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Gravity inversion method based on cubic b-spline function

A spline function and gravity inversion technology, which is applied in the field of geophysical gravity exploration, can solve problems such as inability to invert smooth density field models, achieve reliable inversion results and avoid calculation errors

Active Publication Date: 2021-04-27
OCEAN UNIV OF CHINA
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  • Claims
  • Application Information

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Problems solved by technology

None of the above gravity inversion methods can invert the spatial second-order continuously differentiable smooth density field model

Method used

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  • Gravity inversion method based on cubic b-spline function
  • Gravity inversion method based on cubic b-spline function
  • Gravity inversion method based on cubic b-spline function

Examples

Experimental program
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Effect test

Embodiment 1

[0061] In order to illustrate the realization idea and implementation process of this method and prove the effectiveness of the method, the anomaly body (model 1) with density anomalies, one positive and one negative, is tested and compared with the results of conventional constant density unit L2 mode constrained inversion.

[0062] S1: will be as figure 2 Model 1 is shown as the true density model. The real density model is composed of a positive and a negative density anomaly, the two anomalous cross-sections are squares with a side length of 1.1 km, and the density difference is 0.5 g / cm 3 and -0.5g / cm 3 .

[0063] S2: Gravity observation points are arranged along the horizontal surface, with a distance of 100 m, and a total of 95 observation points.

[0064] S3: Calculate the gravity anomaly produced by model 1, such as figure 2 shown in the curve.

[0065] S4: The calculated gravity anomaly data is used as the observation data, the cubic B-spline node spacing is s...

Embodiment 2

[0071] In order to further illustrate the practicability of this method, three density anomaly bodies (model 2) of different sizes are tested, and compared with the results of conventional constant density unit L2 mode constrained inversion. Model 2 is composed of three positive density anomalies with different central buried depths and sizes. The cross-sections of the three anomalous bodies are squares with side lengths of 1.1 km, 0.6 km, and 0.3 km, respectively, and the density difference is 0.5 g / cm 3 ,Such as Figure 5 shown. Calculate the gravity anomaly produced by Model 2 as Figure 5 As shown in the curve, the inversion steps of Example 2 are the same as S4~S7 of Example 1. Image 6 is the inversion result of the conventional constant density element L2 mode constraint method. It can be clearly seen from the figure that the inversion density amplitude of this method is relatively small, the deeper the depth, the more divergent the density distribution, and the boun...

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Abstract

The invention relates to a gravity inversion method based on a cubic B-spline function, and belongs to the technical field of geophysical gravity exploration. It includes the following steps: determine the scope of the underground inversion area; parameterize the density model of the inversion area, that is, set the density node; calculate the gravity core caused by each node at a certain gravity observation point; complete the calculation of all observation points in the previous step of the loop The gravity kernel caused by each node is generated, and the gravity kernel function matrix is ​​generated; the objective function is established, and the density value of each node is obtained by solving; the smooth density field of the entire inversion area is obtained by using cubic B-spline function interpolation. The invention has the advantage of being able to calculate the analytical expression of the gravity response of the smooth density field, avoiding the numerical solution of the superposition of the gravity field of the constant density unit, and solving the problem that the existing method cannot invert the second-order continuous and differentiable density field in space. The process is controlled by the density node, no additional spatial smoothness constraints are required, and the inversion effect is better than the commonly used L2 mode constraint inversion.

Description

technical field [0001] The invention relates to a gravity inversion method based on a cubic B-spline function, and belongs to the technical field of geophysical gravity exploration. Background technique [0002] Gravity inversion is divided into interface model inversion and density model inversion. The former is to invert the shape of the undulating interface when the density distribution law is known; the latter is to directly invert the spatial density distribution of the underground area. In the density model inversion of gravity, people generally adopt the method of constant density grid division, the density of each grid cell is a constant, and the gravity anomalies generated by all constant density cells are accumulated as the gravity of a certain observation point response. The disadvantage of this method is that when the grid spacing is large, the density of adjacent grid cells will change abruptly, and it is impossible to simulate the situation where the density c...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G01V7/06
CPCG01V7/06
Inventor 刘洁张建中
Owner OCEAN UNIV OF CHINA
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