A fast inversion method based on the principles of concurrency and equidistant equivalence.

Abstract

This invention relates to the field of geophysics and provides a rapid inversion method based on the principles of co-location and equidistant equivalence. The method includes the following steps: starting from the bottom interface of the subsurface, the subsurface region is divided into subdivisions using cuboids of equal length in the x and y directions. The distribution of the subdivision grid corresponds to the topographic relief, and each observation point corresponds one-to-one with a subdivision unit. The relationship function between the nodes of the subsurface subdivision grid and the surface observation points is calculated. Subdivision nodes at the same horizontal level with equal distances to the observation points have equivalent relationships. Based on the node positions, the complex function calculation process is replaced by the equivalent relationships to obtain the relationship function matrix between the subdivision nodes and the observation grid. The subdivision nodes are combined according to the distribution of subsurface units to obtain the kernel function matrix. Finally, the conjugate gradient method is used for inversion to obtain the density distribution of the inverted region. This method achieves rapid inversion while ensuring inversion accuracy and resolution.

Description

Technical Field

[0001] This invention belongs to the field of geophysics, and particularly relates to a fast inversion method based on the principles of co-location and equidistant equivalence. Background Technology

[0002] Current gravity exploration often employs ground-based or ground-following aerial surveys in mountainous and hilly areas, meaning the data observation surface is undulating. Physical property inversion of gravity data is a crucial method for obtaining subsurface density distribution. However, due to the long computation time of the physical property inversion process, it is difficult to achieve rapid inversion for undulating areas using simple algorithms.

[0003] Since the forward modeling of the kernel function consumes a significant amount of time in the inversion process, achieving rapid gravity inversion in undulating terrain areas can be accomplished by accelerating the forward modeling process. Currently, this can be achieved in two ways. One method is to reduce the parameters of the kernel function, thereby reducing the computational load. For example, wavelet transform can be used to convert the kernel matrix into a sparse matrix, or the Moving-footprint method can be used to reduce the number of cells involved in the calculation, thereby changing the size of the kernel function and reducing the computational load. However, this process involves approximation of the kernel matrix, which inevitably leads to a decrease in computational accuracy.

[0004] Another approach is to first flatten the anomalies to establish specific geometric relationships between observation points and subdivided units, reducing the number of calculations required to generate the kernel matrix. For example, this can be achieved by establishing an equivalent geometric framework through translational and cross-equivalence, or by using a multi-level model to generate a BTTB matrix using equivalence, and then converting matrix convolution operations into multiplication using FFT for faster computation. However, this process requires data flattening, which not only adds a preprocessing step before inversion but may also lead to fuzzy anomalies and reduce inversion resolution. Summary of the Invention

[0005] The purpose of this invention is to provide a fast inversion method based on the principles of co-point and equidistant equivalence, in order to solve the problems mentioned in the background art.

[0006] The present invention is implemented as follows: a fast inversion method based on the principles of co-location and equidistant equivalence includes the following steps:

[0007] Step 1: Starting from the bottom interface of the partition space, the underground area is partitioned using cuboids of equal length in the x and y directions. The distribution of the partition grid is consistent with the topographic relief, and the observation points correspond one-to-one with the partition units.

[0008] Step 2: Calculate the relationship function between the nodes of the underground subdivision grid and the surface observation points. Subdivision nodes that are equidistant from the observation points on the same horizontal layer have equivalent relationships. Based on the node positions, the complex function calculation process is replaced by a simple equivalent relationship, thereby quickly obtaining the relationship function matrix between the subdivision nodes and the observation grid.

[0009] Step 3: Combine the subdivided nodes according to the distribution of underground units to obtain the kernel function matrix. Finally, use the conjugate gradient method to invert the density distribution of the inverted area.

[0010] A further technical solution is that, in step 1, for nodes at the same horizontal level and a fixed observation point, the functional relationship between the partitioning nodes and the observation point is defined as follows:

[0011]

[0012] Among them, g i,j Let P represent the observation point located at position (i,j) in the observation point grid, with coordinates (ξ,η,ζ). Let P represent the observation point located at (x,y,z) in the partition space, with coordinates (x,y,z). Let r represent the distance from partition node P to observation point g. i,j The distance.

[0013] In a further technical solution, there is an equivalent relationship in step 2:

[0014]

[0015] At the same time, an identity relationship also exists:

[0016] f(g i,j ,P1)+f(g i,j ,P2)+f(g i,j ,P3)+f(g i,j (3) P4) = 0

[0017] When a = b, equidistant points will reach the diagonal of the square centered at the observation point. At this time, formula (2) simplifies to:

[0018]

[0019] Then formula (3) becomes:

[0020] f(g i,j ,Q1)+f(g i,j ,Q2)+f(g i,j ,Q3)+f(g i,j ,Q4)=0 (5).

[0021] A further technical solution involves combining the functions of the nodes and observation points in step 3 into a kernel function from the element to the observation point, using the following combination formula:

[0022]

[0023] Where G represents the gravitational constant, and A g Represents the kernel function matrix.

[0024] This invention provides a fast inversion method based on the principles of co-location and equidistant equivalence. This method reduces the amount of computation by reducing redundant calculations and simplifying complex calculations, thereby effectively improving computational efficiency. It can realize fast inversion calculations for undulating terrain areas, and compared with traditional inversion schemes, it does not lose inversion accuracy and resolution. Attached Figure Description

[0025] Figure 1 A flowchart illustrating a fast inversion method based on the principles of concurrency and equidistant equivalence provided in this embodiment of the invention;

[0026] Figure 2 A schematic diagram of the equidistant equivalence principle in a fast inversion method based on the principles of concurrency and equidistant equivalence provided in an embodiment of the present invention;

[0027] Figure 3 A schematic diagram illustrating the diagonal corner point equivalence principle in a fast inversion method based on the principles of concurrency and equidistant equivalence provided in an embodiment of the present invention;

[0028] Figure 4 This is a schematic diagram of the corner point coordinates in a fast inversion method based on the principles of co-location and equidistant equivalence, provided in an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0030] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0031] like Figure 1 As shown, an embodiment of the present invention provides a fast inversion method based on the principles of co-location and equidistant equivalence, comprising the following steps:

[0032] Step 1: Starting from the bottom interface of the partition space, the underground area is partitioned using cuboids of equal length in the x and y directions. The distribution of the partition grid is consistent with the topographic relief, and the observation points correspond one-to-one with the partition units.

[0033] Step 2: Calculate the relationship function between the nodes of the underground subdivision grid and the surface observation points. Subdivision nodes that are equidistant from the observation points on the same horizontal layer have equivalent relationships. Based on the node positions, the complex function calculation process is replaced by a simple equivalent relationship, thereby quickly obtaining the relationship function matrix between the subdivision nodes and the observation grid.

[0034] Step 3: Combine the subdivided nodes according to the distribution of underground units to obtain the kernel function matrix. Finally, use the conjugate gradient method to invert the density distribution of the inverted area.

[0035] In this embodiment of the invention, when performing gravity inversion on undulating terrain, if the traditional method is used to calculate the response function of each unit cell to the observation point individually, a large amount of redundant calculation will occur during the calculation process because each subdivision node is shared by eight subdivision units, thus increasing the computational load. Furthermore, nodes at the same horizontal level that are equivalent to the observation point also exhibit a certain degree of equivalence. Since these redundant calculations can be replaced by the principles of co-location and equivalence, the computational load can be saved by replacing redundant calculations with the principles of co-location and equivalence, thereby improving computational efficiency.

[0036] In a preferred embodiment of the present invention, in step 1, the positional relationship between nodes on the same horizontal layer and a fixed observation point is as follows: Figure 2 As shown. The functional relationship between the partition nodes and the observation points is defined as follows:

[0037]

[0038] Among them, g i,j Let P represent the observation point located at position (i,j) in the observation point grid, with coordinates (ξ,η,ζ). Let P represent the observation point located at (x,y,z) in the partition space, with coordinates (x,y,z). Let r represent the distance from partition node P to observation point g. i,j The distance.

[0039] In a preferred embodiment of the present invention, in step 2, there is an equivalent relationship:

[0040]

[0041] Figure 2 In the text, a and b represent g respectively. i,j The distance to point P in the x and y directions.

[0042] At the same time, an identity relationship also exists:

[0043] f(g i,j ,P1)+f(g i,j ,P2)+f(g i,j ,P3)+f(gi,j ,P4)=0 (3).

[0044] When a = b, equidistant points will reach the diagonal of the square centered at the observation point, such as... Figure 3 As shown, at this point, formula (2) simplifies to:

[0045] f(g i,j ,Q2)=f(g i,j ,Q4) (4)

[0046] Then formula (3) becomes:

[0047] f(g i,j ,Q1)+f(g i,j ,Q2)+f(g i,j ,Q3)+f(g i,j ,Q4)=0 (5)

[0048] In this embodiment of the invention, the calculation of the function between the node and the observation point using formulas (2), (3) and (4) can save more than half of the calculation.

[0049] In a preferred embodiment of the present invention, in step 3, the functions of the nodes and the observation points are combined into a kernel function from the unit cell to the observation point, and the combination formula is as follows:

[0050]

[0051] Where G represents the gravitational constant, and A g Represents the kernel function matrix, with corner coordinates as follows: Figure 4 As shown.

[0052] Using formulas (1) to (5) to perform forward modeling of the kernel function can significantly improve the forward modeling speed of the kernel function, thereby improving the inversion efficiency. At the same time, since this invention only accelerates the forward modeling of the kernel function, it can also be used to accelerate gravity-related joint inversions.

[0053] In practical calculations, under the same partitioning principle, not only is there no loss of inversion accuracy and resolution, but the forward modeling speed of the kernel function is also effectively improved. This method reduces computational load and improves computational efficiency by reducing redundant calculations and simplifying complex calculations. Model experiments show that on a computer with a 3.60GHz CPU and 32.0GB of memory, the forward modeling time for a 50×50×50 kernel function using MATLAB is approximately 33 seconds, representing a speed improvement of about 9.95 times. Furthermore, the inversion results are completely consistent with those obtained using traditional methods. This demonstrates that while achieving rapid inversion, inversion accuracy and resolution are also maintained.

[0054] Using this method to perform joint gravity and magnetic inversion in the Baiyinnuoer region, the inversion speed was effectively improved, and the calculation time of the gravity kernel matrix was compressed to about 21 seconds, with the overall inversion speed improved by more than 6 times.

[0055] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A fast inversion method based on the principles of concurrency and equidistant equivalence, characterized in that, Includes the following steps: Step 1: Starting from the bottom interface of the partition space, the underground area is partitioned using cuboids of equal length in the x and y directions. The distribution of the partition grid is consistent with the topographic relief, and the observation points correspond one-to-one with the partition units. Step 2: Calculate the relationship function between the nodes of the underground subdivision grid and the surface observation points. Subdivision nodes that are equidistant from the observation points on the same horizontal layer have equivalent relationships. Based on the node positions, the calculation process of the function is replaced by the equivalent relationship, thereby shortening the time to obtain the relationship function matrix between the subdivision nodes and the observation grid. Step 3: Combine the subdivided nodes according to the distribution of underground units to obtain the kernel function matrix. Finally, use the conjugate gradient method to invert the density distribution of the inverted area. In step 1, for nodes at the same horizontal level and a fixed observation point, the functional relationship between the partitioning nodes and the observation point is defined as follows: （1） in, The representative is located in the observation point grid. The location of the observation point, its coordinates are P represents the region located in the partition space. The observation point has the following coordinates: r represents the distance from the partition node P to the observation point. The distance; In step 2, there exists an equivalent relationship: （2） At the same time, an identity relationship also exists: （3） When a=b, equidistant points will reach the diagonal of the square centered at the observation point. At this time, formula (2) simplifies to: （4） Then formula (3) becomes: （5）。 2. The fast inversion method based on the principles of co-location and equidistant equivalence as described in claim 1, characterized in that, In step 3, the functions of the nodes and the observation points are combined into a kernel function from the element to the observation point, and the combination formula is as follows: （6） Where G represents the gravitational constant, Represents the kernel function matrix.

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