Optimal earth radial parameter determination method, device, equipment and medium

Abstract

The invention provides an optimal earth radial parameter determination method and device, equipment and a medium, and the method comprises the steps: obtaining the original observation data of a plurality of seabed stations in a seabed earthquake epicentral region; based on the original observation data of each seabed station, determining the coordinate position resolving data of the seabed station and the observation value of the displacement time sequence; constructing a Burgers viscoelastic body earth model, and determining a reset error Love number and a complex green function based on the Burgers viscoelastic body earth model; determining a calculated value of the displacement time sequence according to the observed value of the displacement time sequence based on the wrong reset Love number and a complex green function; and determining an optimal transient viscosity parameter and an optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time sequence, and jointly forming the optimal earth radial parameter by the transient viscosity parameter and the optimal steady-state viscosity parameter. By adopting the scheme, the radial parameters of the earth can be accurately determined, and correct understanding and accurate prediction of the earthquake process are ensured.

Description

Technical Field

[0001] The present invention relates to the field of GNSS marine application technology, and in particular to a method, device, equipment and medium for determining an optimal earth radial parameter. Background Art

[0002] At present, the research on the viscoelastic structure of the earth model is mainly focused on the radial stratification of land. This is because land areas usually have denser observation networks that can provide data with high temporal sampling rates, which are essential for constraining the inversion process. GNSS stations on land are widely distributed and can provide continuous, high-precision location information, allowing researchers to more accurately monitor the movement and deformation of the crust. This rich data resource provides a solid foundation for the study of earth models in land areas, allowing the radial stratification model of land to better reflect the viscoelastic properties of the crust.

[0003] However, when the research perspective is turned to the seabed, the situation is quite different. The complexity of the seabed environment far exceeds that of the land. Its structure is not only layered in the vertical direction, but also has significant differences in the horizontal direction. This lateral difference is mainly due to factors such as the diversity of seabed topography, changes in the thickness of the lithosphere, and the interaction between different plates. For example, at the plate boundaries in the subduction zone, the crustal structure and rock properties change dramatically, resulting in obvious spatial inhomogeneity in the viscoelastic properties. In addition, submarine volcanic activity, sediment distribution, and marine geological structures will also have an important impact on the seabed structure, making the viscoelastic properties of the seabed more complex and diverse.

[0004] Due to the existence of these complex factors, the viscoelastic properties of submarine structures can no longer be accurately described by using only a simple radial layering model. The traditional radial layering method ignores the structural changes in the horizontal direction and cannot fully consider the influence of submarine topography and geological structure on viscoelastic properties. Therefore, if this simplified model is continued to be used in submarine earthquake research, it will lead to deviations in the simulation and prediction of earthquake processes. Specifically, key processes such as the source mechanism of earthquakes, the propagation path of seismic waves, and the crustal deformation caused by earthquakes may not be correctly explained and predicted due to inaccurate models. The radial parameters of the earth, as the core component of the earth model, are of great significance for the study of earthquake processes. These parameters not only affect the source mechanism of earthquakes and the propagation characteristics of seismic waves, but are also closely related to the crustal deformation and stress distribution caused by earthquakes. If the radial parameters of the earth cannot be accurately determined, it will directly affect the understanding and prediction of earthquake processes. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a method, device, equipment and medium for determining the optimal radial parameters of the earth, so as to accurately determine the radial parameters of the earth and ensure the correct understanding and accurate prediction of the earthquake process.

[0006] In a first aspect, an embodiment of the present application provides a method for determining an optimal earth radial parameter, the method comprising: Obtain the original observation data of several seafloor stations in the epicenter area of ​​seafloor earthquakes; Based on the original observation data of each seafloor station, the coordinate position solution data and the observation value of the displacement time series of the seafloor station are determined; Constructing a Burgers viscoelastic earth model, and determining a reset Love number and a complex Green's function based on the Burgers viscoelastic earth model, wherein the Burgers viscoelastic earth model includes a transient viscosity parameter and a steady-state viscosity parameter, and the transient viscosity parameter and the steady-state viscosity parameter together constitute the radial parameter of the earth; Based on the reset error Love number and the complex Green's function, a calculated value of the displacement time series is determined according to the observed value of the displacement time series; Based on the observed value and calculated value of the displacement time series, the optimal transient viscosity parameter and the optimal steady-state viscosity parameter are determined, and the transient viscosity parameter and the optimal steady-state viscosity parameter are combined to form the optimal earth radial parameter.

[0007] Optionally, the obtaining of original observation data of several seafloor stations in the epicenter area of ​​a seafloor earthquake includes: Determine the actual seafloor station information of the study area based on the location information of the study area; The information of the seabed stations in the epicenter area is obtained by screening the actual seabed station information in the study area; The original observation data of each seafloor station is extracted from the seafloor station information in the epicenter area, wherein the original observation data includes the GNSS data, attitude data, and acoustic ranging data of each seafloor station in the epicenter area of ​​the seafloor earthquake.

[0008] Optionally, the determining of the seabed station coordinate position solution data and the observation value of the displacement time series based on the original observation data of each seabed station includes: According to the original observation data of each seabed station, the coordinate position of the seabed station is solved by using the sound speed time-space variation error compensation positioning model to obtain the coordinate position solution data of the seabed station; The displacement time series of each seafloor station is screened and extracted according to the coordinate position solution data of the seafloor station to determine the observation value of the displacement time series.

[0009] Optionally, determining the reset Love number and the complex Green's function based on the Burgers viscoelastic earth model includes: Introducing a complex variable parameter s into the stress-strain constitutive relation of the Burgers viscoelastic earth model, and performing Laplace transformation to obtain the constitutive relation in the complex domain; The target equation group in the complex domain is solved according to the constitutive relation in the complex domain to obtain the reset error Love number and the complex Green's function.

[0010] Optionally, the target equation group includes: The initial condition function of the center of the sphere, the inner core-outer core boundary condition function, the outer core-mantle boundary condition function, the free boundary condition function of the surface and the earthquake source function.

[0011] Optionally, the determining the calculated value of the displacement time series based on the reset error Love number and the complex Green's function according to the observed value of the displacement time series specifically includes: Using the Riemann-Mellin inversion formula, inversely transforming the reset dislocation Love number and the complex Green's function to obtain the dislocation Love number and the Green's function in the time domain; The dislocation Love number and the Green's function are solved using the coordinate position solution data of the seafloor station to obtain the calculated value of the displacement time series.

[0012] Optionally, determining the optimal transient viscosity parameter and the optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time series includes: Constraining and adjusting the observed values ​​and calculated values ​​of the displacement time series, and determining the optimal calculated value of the displacement time series that minimizes the root mean square error between the observed values ​​and the calculated values ​​of the displacement time series; The transient viscosity parameter and the steady-state viscosity parameter corresponding to the optimal calculated value of the displacement time series in the Burgers viscoelastic earth model are respectively determined as the optimal transient viscosity parameter and the optimal steady-state viscosity parameter.

[0013] In a second aspect, an embodiment of the present application provides a device for determining an optimal earth radial parameter, the device comprising: An observation data acquisition module is used to acquire the original observation data of several seafloor stations in the epicenter area of ​​the seafloor earthquake; A displacement time series observation value determination module is used to determine the seabed station coordinate position solution data and the displacement time series observation value based on the original observation data of each seabed station; A viscoelastic earth model construction module is used to construct a Burgers viscoelastic earth model, and determine a reset Love number and a complex Green's function based on the Burgers viscoelastic earth model, wherein the Burgers viscoelastic earth model includes a transient viscosity parameter and a steady-state viscosity parameter, and the transient viscosity parameter and the steady-state viscosity parameter together constitute the earth radial parameter; A displacement time series calculated value determination module, used to determine the calculated value of the displacement time series according to the observed value of the displacement time series based on the reset error Love number and the complex Green's function; The optimal earth radial parameter determination module is used to determine the optimal transient viscosity parameter and the optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time series, and the transient viscosity parameter and the optimal steady-state viscosity parameter are combined into the optimal earth radial parameter.

[0014] Optionally, the obtaining of original observation data of several seafloor stations in the epicenter area of ​​a seafloor earthquake includes: Determine the actual seafloor station information of the study area based on the location information of the study area; The information of the seabed stations in the epicenter area is obtained by screening the actual seabed station information in the study area; The original observation data of each seafloor station is extracted from the seafloor station information in the epicenter area, wherein the original observation data includes the GNSS data, attitude data, and acoustic ranging data of each seafloor station in the epicenter area of ​​the seafloor earthquake.

[0015] Optionally, the determining of the seabed station coordinate position solution data and the observation value of the displacement time series based on the original observation data of each seabed station includes: According to the original observation data of each seabed station, the coordinate position of the seabed station is solved by using the sound speed time-space variation error compensation positioning model to obtain the coordinate position solution data of the seabed station; The displacement time series of each seafloor station is screened and extracted according to the coordinate position solution data of the seafloor station to determine the observation value of the displacement time series.

[0016] Optionally, determining the reset Love number and the complex Green's function based on the Burgers viscoelastic earth model includes: Introducing a complex variable parameter s into the stress-strain constitutive relation of the Burgers viscoelastic earth model, and performing Laplace transformation to obtain the constitutive relation in the complex domain; The target equation group in the complex domain is solved according to the constitutive relation in the complex domain to obtain the reset error Love number and the complex Green's function.

[0017] Optionally, the target equation group includes: The initial condition function of the center of the sphere, the inner core-outer core boundary condition function, the outer core-mantle boundary condition function, the free boundary condition function of the surface and the earthquake source function.

[0018] Optionally, the determining the calculated value of the displacement time series based on the reset error Love number and the complex Green's function according to the observed value of the displacement time series includes: Using the Riemann-Mellin inversion formula, inversely transforming the reset dislocation Love number and the complex Green's function to obtain the dislocation Love number and the Green's function in the time domain; The dislocation Love number and the Green's function are solved using the coordinate position solution data of the seafloor station to obtain the calculated value of the displacement time series.

[0019] Optionally, determining the optimal transient viscosity parameter and the optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time series includes: Constraining and adjusting the observed values ​​and calculated values ​​of the displacement time series, and determining the optimal calculated value of the displacement time series that minimizes the root mean square error between the observed values ​​and the calculated values ​​of the displacement time series; The transient viscosity parameter and the steady-state viscosity parameter corresponding to the optimal calculated value of the displacement time series in the Burgers viscoelastic earth model are respectively determined as the optimal transient viscosity parameter and the optimal steady-state viscosity parameter.

[0020] In a third aspect, an embodiment of the present application provides a computer device, comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the method for determining the optimal earth radial parameters described in any optional implementation manner of the first aspect are performed.

[0021] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, executes the steps of the method for determining the optimal earth radial parameters described in any optional implementation manner in the first aspect above.

[0022] The technical solution provided by this application includes but is not limited to the following beneficial effects: This application first obtains the original observation data of the seafloor station in the epicenter area of ​​the seafloor earthquake, which can directly supplement the insufficiency of land observation data and provide more comprehensive and accurate earthquake monitoring information. These data include GNSS data, attitude data, and acoustic ranging data, which can reflect the precise position and displacement changes of the seafloor station. By obtaining these data, the source mechanism and seismic process of the seafloor earthquake can be understood more accurately, providing basic data support for subsequent model construction and parameter inversion.

[0023] Then, based on the original observation data of each seabed station, the coordinate position solution data and the observation values ​​of the displacement time series of the seabed station are determined, which can accurately determine the position changes of the seabed station and reflect the displacement changes of the seabed station during the earthquake. These observation values ​​are important input data for subsequent model construction and parameter inversion, and can help to more accurately describe the earthquake process and crustal deformation.

[0024] Then, the Burgers viscoelastic earth model is constructed. Based on the Burgers viscoelastic earth model, the reset Love number and complex Green's function are determined, which can more accurately describe the viscoelastic properties of the seabed structure. The model contains transient viscosity parameters and steady-state viscosity parameters, which can simultaneously consider transient and steady-state deformations during earthquakes. By calculating the reset Love number and complex Green's function, the theoretical solution of the displacement field caused by the earthquake can be obtained. These theoretical solutions provide a basis for the subsequent displacement time series calculation, which can help to more accurately simulate the earthquake process and crustal deformation.

[0025] Next, based on the reset error Love number and complex Green's function, the calculated value of the displacement time series is determined according to the observed value of the displacement time series, which can compare the theoretical solution of the model with the actual observation data to verify the accuracy and reliability of the model. By comparing the observed value and the calculated value, the performance of the model can be evaluated, providing a basis for the subsequent parameter inversion.

[0026] Finally, based on the observed and calculated values ​​of the displacement time series, the optimal transient viscosity parameters and the optimal steady-state viscosity parameters are determined. The transient viscosity parameters and the optimal steady-state viscosity parameters are combined into the optimal earth radial parameters, which can minimize the error between the calculated and observed values ​​of the model and improve the accuracy and reliability of the model. Combining the optimal transient viscosity parameters and the steady-state viscosity parameters into the optimal earth radial parameters can more accurately describe the viscoelastic properties of the submarine structure and provide important parameter support for the study of earthquake processes. These parameters help to more accurately simulate earthquake processes, predict earthquake impacts, and formulate more effective disaster prevention and mitigation measures.

[0027] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0029] Figure 1 A flow chart of a method for determining an optimal earth radial parameter provided by the first embodiment of the present invention is shown; Figure 2 A flow chart of a method for acquiring original observation data provided by Embodiment 1 of the present invention is shown; Figure 3 A schematic diagram showing a partial location of a submarine station provided by the first embodiment of the present invention; Figure 4 A flow chart of a method for determining a displacement time series observation value provided by the first embodiment of the present invention is shown; Figure 5 A flow chart of a viscoelastic earth model construction method provided by the first embodiment of the present invention is shown; Figure 6 A schematic diagram of a viscoelastic earth model provided by the first embodiment of the present invention is shown; Figure 7 A flow chart showing a displacement time series calculation value provided by the first embodiment of the present invention is shown; Figure 8 A flow chart of a method for determining an optimal parameter provided by the first embodiment of the present invention is shown; Fig. 9 A schematic diagram showing the structure of an optimal earth radial parameter determination device provided by the second embodiment of the present invention; Fig.10 A schematic diagram of the structure of a computer device provided in Embodiment 3 of the present invention is shown. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present invention.

[0031] Embodiment 1 To facilitate understanding of this application, Figure 1 The flowchart of a method for determining an optimal earth radial parameter provided by the first embodiment of the present invention is described in detail to explain the first embodiment of the present application.

[0032] See also Figure 1 As shown, Figure 1 A flowchart of a method for determining an optimal earth radial parameter provided by the first embodiment of the present invention is shown, wherein the method comprises steps S101 to S105: S101: Obtain original observation data of several seafloor stations in the epicenter area of ​​a seafloor earthquake.

[0033] Specifically, according to the location information of the study area, the actual seafloor station information is determined, including the coordinate position of the seafloor station, the plate it is located in, and the number of seafloor stations. The seafloor station information in the epicenter area is selected from the actual seafloor station information in the study area, and the GNSS-A (GNSS-Acoustic, Global Navigation Satellite System-Sonar Observation Model) original observation data of each seafloor station is extracted, such as GNSS (Global Navigation Satellite System) data, attitude data, and acoustic ranging data.

[0034] S102: Determine the observed values ​​of the seafloor station coordinate position solution data and displacement time series based on the original observation data of each seafloor station.

[0035] Specifically, based on the original observation data of each seabed station, the coordinate position of the seabed station is solved using the sound speed time-space variation error compensation positioning model. This process can compensate for the change of sound speed under different time and space conditions, thereby improving the positioning accuracy. Through this solution process, the coordinate position solution data of the seabed station can be obtained, and then the displacement time series of each seabed station is screened and extracted based on the coordinate position solution data of the seabed station to determine the observed value of the displacement time series. These observations reflect the displacement changes of the seabed station after the earthquake, and provide important input data for subsequent model construction and parameter inversion.

[0036] S103: constructing a Burgers viscoelastic earth model, and determining a reset Love number and a complex Green's function based on the Burgers viscoelastic earth model, wherein the Burgers viscoelastic earth model includes a transient viscosity parameter and a steady-state viscosity parameter, and the transient viscosity parameter and the steady-state viscosity parameter together constitute an earth radial parameter.

[0037] Specifically, a Burgers viscoelastic earth model is constructed, which combines the Kelvin body and the Maxwell body and can describe the viscoelastic behavior of the earth medium. The model contains transient viscosity parameters and steady-state viscosity parameters. These two parameters together constitute the radial parameters of the earth and are the target of subsequent parameter inversion. Next, the complex variable parameter s is introduced into the stress-strain constitutive relation of the model, and the Laplace transform is performed to obtain the constitutive relation in the complex domain. This process transforms the viscoelastic problem into an equivalent elastic problem in the complex domain, simplifying the calculation process. Finally, according to the constitutive relation in the complex domain, the target equation group in the complex domain is solved to obtain the reset error Love number and complex Green's function. These functions describe the displacement field caused by the earthquake and provide a basis for the subsequent displacement time series calculation.

[0038] S104: Based on the reset error Love number and the complex Green's function, determine the calculated value of the displacement time series according to the observed value of the displacement time series.

[0039] Specifically, the Riemann-Mellin inversion formula is used to inversely transform the reset Love number and complex Green's function to obtain the Love number and Green's function in the time domain. Then, the coordinate position of the seafloor station is used to solve the Love number and Green's function to obtain the calculated values ​​of the displacement time series, which reflect the displacement changes of the seafloor station after the earthquake.

[0040] S105: Determine an optimal transient viscosity parameter and an optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time series, and combine the transient viscosity parameter and the optimal steady-state viscosity parameter into an optimal earth radial parameter.

[0041] Specifically, the least squares principle is used to constrain and adjust the observed and calculated values ​​of the displacement time series, and the optimal calculated value of the displacement time series that minimizes the root mean square error between the observed and calculated values ​​is determined. This process minimizes the difference between the observed and calculated values ​​by adjusting the model parameters. Next, the transient viscosity parameter and the steady-state viscosity parameter corresponding to the optimal calculated value of the displacement time series in the Burgers viscoelastic earth model are determined as the optimal transient viscosity parameter and the optimal steady-state viscosity parameter, respectively. These two optimal parameters together constitute the optimal earth radial parameter, which can accurately describe the viscoelastic properties of the earth medium and provide important parameter support for earthquake research and geophysical modeling.

[0042] In an alternative embodiment, see Figure 2 As shown, Figure 2 A flow chart of a method for acquiring original observation data provided by the first embodiment of the present invention is shown, wherein the method for acquiring original observation data of several seafloor stations in the epicenter area of ​​a seafloor earthquake comprises steps S201 to S203: S201: Determine the actual submarine station information of the study area based on the location information of the study area.

[0043] Specifically, according to the location information of the study area, the information of all the seafloor stations in the area is determined, that is, the actual seafloor station information of the study area, which at least includes: the coordinate location information of the seafloor station, the plate where each seafloor station is located, and the number of seafloor stations. For example, when studying the major earthquake that occurred in a certain area in 2011, the study area is the area where the earthquake occurred, and it is necessary to determine all the seafloor stations in the area and their related information. This information can be obtained by consulting relevant materials, databases or cooperating with research institutions. Determining the actual seafloor station information in the study area is a prerequisite for subsequent steps, ensuring the integrity and accuracy of the data.

[0044] S202: Filtering the actual seabed station information in the study area to obtain the seabed station information in the epicenter area.

[0045] Specifically, according to the actual submarine station information in the study area, the submarine stations located in the epicenter area are screened out. The epicenter area usually refers to a certain range within the epicenter of the earthquake, and this range can be determined based on research needs and the scale of the earthquake. The screened submarine station information in the epicenter area includes at least: the name of the submarine station, the coordinate location information of the submarine station, the plate where each submarine station is located, and the number of submarine stations.

[0046] S203: extracting original observation data of each seafloor station from the seafloor station information in the epicenter area, wherein the original observation data includes GNSS data, attitude data, and acoustic ranging data of each seafloor station in the epicenter area of ​​the seafloor earthquake.

[0047] Specifically, according to the information of the seabed stations in the epicenter area, the original observation data of each seabed station, that is, the GNSS-A data of each seabed station, including GNSS data, attitude data and acoustic ranging data, are extracted. GNSS data is used to determine the position and movement of the seabed station, attitude data is used to describe the attitude changes of the seabed station, and acoustic ranging data is used to measure the distance between the seabed station and the surrounding environment. These original observation data provide the basis for the subsequent coordinate position solution and displacement time series extraction, ensuring the accuracy and reliability of the data. The extracted original observation data needs to be preprocessed, such as data cleaning, noise removal and data correction, to improve the quality and availability of the data.

[0048] For example, see Figure 3 As shown, Figure 3 A schematic diagram of the partial location of a submarine station provided by the first embodiment of the present invention is shown, wherein the original observation data of each submarine station is obtained from the submarine GNSS-A original data of six submarine points in the past ten years (2011.3-2020.6) disclosed by the JCG (the Group of Japan CoastGuard) team. In the figure, the location of each submarine station is marked with north latitude (°N) and east longitude (°E), the five-pointed star indicates the epicenter position, the light arrow indicates the calculated value, the dark arrow indicates the observed value, the displacement rate of the submarine station on the left side of the figure is 3cm / a, and the displacement rate of the submarine station on the right side of the figure is 1.5cm / a. The data for FUKU, MYGI and MYGW stations are from March 28, 2011 to mid-June 2020, with 35-36 sets of data for each station; the data for KAMN and KAMS stations started on April 4, 2011, and ended in mid-June 2020, with 26 and 29 sets of data respectively; the observation time of CHOS station is from April 17, 2011 to late June 2020, with a total of 28 sets of data; the observation period involved in the six stations is from March 28, 2011 to June 30, 2020, during which time a total of 4 earthquakes with a moment magnitude of Mw 7.0 or above occurred.

[0049] In an alternative embodiment, see Figure 4 As shown, Figure 4 A flow chart of a method for determining displacement time series observation values ​​provided in the first embodiment of the present invention is shown, wherein the method for determining the coordinate position solution data of the seafloor station and the observation value of the displacement time series based on the original observation data of each seafloor station comprises steps S401-S402: S401: Based on the original observation data of each seafloor station, the coordinate position of the seafloor station is solved by using the sound speed time-space variation error compensation positioning model to obtain the coordinate position solution data of the seafloor station.

[0050] Specifically, according to the original observation data of each seafloor station, based on the sound ray tracking technology, the sound speed time-space variation error compensation positioning model is used to solve the coordinate position of each seafloor station to obtain the coordinate position solution data of the seafloor station. The sound speed time-space variation error compensation positioning model can compensate for the change of sound speed under different time and space conditions, thereby improving the positioning accuracy. Through this solution process, the coordinate position solution data of the seafloor station can be obtained, which provides a basis for the subsequent displacement time series extraction.

[0051] S402: Screening and extracting the displacement time series of each seafloor station according to the seafloor station coordinate position solution data to determine the observed value of the displacement time series.

[0052] Specifically, the coordinate position solution data of the seafloor stations are collected, which usually include the three-dimensional coordinate information of each seafloor station at different time points. Determine the time range of the study, such as data from a certain time point before the earthquake to several years after the earthquake. For each seafloor station, construct its displacement time series within the study time range based on its coordinate position solution data. This usually involves comparing the coordinates of each time point with the initial coordinates (the coordinates before the earthquake) and calculating the displacement vector. Calculate the displacement of each seafloor station at each time point. The displacement can be calculated by the following formula: According to the research needs, filter out the displacement components of interest. For example, if the vertical displacement is being studied, only the displacement component in the vertical direction can be extracted. Ensure the integrity and consistency of the data and handle missing data or outliers. Store the screened and extracted displacement time series as observations, usually in the form of a table or time series database for subsequent analysis and modeling.

[0053] In an alternative embodiment, see Figure 5 As shown, Figure 5 A flowchart of a viscoelastic earth model construction method provided by the first embodiment of the present invention is shown, wherein the reset error Love number and the complex Green's function are determined based on the Burgers viscoelastic earth model, including steps S501-S502: S501: Introducing a complex variable parameter s into the stress-strain constitutive relation of the Burgers viscoelastic earth model, and performing Laplace transformation to obtain the constitutive relation in the complex domain.

[0054] Specifically, before performing step S501, a Burgers viscoelastic earth model combining Kelvin body and Maxwell body is constructed according to the viscoelastic semi-infinite space dislocation theory, see Figure 6 As shown, Figure 6A schematic diagram of a viscoelastic earth model provided in the first embodiment of the present invention is shown, in which a fault rupture (shown as a rupture zone in the figure) is generated by the subduction and compression of a continental plate and a submarine plate (when two plates meet, one plate is inserted under another relatively passive plate, and the inserted plate is the subducting plate shown in the figure), wherein the Burgers viscoelastic earth model refers to the existing continental crust model and the CRUST 1.0 ocean crust model, and takes the elastic lithosphere thickness of the area where the submarine reference station is located as 25 km deep, that is, 0-25 km is taken as a pure elastic layer, and 25 km to the core-mantle boundary is a viscous structure layer; the Burgers viscoelastic model includes two viscosity parameters, transient and steady, and uses them as radial parameters of the earth. is the viscosity parameter of the viscoelastic continental mantle wedge in the Maxwell body (i.e., the viscoelastic mantle wedge), is the viscosity parameter of the viscoelastic oceanic mantle wedge in the Maxwell body, is the viscosity parameter of the viscoelastic continental mantle wedge in the Kelvin body, is the viscosity parameter of the viscoelastic oceanic mantle wedge in the Kelvin body. is the viscosity parameter of the Kelvin body, is the viscosity parameter of the Maxwell body, is the Lamé constant of the Kelvin body, is the Lamé constant of the Maxwell body.

[0055] In step S501, a complex variable parameter s is introduced into the stress-strain constitutive relation of the viscoelastic model; wherein, is the stress-strain constitutive relation of the viscoelastic model, is stress, and the “·” above indicates the derivative with respect to time t. and is the Lamé constant, is the viscosity parameter, I is the unit matrix, is the trace of the matrix, subscript represents the viscoelastic model; is a function of the time derivative of displacement; Laplace transformation is performed on the stress-strain constitutive relation of the viscoelastic model with the complex variable parameter s, and the constitutive relation in the complex domain is obtained; wherein, the expression in the complex domain obtained by Laplace transformation by introducing a new complex variable parameter s is: .

[0056] S502: Solving the target equation group in the complex domain according to the constitutive relation in the complex domain to obtain the reset error Love number and the complex Green's function.

[0057] Specifically, the equations consisting of the source function, the initial condition of the sphere center, the inner core-outer core boundary condition, the outer core-mantle boundary condition, the surface free boundary condition and the source function in the complex domain are solved to obtain the reset error Love number and complex Green's function generated by the four independent point sources in the complex domain; among them, is the final solution formula of the reset Love number and complex Green's function; wherein the reset Love number and complex Green's function are very similar to the constitutive relation of elasticity, and the Lamé parameters λ(s) and μ(s) of the reset Love number and complex Green's function are complex functions, and are expressed as express.

[0058] Where r is the distance from the spherical center, θ is the co-latitude, is the longitude, t is the time, y1 and y3 are the radial and horizontal components of the displacement, the superscript T represents the annular deformation, n is the order, and m is the degree. , , They are all surface vector spherical harmonic functions. Any vector on the unit sphere can be expressed by these three spherical harmonic functions.

[0059] In an optional embodiment, the target set of equations includes: The initial condition function of the center of the sphere, the inner core-outer core boundary condition function, the outer core-mantle boundary condition function, the free boundary condition function of the surface and the earthquake source function.

[0060] In an alternative embodiment, see Figure 7 As shown, Figure 7 A flow chart of calculating a displacement time series value provided by the first embodiment of the present invention is shown, wherein the calculation value of the displacement time series is determined based on the reset error Love number and the complex Green's function according to the observed value of the displacement time series, including steps S701-S702: S701: using the Riemann-Mellin inversion formula, inversely transform the reset dislocation Love number and the complex Green's function to obtain the dislocation Love number and the Green's function in the time domain.

[0061] Specifically, the Riemann-Mellin inversion formula is used to inversely transform the dislocation Love number and complex Green's function to obtain the dislocation Love number and Green's function in the time domain. The Riemann-Mellin inversion formula is a mathematical tool that can transform functions in the complex domain into functions in the time domain, so that complex complex domain functions can be compared and analyzed with actual observation data. Through this inverse transformation process, the dislocation Love number and Green's function in the time domain can be obtained, which provides a basis for the subsequent displacement time series calculation.

[0062] S702: Solve the dislocation Love number and the Green's function using the coordinate position solution data of the seafloor station to obtain the calculated value of the displacement time series.

[0063] Specifically, according to the coordinate position solution data of the seafloor station, the dislocation Love number and Green's function are solved to obtain the calculated values ​​of the displacement time series. These calculated values ​​reflect the displacement changes of the seafloor station at different time points. They are theoretical values ​​calculated based on the Burgers viscoelastic earth model and the dislocation Love number and complex Green's function. By comparing with the observed values, the accuracy of the model and the rationality of the parameters can be evaluated, which provides an important basis for subsequent parameter inversion and model optimization.

[0064] Specifically, according to the reset Love number and complex Green's function, the Riemann-Mellin inversion formula is used for inverse transformation to calculate the displacement time series of each seafloor station, and use it as the calculated value of the displacement time series; wherein, the reset Love number and complex Green's function can be uniformly expressed as y(s), which represent the deformation under the viscoelastic model. In order to further obtain y(t) in the time domain, it is necessary to further perform Laplace inverse transformation; the Riemann-Mellin inversion formula is .

[0065] Where i is the imaginary unit, c needs to be larger than all singular points of the integrand, and s is a complex variable parameter.

[0066] In an alternative embodiment, see Figure 8 As shown, Figure 8 A flow chart of an optimal parameter determination method provided in the first embodiment of the present invention is shown, wherein the optimal transient viscosity parameter and the optimal steady-state viscosity parameter are determined based on the observed value and the calculated value of the displacement time series, including steps S801-S802: S801: constraining and adjusting the observed value and calculated value of the displacement time series, and determining the optimal calculated value of the displacement time series that minimizes the root mean square error between the observed value and the calculated value of the displacement time series.

[0067] Specifically, we first define the error function, usually the root mean square error (RMSE), to quantify the difference between the observed and calculated values. By adjusting the transient viscosity parameters and steady-state viscosity parameters in the Burgers viscoelastic earth model, we calculate the displacement time series under different parameter combinations, and use optimization algorithms (such as gradient descent, genetic algorithm, or simulated annealing) to find the parameter combination that minimizes the RMSE. In this process, starting from the initial parameters, the parameter values ​​are gradually adjusted, and the RMSE is recalculated after each adjustment until the optimal parameter combination that minimizes the error is found.

[0068] S802: Determine the transient viscosity parameter and the steady-state viscosity parameter corresponding to the optimal calculated value of the displacement time series in the Burgers viscoelastic earth model as the optimal transient viscosity parameter and the optimal steady-state viscosity parameter, respectively.

[0069] Specifically, once the optimal parameter combination is determined, the corresponding transient viscosity parameter and steady-state viscosity parameter are determined as the optimal transient viscosity parameter and the optimal steady-state viscosity parameter, respectively. These parameters not only make the model calculation results closest to the actual observation data, but also can accurately reflect the viscoelastic properties of the earth medium. Through this process, the optimal radial parameters of the earth can be obtained, providing important data support for seismic research and geophysical modeling.

[0070] Specifically, according to the observed values ​​of the displacement time series and the calculated values ​​of the displacement time series, the least squares principle is used to constrain the observed values ​​and the calculated values ​​of the displacement time series and adjust them so that the root mean square error between the theoretical calculated values ​​and the observed values ​​in the period 2 to 10 years after the earthquake is minimized, thereby obtaining the transient and steady-state viscosity parameters of the Burgers viscoelastic model on the ocean side and using them as the optimal earth radial parameters; wherein, in the least squares principle, the functional relationship between the calculated value and the observed value is defined as , is the observed value, is the parameter to be estimated, is the calculated value, is the number of parameters to be estimated, Indicates parameters to be estimated, Indicates calculated values, where .Will Substitute the displacement time series into the least squares equation to obtain the solution; among them, the displacement time series is substituted into

[0071] , the solution of the least squares equation is ; X is the design matrix, Indicates The observation equation calculated values, and H is the observation matrix.

[0072] The present application provides a method for determining optimal earth radial parameters, which utilizes seabed GNSS-A data to solve the displacement change of seabed reference points, that is, the observed value of the displacement time series, and constructs a viscoelastic earth model through complex domain transformation of the viscoelastic seismic dislocation theory, and calculates the displacement change of the seabed reference points after the earthquake through inversion and inverse transformation, that is, the calculated value of the displacement time series, and adjusts the viscoelastic parameters of the seabed according to the least squares constraint principle to obtain the optimal earth radial parameters, which is conducive to the refined description of the seabed structure near the source area in the earth model, the inversion of the viscoelastic structure of the earth, and the more accurate characterization of the source mechanism of the seabed earthquake, and is also conducive to the refined management of post-earthquake spatiotemporal changes.

[0073] Embodiment 2 See also Fig. 9 As shown, Fig. 9 A schematic diagram of the structure of an optimal earth radial parameter determination device provided by Embodiment 2 of the present invention is shown, wherein the device comprises: The observation data acquisition module 901 is used to acquire the original observation data of several seafloor stations in the epicenter area of ​​the seafloor earthquake; The displacement time series observation value determination module 902 is used to determine the seabed station coordinate position solution data and the displacement time series observation value based on the original observation data of each seabed station; A viscoelastic earth model construction module 903 is used to construct a Burgers viscoelastic earth model, and determine a reset Love number and a complex Green's function based on the Burgers viscoelastic earth model, wherein the Burgers viscoelastic earth model includes a transient viscosity parameter and a steady-state viscosity parameter, and the transient viscosity parameter and the steady-state viscosity parameter together constitute the earth radial parameter; A displacement time series calculated value determination module 904 is used to determine the calculated value of the displacement time series according to the observed value of the displacement time series based on the reset error Love number and the complex Green's function; The optimal earth radial parameter determination module 905 is used to determine the optimal transient viscosity parameter and the optimal steady-state viscosity parameter based on the observed value and calculated value of the displacement time series, and to combine the transient viscosity parameter and the optimal steady-state viscosity parameter into the optimal earth radial parameter.

[0074] In an optional embodiment, the obtaining of raw observation data of several seafloor stations in the epicenter area of ​​the seafloor earthquake includes: Determine the actual seafloor station information of the study area based on the location information of the study area; The information of the seabed stations in the epicenter area is obtained by screening the actual seabed station information in the study area; The original observation data of each seafloor station is extracted from the seafloor station information in the epicenter area, wherein the original observation data includes the GNSS data, attitude data, and acoustic ranging data of each seafloor station in the epicenter area of ​​the seafloor earthquake.

[0075] In an optional embodiment, the determination of the seabed station coordinate position solution data and the observation value of the displacement time series based on the original observation data of each seabed station includes: According to the original observation data of each seabed station, the coordinate position of the seabed station is solved by using the sound speed time-space variation error compensation positioning model to obtain the coordinate position solution data of the seabed station; The displacement time series of each seafloor station is screened and extracted according to the coordinate position solution data of the seafloor station to determine the observation value of the displacement time series.

[0076] In an optional embodiment, determining the reset Love number and the complex Green's function based on the Burgers viscoelastic earth model includes: Introducing a complex variable parameter s into the stress-strain constitutive relation of the Burgers viscoelastic earth model, and performing Laplace transformation to obtain the constitutive relation in the complex domain; The target equation group in the complex domain is solved according to the constitutive relation in the complex domain to obtain the reset error Love number and the complex Green's function.

[0077] In an optional embodiment, the target set of equations includes: The initial condition function of the center of the sphere, the inner core-outer core boundary condition function, the outer core-mantle boundary condition function, the free boundary condition function of the surface and the earthquake source function.

[0078] Optionally, the determining the calculated value of the displacement time series based on the reset error Love number and the complex Green's function according to the observed value of the displacement time series includes: Using the Riemann-Mellin inversion formula, inversely transforming the reset dislocation Love number and the complex Green's function to obtain the dislocation Love number and the Green's function in the time domain; The dislocation Love number and the Green's function are solved using the coordinate position solution data of the seafloor station to obtain the calculated value of the displacement time series.

[0079] In an optional embodiment, determining the optimal transient viscosity parameter and the optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time series includes: Constraining and adjusting the observed values ​​and calculated values ​​of the displacement time series, and determining the optimal calculated value of the displacement time series that minimizes the root mean square error between the observed values ​​and the calculated values ​​of the displacement time series; The transient viscosity parameter and the steady-state viscosity parameter corresponding to the optimal calculated value of the displacement time series in the Burgers viscoelastic earth model are respectively determined as the optimal transient viscosity parameter and the optimal steady-state viscosity parameter.

[0080] Embodiment 3 Based on the same application concept, see Fig.10 As shown, Fig.10 FIG. 4 shows a schematic diagram of the structure of a computer device provided by Embodiment 3 of the present invention, wherein: Fig.10 As shown, a computer device 1000 provided in Embodiment 3 of the present application includes: A processor 1001, a memory 1002 and a bus 1003, wherein the memory 1002 stores machine-readable instructions executable by the processor 1001. When the computer device 1000 is running, the processor 1001 communicates with the memory 1002 via the bus 1003. When the processor 1001 is running, the machine-readable instructions execute the steps of the method for determining the optimal earth radial parameters shown in the first embodiment.

[0081] Embodiment 4 Based on the same application concept, an embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method for determining the optimal earth radial parameters described in any one of the above embodiments are executed.

[0082] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system and device described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0083] The computer program product for determining the optimal earth radial parameters provided in the embodiment of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the method described in the previous method embodiment. The specific implementation can be found in the method embodiment, which will not be repeated here.

[0084] The optimal earth radial parameter determination device provided in the embodiment of the present invention can be specific hardware on the device or software or firmware installed on the device. The system provided in the embodiment of the present invention has the same implementation principle and technical effects as the aforementioned method embodiment. For the sake of brief description, the parts not mentioned in the system embodiment can refer to the corresponding contents in the aforementioned method embodiment. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, devices and units described above can all refer to the corresponding processes in the aforementioned method embodiment, and will not be repeated here.

[0085] In the embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The system embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some communication interface, device or unit, which can be electrical, mechanical or other forms.

[0086] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0087] In addition, each functional unit in the embodiment provided by the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0088] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0089] It should be noted that similar numbers and letters represent similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description and are not to be understood as indicating or implying relative importance.

[0090] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, those skilled in the art should understand that any person skilled in the art can still modify the technical solutions described in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or perform equivalent replacements on some of the technical features thereof; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. They should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for determining an optimal earth radial parameter, characterized in that: The method comprises: Obtain the original observation data of several seafloor stations in the epicenter area of ​​seafloor earthquakes; Based on the original observation data of each seafloor station, the coordinate position solution data and the observation value of the displacement time series of the seafloor station are determined; Constructing a Burgers viscoelastic earth model, and determining a reset Love number and a complex Green's function based on the Burgers viscoelastic earth model, wherein the Burgers viscoelastic earth model includes a transient viscosity parameter and a steady-state viscosity parameter, and the transient viscosity parameter and the steady-state viscosity parameter together constitute the radial parameter of the earth; Based on the reset error Love number and the complex Green's function, a calculated value of the displacement time series is determined according to the observed value of the displacement time series; Based on the observed value and calculated value of the displacement time series, the optimal transient viscosity parameter and the optimal steady-state viscosity parameter are determined, and the transient viscosity parameter and the optimal steady-state viscosity parameter are combined to form the optimal earth radial parameter.

2. The method according to claim 1, characterized in that The method of obtaining the original observation data of several seafloor stations in the epicenter area of ​​the seafloor earthquake includes: Determine the actual seafloor station information of the study area based on the location information of the study area; The information of the seabed stations in the epicenter area is obtained by screening the actual seabed station information in the study area; The original observation data of each seafloor station is extracted from the seafloor station information in the epicenter area, wherein the original observation data includes the GNSS data, attitude data, and acoustic ranging data of each seafloor station in the epicenter area of ​​the seafloor earthquake.

3. The method according to claim 1, characterized in that The method of determining the coordinate position solution data of the seabed station and the observation value of the displacement time series based on the original observation data of each seabed station includes: According to the original observation data of each seabed station, the coordinate position of the seabed station is solved by using the sound speed time-space variation error compensation positioning model to obtain the coordinate position solution data of the seabed station; The displacement time series of each seafloor station is screened and extracted according to the coordinate position solution data of the seafloor station to determine the observation value of the displacement time series.

4. The method according to claim 1, characterized in that: The method of determining the reset Love number and the complex Green's function based on the Burgers viscoelastic earth model includes: Introducing a complex variable parameter s into the stress-strain constitutive relation of the Burgers viscoelastic earth model, and performing Laplace transformation to obtain the constitutive relation in the complex domain; The target equation group in the complex domain is solved according to the constitutive relation in the complex domain to obtain the reset error Love number and the complex Green's function.

5. The method according to claim 4, characterized in that The target equations include: The initial condition function of the center of the sphere, the inner core-outer core boundary condition function, the outer core-mantle boundary condition function, the free boundary condition function of the surface and the earthquake source function.

6. The method according to claim 1, characterized in that The method of determining the calculated value of the displacement time series based on the reset error Love number and the complex Green's function according to the observed value of the displacement time series includes: Using the Riemann-Mellin inversion formula, inversely transforming the reset dislocation Love number and the complex Green's function to obtain the dislocation Love number and the Green's function in the time domain; The dislocation Love number and the Green's function are solved using the coordinate position solution data of the seafloor station to obtain the calculated value of the displacement time series.

7. The method according to claim 1, characterized in that The step of determining the optimal transient viscosity parameter and the optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time series comprises: Constraining and adjusting the observed values ​​and calculated values ​​of the displacement time series, and determining the optimal calculated value of the displacement time series that minimizes the root mean square error between the observed values ​​and the calculated values ​​of the displacement time series; The transient viscosity parameter and the steady-state viscosity parameter corresponding to the optimal calculated value of the displacement time series in the Burgers viscoelastic earth model are respectively determined as the optimal transient viscosity parameter and the optimal steady-state viscosity parameter.

8. An optimal earth radial parameter determination device, characterized in that: The device comprises: An observation data acquisition module is used to acquire the original observation data of several seafloor stations in the epicenter area of ​​the seafloor earthquake; A displacement time series observation value determination module is used to determine the seabed station coordinate position solution data and the displacement time series observation value based on the original observation data of each seabed station; A viscoelastic earth model construction module is used to construct a Burgers viscoelastic earth model, and determine a reset Love number and a complex Green's function based on the Burgers viscoelastic earth model, wherein the Burgers viscoelastic earth model includes a transient viscosity parameter and a steady-state viscosity parameter, and the transient viscosity parameter and the steady-state viscosity parameter together constitute the earth radial parameter; A displacement time series calculated value determination module, used to determine the calculated value of the displacement time series according to the observed value of the displacement time series based on the reset error Love number and the complex Green's function; The optimal earth radial parameter determination module is used to determine the optimal transient viscosity parameter and the optimal steady-state viscosity parameter based on the observed value and the calculated value of the displacement time series, and the transient viscosity parameter and the optimal steady-state viscosity parameter are combined into the optimal earth radial parameter.

9. A computer device, characterized in that: include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of the method for determining the optimal earth radial parameters as described in any one of claims 1 to 7 are performed.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of the method for determining the optimal earth radial parameters as claimed in any one of claims 1 to 7.

Images