A method for constructing a generalized non-fully closed fault model

Abstract

The application discloses a kind of generalized non-complete closure fault model construction method, belong to geophysics, earthquake engineering and tectonic geology field.This method will be the area below fault closure depth equally divided into several small sections, each small section is provided with position random small sliding section, sliding section and closure section are alternately distributed, and by regulating sliding section and closure section proportion and distribution mode, the non-complete closure characteristics of fault is accurately simulated.The model constructed is suitable for describing the diverse deformation process of surface, and can adjust the number of segmentation and sliding section distribution according to demand, to adapt to different types and state of fault.The method is based on elastic theory and superposition principle, not only improves the accuracy of fault surface deformation simulation, but also provides theoretical basis and technical support for research and application in the field of earthquake engineering, surface deformation prediction and geological disaster prevention.

Description

Technical Field

[0001] This invention belongs to the fields of geophysics, earthquake engineering and structural geology, and more specifically relates to a generalized method for constructing a non-completely locked fault model. Background Technology

[0002] The degree of locking reflects the extent of displacement deficit in the seismogenic zone of a fault and is an important parameter for studying the seismic hazard of a fault. Based on negative dislocation theory and the superposition principle, the fault plane is divided into multiple small "fault slices," and the degree of locking on each small "fault slice" is inverted, thereby estimating the degree of displacement deficit on the entire fault. The degree of locking on the fault plane during the inter-seismic period is inverted using an inversion procedure based on the Okada fault model. However, research on the physical mechanisms of locking seems to be scarce. For example, when the degree of locking is less than 1, it indicates that the fault is not completely locked, meaning that "locking" and "slip" coexist on the fault plane. How can we explain this phenomenon of both sliding and locking on the fault plane? In earthquake research, fault models involved in fault deformation analysis, such as strike-slip, dip-slip, and the Okada fault model, involve faults that are either completely locked or completely slipping. There is no intermediate state where they are both locked and slipping. Furthermore, the degree of locking is derived from inversion based on fault models without such intermediate states. Therefore, is there a correlation between partially locked faults and these fault models? These questions arise from the lack of physical models for partially locked faults. Previous models of partially locked faults were limited to vertical strike-slip faults with a dip angle of 90°.

[0003] The paper "Coupling fraction model to interpret the motion of non-fully coupled strike-slip faults" (doi: 10.3389 / feart.2023.1059300) proposes a fault model that can describe incompletely locked faults. This paper creatively divides the fault into n equal parts, then sets a slip segment and a locking segment in each part, and then approaches n close to infinity, thus obtaining an ideal fault model that can well explain the "degree of locking".

[0004] The parameter "degree of closure" was first proposed by foreign scholar McCaffrey in 2002 and has since been widely used. However, no suitable fault model has been found to explain this parameter.

[0005] The fault model described in this paper is only applicable to vertical strike-slip faults with an infinitely long half-space (dip angle of 90°), and the conclusions are not applicable to general faults, such as dip-slip faults or faults with dip angles. Although this technique represents a breakthrough, the conclusions are not applicable to general fault models. Summary of the Invention

[0006] Existing technologies are only applicable to vertical strike-slip faults. This invention goes a step further, proposing a partially locked segment model that, using abstract mathematical forms, can represent general faults, such as dip-angled reverse faults and dip-angled normal faults. This generalizes existing models, which are limited to vertical strike-slip faults, greatly expanding the applicability of the partially locked segment model.

[0007] To achieve the above objectives, the present invention employs the following technical solution: the method comprising: The fault segment below the blocking depth is divided into several smaller segments, with each smaller segment having the same length, and each smaller segment containing a small sliding segment with a random position. The length of the small sliding segment is less than the length of the small fault segment in which it is located. The small sliding segments are distributed uniformly or unevenly in each small fault segment. The locked segment and the sliding segment are arranged alternately in different small segments. The fault that is not completely locked consists of multiple sliding segments and locked segments. By controlling the distribution and length ratio of each sliding segment and locking segment, the proportion of the sum of the lengths of the sliding segments to the total length of the fault segments is formed. Macroscopically, this is manifested as small and numerous sliding segments, with locking segments and sliding segments distributed at intervals, thus forming a non-completely locked fault model with generalized properties.

[0008] In one approach, the number of equal divisions of the fault segment is set to different numbers according to the modeling requirements. When the number of equal divisions increases, the length of each small sliding segment is further reduced, the distribution of the sliding segments becomes more continuous, the model accuracy increases with the increase of the number of segments, and the final model result is proportional to the total length of the overall sliding segment.

[0009] In one approach, the sliding and locking segments are distributed equidistantly, randomly, or otherwise as needed along the fault segment to meet the physical or observational characteristics of the specific fault, which is beneficial for describing and fitting the deformation behavior of the fault in different regions.

[0010] In one approach, the specific length and distribution of the small slip segment within each small fault segment are adjusted according to actual observation or physical simulation requirements, thereby achieving a precise characterization of the degree of fault locking and adapting to different fault types, including strike-slip faults and dip-slip faults.

[0011] In one scheme, the model uses macroscopic statistics to sum the lengths of small slip segments and the lengths of locked segments, and defines slip rate and degree of locking accordingly. Slip rate is the ratio of the total length of slip segments to the total length of fault segments, and degree of locking is the ratio of the total length of locked segments to the total length of fault segments. The sum of slip rate and degree of locking is one.

[0012] In one scheme, the model satisfies the superposition principle under the elasticity theory. The surface deformation generated by different small slip segments can be calculated in a linear superposition manner. When the number of segments is large enough, the simulation results can accurately approximate the overall fault surface deformation distribution under the slip rate, which is beneficial to improving the modeling and fitting accuracy between faults and surface deformation.

[0013] In one scheme, the model can adapt to different geological environments and slip characteristics by freely setting the distribution and length ratio of the sliding segment and the locked segment, and can simulate the surface deformation distribution of various fault stages such as inter-seismic deformation, co-seismic deformation and relative block movement, so as to achieve accurate characterization of the entire fault movement process.

[0014] Beneficial effects of this invention: Based on the dislocation model and the superposition principle, this invention proposes a generalized fault model for incompletely locked faults. This fault model is universal and is not limited to specific fault models (strike-slip, dip-slip, or other fault models with dip angles). Instead, it is presented in an abstract form, so that the conclusions can satisfy any fault model.

[0015] This invention extends existing models, which are only applicable to vertical strike-slip faults, to general faults. In locked-down inversion, faults are generally not vertical strike-slip, but rather exhibit strike-slip, dip-slip, or dip angles. The fault model in this invention is therefore applicable, as its incompletely locked fault model is a generalized fault model. Attached Figure Description

[0016] Figure 1 This is a fault model in the general sense; Figure 2 Three fault models derived from finite-length faults; Figure 3 This is a generalized incompletely locked fault model; Figure 4 This is the "locking degree" parameter for a generalized fault model. Detailed Implementation

[0017] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Typical embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0018] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. To facilitate understanding, the invention will now be described more fully with reference to the accompanying drawings. Typical embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to make the disclosure of the invention more thorough and complete.

[0019] Figure 1 This is a schematic diagram of an elastic fault model. Figure 1 a and Figure 1 b is equivalent (for convenience, the following text will use b). Figure 1 (represented as a front view in b). The physical quantities controlling surface distribution are usually different under different elastic fault models. For example, in vertical strike-slip or dip-slip fault models, the physical quantity controlling surface distribution is the slip rate. and locking depth If the effect of tilt angle is considered, the control parameter is: , and tilt angle If the length and width of the fault plane are also taken into account, then the control parameters are: , , Fault length and fault width Furthermore, the lateral deformation of the medium can be considered according to actual needs... The more control parameters there are, the more complex the fault model becomes. For any fault model, if only the surface deformation distribution and... The relationship between them, that is, apart from When all other parameters are constants, it can be used Indicates the distribution of surface deformation, where Indicates the distance from the fault. It is the locking depth ( Figure 1 For specific elastic fault models, There are corresponding specific expressions, such as the vertical strike-slip fault model in Technique 1. ,in It is a constant.

[0020] Abstract representation of deformation distribution in faults of finite segment length: For ease of discussion, when a fault segment is completely locked / coupled, it is called a locked segment; when a fault segment is completely slipped / creeped, it is called a slipped segment; the vertical depth of a fault segment is called the segment length. Indicates a such Figure 2The surface deformation distribution caused by the fault in the finite-length slip segment of fault a, and the locking depth of the slip segment of this fault is The length of the section is ( Figure 2 a). The resulting surface deformation distribution is as follows: (1) Equation (1) can be directly understood from the perspective of the superposition principle under the strike-slip fault model.

[0021] Abstract representation of inter-fault and co-seismic deformation distribution and relative block motion: Equation (1) represents the surface deformation caused by the sliding of a fault plane of finite length. By controlling the position and depth of the fault plane, the surface deformation formulas for inter-fault deformation, co-seismic deformation and relative block motion can be obtained.

[0022] when At infinity, The locking depth is Inter-seismic deformation formula ( Figure 2 b): (2) when When it approaches 0, Then it becomes the coseismic deformation formula ( Figure 2 c): (3) when At the same time, tending to 0 At infinite depth, the formula for the relative motion of the block can be obtained ( Figure 2 d): (4) Equations (2, 3, and 4) are formulas for the deformation distribution of faults during inter-seismic, co-seismic, and relative fault motions, expressed in an abstract form. While the expressions for specific fault models may differ significantly, they share a unified form under this abstract representation. Equations (2, 3, and 4) will be used in the following text.

[0023] The construction of a generalized incompletely locked fault model, utilizing Constructing a partially locked fault model :like Figure 3 Locking depth The following paragraphs are of length The fault segments are divided into equal parts. If the length of each small fault segment is [missing information], then the length of each small fault segment is [missing information]. Small slip segments are randomly placed at locations within each small fault segment, with a length of [missing information]. Due to the superposition principle, the deformation of the Earth's surface... It is the sum of the surface deformation produced by each small sliding segment: in , , This represents the vertical distance from the upper edge of the small sliding segment to the ground surface. , .when At this time, the fault model is a non-completely locked fault model. : (5) The characteristics of a partially locked fault model are numerous, small, and spaced-apart slip segments. Mathematically, because... Resulting in a length of Slip segments are present throughout the fault segment but are discontinuous, indicating that, macroscopically, the slip segments are small and numerous, and are interspersed with the locked segments, with a segment length of [missing information]. On the fault segment ( Figure 3 It can be proven that when hour, The limit exists.

[0024] (6) Equation (6) explains when When large enough, the results of the incompletely locked fault model and The results are consistent, differing only by a scaling factor. Meanwhile, the numerical simulation results also proved the correctness of the conclusion: the deformation formulas for strike-slip, dip-slip, or Okada fault models are different, but when When the values ​​are sufficiently large, their summation results are in high agreement with equation (6), with very small relative error. This shows that equation (6) generally holds true for most fault models (elastic models that conform to the superposition principle), and and They are highly similar in shape, differing only by a ratio factor. ,say The slip ratio is the ratio of the sum of the lengths of the slip segments to the total length of the slip segments in the incompletely locked fault model.

[0025] The relationship between the generalized incompletely locked segment model and the parameter "locking degree", where the locking degree is defined as: , in It refers to the degree of locking. Indicates the free slip rate of the fault. This indicates the slip rate of the slip portion of a non-fully locked fault.

[0026] First, we study a simple fault model that is not completely closed, such as... Figure 4 The vertical distance downward from the ground surface is The degree of closure of the fault plane is , The following fault plane slides freely. Utilizing the principle of negative dislocation, the inter-seismic deformation of a partially locked fault equals the relative motion of the blocks minus... The coseismic deformation is times greater than that of a fault. From equations (2, 3, 4, and 7), the inter-seismic deformation caused by a non-completely locked fault can be obtained: (8) For the locking depth is The inter-seismic deformation, Equation (8) shows the vertical distance downward from the Earth's surface as The degree of locking is Deformation caused by faults and The resulting deformations are exactly the same. The sum of the degree of closure and the slip ratio in the incompletely closure fault model is equal to 1, indicating that the degree of closure is the ratio of the sum of the lengths of the segments shorter than the closure segments to the total length of the segments in the incompletely closure fault model. The incompletely closure fault model can well explain the physical meaning of the degree of closure.

[0027] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0028] It should be understood that the above detailed description of the technical solutions of the present invention with reference to preferred embodiments is illustrative and not restrictive. Those skilled in the art can modify the technical solutions described in the embodiments or make equivalent substitutions for some of the technical features based on reading this specification; however, these modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a generalized incompletely locked fault model, characterized in that: The method includes: The fault segment below the blocking depth is divided into several smaller segments, with each smaller segment having the same length, and each smaller segment containing a small sliding segment with a random position. The length of the small sliding segment is less than the length of the small fault segment in which it is located. The small sliding segments are distributed uniformly or unevenly in each small fault segment. The locked segment and the sliding segment are arranged alternately in different small segments. The fault that is not completely locked consists of multiple sliding segments and locked segments. By controlling the distribution and length ratio of each sliding segment and locking segment, the proportion of the sum of the lengths of the sliding segments to the total length of the fault segments is formed. Macroscopically, this is manifested as small and numerous sliding segments, with locking segments and sliding segments distributed at intervals, thus forming a non-completely locked fault model with generalized properties.

2. The method for constructing a generalized incompletely locked fault model according to claim 1, characterized in that, The number of equal divisions of the fault segment is set to different numbers according to the modeling requirements. When the number of equal divisions increases, the length of each small sliding segment is further reduced, the distribution of sliding segments becomes more continuous, the model accuracy increases with the increase of the number of segments, and the final model result is proportional to the total length of the overall sliding segment.

3. The method for constructing a generalized incompletely locked fault model according to claim 1, characterized in that, The sliding and locking segments are distributed at equal intervals or randomly along the fault segments to meet the physical or observational characteristics of specific faults, which is beneficial for describing and fitting the deformation behavior of faults in different regions.

4. The method for constructing a generalized incompletely locked fault model according to claim 1, characterized in that, The specific length and distribution of the small slip segments within each small fault segment are adjusted according to actual observation or physical simulation requirements, so as to accurately characterize the degree of fault locking and adapt to different fault types, including strike-slip faults and dip-slip faults.

5. The method for constructing a generalized incompletely locked fault model according to claim 1, characterized in that, The model uses macroscopic statistics to sum the lengths of small slip segments and the lengths of locked segments, and defines slip rate and degree of locking based on this. Slip rate is the ratio of the total length of slip segments to the total length of fault segments, and degree of locking is the ratio of the total length of locked segments to the total length of fault segments. The sum of slip rate and degree of locking is one.

6. The method for constructing a generalized incompletely locked fault model according to claim 1, characterized in that, The model satisfies the superposition principle under the elasticity theory. The surface deformation generated by different small slip segments can be calculated in a linear superposition manner. When the number of segments is large enough, the simulation results can accurately approximate the overall fault surface deformation distribution under the slip rate, which is beneficial to improving the modeling and fitting accuracy between faults and surface deformation.

7. The method for constructing a generalized incompletely locked fault model according to claim 1, characterized in that, The model allows for the free setting of the distribution and length ratio of the sliding and locked segments, adapting to different geological environments and slip characteristics. It can also simulate the surface deformation distribution of various fault stages, including inter-seismic deformation, co-seismic deformation, and relative block movement, thereby achieving accurate characterization of the entire fault movement process.

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