km (that is, the actual radius of the moon), and the spherical shell density is set to 1000kg / m 3 , the observation surface is a spherical surface at a height of 10km from the outer spherical shell, and the spherical shell is divided into 10 sections in the radial direction, with an interval of 10km. The interval between the longitude and latitude is 0.5° to 10°, and the relationship between the maximum relative error and the calculation time and the subdivision interval is calculated.

[0120] The relationship between the maximum relative error and the subdivision interval is as follows: image 3 As shown, the relationship between the relative calculation time and the subdivisi...

Embodiment 2

[0125] In order to further prove the validity and efficiency of the fast forward modeling method of the spherical coordinate system gravity field based on the Toplitze matrix frequency-domain FFT algorithm proposed in the application of the present invention, the following example provides an actual data inversion case, and the proposed The method is applied to the global-scale three-dimensional density imaging research of the moon, the details are as follows:

[0126] The global terrain of the moon is obtained by solving the latest lunar terrain spherical harmonic model LRO_LTM05_2050, such as Figure 5 Shown in (a).

[0127] The present invention uses the latest lunar gravity field model GL1500E to calculate free air gravity anomalies, such as Figure 5 As shown in (b), the terrain correction result is as follows Figure 5 Shown in (c). Boog Gravity Anomaly via Free Air Gravity Anomaly ( Figure 5 Middle (b)) minus the terrain correction ( Figure 5 In (c)) get, such as...

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Abstract

The invention provides a rapid forward modeling method for a three-dimensional gravity field under a spherical coordinate system. The method comprises the following steps: dividing a forward kernel matrix into a plurality of Toplite sub-matrixes; adopting the frequency domain FFT rapid calculation for partitioning, performing accumulation summation, and converting the time-consuming matrix-vectorproduct operation into a summation operation, so the calculation time of a kernel matrix in forward modeling is shortened, the repetitive calculation efficiency of multiplication of the kernel matrixand a density vector is improved, and the overall efficiency of forward modeling calculation is improved. According to the method, a special subdivision mode is adopted, all kernel matrix elements donot need to be calculated any more, only the kernel matrix elements generated by the first column of tesseroid unit bodies of the underground field source need to be calculated, values of other elements are mapped out through the equivalent relation, the calculation cost of the kernel matrix is greatly reduced, and meanwhile occupation of a memory is reduced. The invention further provides an inversion method which is combined with the forward modeling method, a large Jacobian matrix does not need to be stored, only a final matrix needs to be stored, and the calculation and storage of intermediate variables are reduced.

Description

technical field [0001] The invention relates to the technical field of geophysics and exploration, in particular to a fast forward modeling method and an inversion method of a gravity field based on a Toplitze kernel matrix. Background technique [0002] With the popularization of high-precision and high-coverage global gravity satellite data, it is possible to explore gravity exploration, deep geological structure, crust and mantle deformation, and the exploration of stars such as the moon and Mars. [0003] Gravity field forward and inversion, as an important technical means, is widely used in underground 3D density imaging research. Gravity field forward and inversion can be carried out on conventional exploration scales, used for resource exploration (mineral, oil, natural gas) and hydrological environment research, mostly based on Cartesian coordinate system, common fast algorithms include FFT method, Gauss-FFT method , multi-level expansion method, etc., so that the c...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/16G06F17/14G01V7/00
CPCG06F17/16G06F17/142G01V7/00
Inventor 赵广东柳建新陈波
Owner CENT SOUTH UNIV
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