CN-122017946-A - Method and system for calculating seismic deformation and stress distribution based on green function

CN122017946ACN 122017946 ACN122017946 ACN 122017946ACN-122017946-A

Abstract

The invention belongs to the field of calculation of earthquake and stress distribution, and particularly relates to a calculation method and a system of earthquake deformation and stress distribution based on a green function; the method comprises the steps of obtaining a triangular grid of a fault and points to be detected, constructing an earth fixed coordinate system, a triangular dislocation coordinate system and an angular dislocation coordinate system based on the triangular grid of the fault, determining a transformation matrix to obtain the coordinate system, calculating the inner angles of three vertexes of the triangular grid in the coordinate system and corresponding complementary angles, selecting equivalent configuration based on the complementary angles, calculating the barycentric coordinates of orthogonal projection of the points to be detected on a triangular dislocation plane, selecting configuration based on the partition inequality of the barycentric coordinates, calculating to obtain Burgers function according to the configuration by using a solid angle formula, superposing incomplete displacement contributions of all angular dislocations to obtain a complete displacement field containing slip continuity correction, and calculating a stress field based on the complete displacement field or a green function through strain. The performance of seismic deformation and stress distribution calculation is remarkably improved.

Inventors

ZHOU LIYE
WANG LEI
TANG RONGJIANG
GAN LU
LIANG SHASHA
LI HAO
LI XIAOYUE

Assignees

地球脉动(宁波)科技有限公司
宁波东方理工产业技术研究有限公司

Dates

Publication Date: 20260512
Application Date: 20260123

Claims (10)

1. A method for computing seismic deformation and stress distribution based on green's function, comprising: Acquiring a triangular grid of a fault and points to be detected; Constructing an earth fixed coordinate system, a triangular dislocation coordinate system and an angular dislocation coordinate system based on a triangular grid of the fault, and determining transformation matrixes among the earth fixed coordinate system, the triangular dislocation coordinate system and the angular dislocation coordinate system to obtain a coordinate system; Calculating the internal angles of three vertexes of a triangular mesh in a coordinate system and corresponding supplementary angles, selecting equivalent configuration based on the supplementary angles, calculating the barycenter coordinates of orthogonal projection of the points to be measured on a triangular dislocation plane, and selecting configuration based on the partition inequality of the barycenter coordinates; according to the selected configuration, calculating to obtain a Burgers function by combining a solid angle formula, and superposing incomplete displacement contribution of each angle dislocation to obtain a complete displacement field containing slip continuity correction; the stress field is calculated based on the complete displacement field or by the green function of the strain.
2. The method for calculating the seismic deformation and stress distribution based on the green's function according to claim 1, wherein the fault-based triangular mesh is used for constructing an earth fixed coordinate system, a triangular dislocation coordinate system and an angular dislocation coordinate system, and determining transformation matrices among the earth fixed coordinate system, the triangular dislocation coordinate system and the angular dislocation coordinate system to obtain the coordinate system, and specifically comprises the following steps: Constructing an earth fixed coordinate system by taking the east, north and upper X, Y, Z axes; taking the second vertex of the triangular grid of the fault as an origin, wherein an x-axis is perpendicular to a triangular dislocation plane, a y-axis is along the trend direction, and a z-axis is along the inclination direction to construct a triangular dislocation coordinate system; The method comprises the steps of taking the coordinates of a unit normal vector, a trend vector and an inclination angle vector of a triangular grid of a fault in an earth fixed coordinate system as a column of a transformation matrix, and combining the translation matrix to determine the transformation matrix from the triangular dislocation coordinate system to the earth fixed coordinate system; based on the triangle dislocation coordinate system, constructing an angle dislocation coordinate system, and determining a transformation matrix from the angle dislocation coordinate system to the triangle dislocation coordinate system.
3. The method for computing the seismic deformation and stress distribution based on the green's function according to claim 1, wherein the computing the internal angles of three vertices of the triangular mesh in the coordinate system and the corresponding complementary angles, selecting the equivalent configuration based on the complementary angles, computing the barycentric coordinates of the orthogonal projection of the points to be measured on the triangular dislocation plane, selecting the configuration based on the partition inequality of the barycentric coordinates, comprises: calculating the internal angles of three vertexes of the triangular mesh: , , The supplementary angle is ; Taking a supplementary angle as an angular dislocation input, adopting two equivalent angular dislocation configurations, and calculating the barycenter coordinates of the orthographic projection of the point to be measured on the triangular dislocation plane; Selecting a configuration based on the partition inequality of the barycentric coordinates; Wherein, the 、 And Representing the interior angles of the triangle at vertex 1, vertex 2, vertex 3, respectively; Representing from the vertex Pointing to a vertex Is used for the direction vector of the unit of (a), 。
4. A method of computing a green's function based seismic deformation and stress distribution according to claim 3, wherein the barycentric coordinates are computed using the formula: In the formula, An abscissa representing a receiving point; Representing a first triangle element abscissa; representing a second triangle element abscissa; representing a third triangle element abscissa; representing the ordinate of the first triangle unit; Representing the ordinate of the receiving point; representing the ordinate of the second triangle unit; representing the ordinate of the third triangle unit; Representing a first barycentric coordinate; The second center of gravity coordinate is represented as, Representing the third center coordinates.
5. The method for computing the seismic deformation and stress distribution based on the green's function according to claim 1, wherein the superposition of incomplete displacement contributions of angular dislocations, obtaining a complete displacement field containing a correction of the slip continuity, is: Wherein, the Is a Burgers function; Components of the complete displacement field in x, y and z directions; 、 The vector components are the Bergers vector components in the x, y and z directions; Is the first Incomplete displacement contributions of the individual angular dislocations in the x-direction; Is the first Incomplete displacement contributions of the individual angular dislocations in the y-direction; Is the first Incomplete displacement of individual angular dislocations in the z direction contributes.
6. A method of computing a stress distribution and a seismic deformation based on a green's function according to claim 1, wherein the stress field is computed based on the complete displacement field or by the green's function of strain, in particular: The strain tensor is calculated from the complete displacement field based on the source of the triangular dislocation: calculating the stress field using Hooke's law: Wherein, the Is strain tensor, subscript And Representing the coordinate direction; Is the displacement vector in A component of direction; representation pair seat mark Is a partial derivative of (2); Is the displacement vector in A component of direction; representation pair seat mark Is a partial derivative of (2); Is the stress tensor; Is the lame constant; in order to indicate the function, Is the volume strain term.
7. A method of computing a seismic deformation and stress distribution based on a green's function according to claim 1, wherein the deformation and stress distribution produced by the fault at any point in space is a linear superposition of the results of all discrete unit computations.
8. The method for calculating the seismic deformation and stress distribution based on the green's function according to claim 1, wherein when the incomplete displacement contributions of the angular dislocation are superimposed, the angle between the angular dislocation and the z-axis is determined, and when the angle is smaller than 1e-2 radian, the angular dislocation component and the stress component are directly set to 0.
9. A green's function based computing system for seismic deformation and stress distribution, comprising: the acquisition unit is used for acquiring the triangular grid of the fault and the points to be detected; the transformation unit is used for constructing an earth fixed coordinate system, a triangular dislocation coordinate system and an angular dislocation coordinate system based on the triangular grid of the fault, and determining transformation matrixes among the earth fixed coordinate system, the triangular dislocation coordinate system and the angular dislocation coordinate system to obtain a coordinate system; The first calculation unit is used for calculating the internal angles of three vertexes of the triangular mesh in the coordinate system and corresponding supplementary angles, selecting equivalent configuration based on the supplementary angles, calculating the barycenter coordinates of orthogonal projection of the to-be-measured point on the triangular dislocation plane, and selecting configuration based on the partition inequality of the barycenter coordinates; The second calculation unit is used for obtaining a Burgers function by combining calculation using a solid angle formula according to the selected configuration, and superposing incomplete displacement contribution of each angle dislocation to obtain a complete displacement field containing slip continuity correction; and a third calculation unit that calculates a stress field based on the complete displacement field or by a green function of the strain.
10. An electronic device comprising a processor and a memory, the processor being configured to execute a computer program stored in the memory to implement the steps of the green function-based method of computing the seismic deformation and stress distribution as claimed in any one of claims 1 to 8.

Description

Method and system for calculating seismic deformation and stress distribution based on green function Technical Field The invention belongs to the field of calculation of earthquake and stress distribution, and particularly relates to a calculation method and a calculation system of earthquake deformation and stress distribution based on a green function. Background The calculation of seismic deformation and stress distribution is an important research content in the fields of seismology, geophysics and engineering geology for evaluating seismic risk, predicting ground movement, analyzing volcanic activity precursors and guiding earthquake-resistant design and disaster early warning. The traditional method is mostly based on elastic medium theory, and displacement, stress and deformation fields caused by a seismic source are simulated through Green's function. The green function is widely applied to integral solution of point source dislocation as a core tool for elastic wave propagation and deformation calculation so as to simulate response of a complex geological structure. For example, based on the green's function method proposed in Steketee (1958), a point source bit error solution for a half-space model was developed, which has become a standard framework for seismic simulation. Since the 50 s of the 20 th century, the method has been widely applied to near-field and far-field seismic simulation through theoretical perfection and numerical optimization, and plays a key role in actual seismic risk assessment. In the prior art, a common calculation method based on the green function comprises (1) an empirical green function method for simulating strong ground movement, correcting an amplitude spectrum of a target event by taking a small earthquake event as the empirical green function, wherein the small earthquake is strictly selected (such as similar in magnitude and similar in position), the small earthquake is susceptible to path effect and source mechanism difference in a complex medium to cause precision reduction, (2) a numerical green function method, combined with a spectral element method or a finite difference method, is used for constructing a green function library in a three-dimensional lamellar earth model, is used for inversion of a seismic source breaking process or calculation of a Centroid Moment Tensor (CMT), is applied to an Australian continental model, can process earthquakes with depth of 50km, but involves a large number of numerical integration and series summation, has low calculation efficiency, is particularly complex in a dead weight compressible sphere model, and has large resource consumption, and (3) a method for calculating stress reduction based on Lg wave, and correcting the path effect by a broadband attenuation model to observe and theory spectrum to estimate stress distribution, the method shows advantages in areas such as a green plateau, but has large quality sensitivity, is used for real-time processing, and is difficult to realize the realization of correlation and noise monitoring by using a passive source monitoring technology, such as a high-time-dependent disturbance environment correlation and high-noise ratio. Furthermore, in the framework of dislocation theory, green's functions are often used for simulations with limited sources of dislocations, such as Rectangular Dislocation (RD) and Triangular Dislocation (TD) models. The rectangular bit misinterpretation proposed by Okada (1992) calculates displacement and stress field in half space, has been widely applied to earthquake and volcanic deformation modeling, but is limited by rectangular geometry, and cannot flexibly simulate curved surfaces or complex faults. In contrast, triangular dislocation models provide greater geometric flexibility by approximating arbitrary surfaces through triangular meshes. Early TD solutions solve for displacements and stresses in full space based on angular dislocation superposition of Yoffe (1960), but suffer from pseudo-singularities (artefact singularities) and numerical instability along the TD edge extension, leading to erroneous results when the calculated points are close to these lines. Subsequent improvements include Jeyakumaran et al (1992) and Meade (2007) half-space TD solutions that approximately eliminate pseudo-singularities by numerical integration and taylor series expansion, but output dependent scale and computational inefficiency. Nikkhoo and Walter (2015) propose a fully analyzed TD solution that avoids pseudo-singularities and numerical instabilities in the full and half spaces, ensuring that the computation is independent of dislocation size, position and slip vector by two equivalent angular dislocation configurations and centroid coordinate partitioning strategies. The method improves Burgers function calculation, is suitable for multi-scale application, and still needs to be further optimized to process complex medium response in a real-time emerge