Moon giant weathered layer thickness estimation method based on gravity and topographic data

Abstract

The invention discloses a method for estimating the thickness of a giant moon weathered layer based on gravity and topographic data, and the method comprises the steps: 1, collecting the gravity data and the topographic data, and carrying out the spherical harmonic analysis and preprocessing of the gravity data and the topographic data in sequence, and obtaining the preprocessed gravity data and topographic data; 2, calculating an effective density spectrum of each node on the lunar surface, namely an observed local effective density spectrum; 3, constructing an underground double-layer density structure model comprising a giant weathered layer and a shell layer, calculating the predicted effective density, carrying out random sampling on a to-be-inverted parameter combination by using a Markov chain Monte Carlo algorithm, carrying out Bayesian inversion to obtain the posterior distribution of the parameter combination on each grid point, and calculating the density of the to-be-inverted parameter combination according to the posterior distribution of the to-be-inverted parameter combination; meanwhile, the fitting degree between the observed local effective density spectrum and the predicted effective density spectrum is calculated; and 4, determining a to-be-inverted parameter combination according to the value of the fitting degree so as to obtain the spatial distribution of the thickness of the giant weathered layer of the moon, and the method has good continuity and relatively high resolution.

Description

Technical Field

[0001] This invention belongs to the field of astrophysics, specifically a method for estimating the thickness of the giant lunar regolith based on gravity and topographic data. Background Technology

[0002] The lunar giant regolith is a thick fractured layer formed in the early stages of intense impacts. It records the cumulative effects of early large impacts and controls the porosity, thermal insulation, and crustal rheology of the lunar surface. It plays an important role in studying the geological evolution and thermal history of the Moon. Therefore, estimating the thickness of the lunar giant regolith is of great significance.

[0003] However, traditional methods for estimating the thickness of lunar giant regolith do not provide adequate constraints on the distribution of giant regolith thickness. They can only estimate the thickness of giant regolith in a region, lacking global or local continuity, and the estimation accuracy is not high, making it difficult to obtain a high-resolution global map of giant regolith thickness distribution. Summary of the Invention

[0004] The purpose of this invention is to provide a method for estimating the thickness of the lunar giant regolith based on gravity and topographic data. By constructing a two-layer density structure model using gravity-topographic data, the accuracy of estimating the thickness of the lunar giant regolith and the continuity of its spatial distribution are improved, which helps to obtain a global high-resolution map of the distribution of the giant regolith thickness.

[0005] This invention is achieved through the following technical solution: A method for estimating the thickness of a giant lunar regolith based on gravity and topographic data includes the following steps: Step 1: Collect raw gravity and terrain data, and perform spherical harmonic analysis on the gravity and terrain data respectively to obtain gravity data of different orders. and terrain data Then and Data is truncated to the same order to obtain preprocessed gravity and terrain data; Step 2: Divide the lunar surface into several discrete grid nodes. For each grid node, use the Slepian window method to localize the unit density corrected Bouguer gravity data and the preprocessed gravity data. Obtain the effective density value of each node in the spatial domain, then convert the effective density value to the spherical harmonic domain, and calculate the effective density spectrum of each node, i.e. the observed local effective density spectrum. Step 3: Construct a two-layer underground density structure model and perform Bayesian inversion. The specific process is as follows: Step 3.1: Construct a subsurface two-layer density structure model including a giant weathered layer and a crust, and express the effective density spectrum predicted by the model as: In the formula: The density of the giant weathering layer; The density difference between the giant weathered layer and the crust; This represents the density gradient of the shell as it changes linearly with depth. R is the thickness of the giant regolith; R is the radius of the moon. For the first The radius of the shell layer, No. The radius of the shell layer; Step 3.2: Use the Markov chain Monte Carlo algorithm to combine the parameters to be inverted. , and Random sampling is performed, and then Bayesian inversion is used to obtain the parameter combination at each grid node. , and The posterior distribution of; Step 3.3: Calculate the observed local effective density spectrum With the predicted effective density spectrum degree of fit between , is represented as: In the formula: The standard deviation of the local effective density spectrum is expressed as: In the formula: This indicates the sensitivity of each noise source to the local effective density spectrum; Represent each noise source Standards; Step 4: Evaluate the uncertainty of parameter combinations based on the goodness-of-fit values, and then select parameter combinations with a goodness-of-fit value of less than 20. M This allows us to obtain the spatial distribution of the thickness of the giant regolith on the moon.

[0006] Furthermore, the specific process of step 1 is as follows: Step 1.1: Acquire raw gravity data: Obtain full-moon gravity data from the Lunar Gravity Recovery and Interior Laboratory mission from the Planetary Data System, perform spherical harmonic analysis on the gravity data, and obtain gravity data of different orders. , is represented as: In the formula: The spherical harmonic coefficients of gravity data; It is a spherical harmonic function; Spherical coordinates; and These represent the order and degree of the spherical harmonics, respectively. Step 1.2: Acquire raw terrain data: Use a lunar orbital laser altimeter to acquire global terrain data of the Moon, perform spherical harmonic analysis on the global terrain data, and obtain terrain data of different orders. , is represented as: In the formula: The spherical harmonic coefficients of the terrain data; It is a spherical harmonic function; Spherical coordinates; and These represent the order and degree of the spherical harmonics, respectively. Step 1.3, Data Preprocessing: SHTools is used to preprocess gravity data of different orders. and terrain data Preprocessing is performed to... and Data is truncated to the same order to obtain preprocessed gravity and terrain data.

[0007] Furthermore, the resolutions of the original gravity data and terrain data in step 1 are 1200th order and 2600th order, respectively.

[0008] Furthermore, step 1.3 will and The data is truncated to order 660.

[0009] Furthermore, the local effective density spectrum of step 2 , is represented as: In the formula: It consists of preprocessed gravity data and Bouguer-corrected cross-power spectra per unit density; The Bouguer-corrected power spectra are expressed as follows: In the formula: It is a gravity signal, which is preprocessed gravity data. At spherical coordinate points The value at; These are the Bouguer gravity data corrected for unit density, expressed as: In the formula: This is the reference radius for the Moon; This represents the elevation of the lunar surface terrain, expressed as: In the formula: This represents the preprocessed terrain data; Represents spherical harmonic functions; Let be spherical coordinates, where: and These correspond to latitude and longitude, respectively.

[0010] Furthermore, the shell in step 3.1 is divided into 400 layers, each with a thickness of 0.1 km.

[0011] Furthermore, the posterior distribution in step 3.2 Represented as: In the formula: It is the likelihood function; It is the prior distribution; M The parameter combination for the two-layer density structure model includes , and .

[0012] The present invention has the following beneficial technical effects: 1) It can accurately estimate the thickness of the giant lunar regolith: By combining local effective density spectrum and Bayesian inversion method, based on high-resolution gravity data and topographic data, it can accurately calculate the spatial distribution of the thickness of the giant lunar regolith, effectively reducing the problem of inaccurate thickness estimation caused by local errors in traditional methods. 2) Solved the problem of uncertainty in the underground structure: By constructing a two-layer density structure model of the underground, including the giant regolith and bedrock, and taking the density of the giant regolith as a prior assumption, a comprehensive analysis of the lunar underground structure is carried out through Bayesian inversion, which eliminates the potential bias of the model assumptions in the calculation of the underground structure, thereby obtaining a more reliable thickness distribution of the lunar giant regolith. 3) Higher computational accuracy and lower error: Using high-resolution gravity and terrain data, the inversion parameters are optimized through the localized Slepian window method and Markov chain Monte Carlo algorithm, which significantly improves the estimation accuracy. Compared with existing low-resolution data and coarse models, it can make accurate calculations on a smaller spatial scale, effectively reducing the uncertainty caused by data noise and computational errors. 4) Expanded the research scope of giant regolith: This invention, for the first time, combines Bayesian inversion method with Markov chain Monte Carlo algorithm to provide the global distribution of giant regolith, providing more evidence for the volcanic history and geological evolution of the moon. This not only enriches people's understanding of the internal structure of the moon, but also provides an important geological foundation for subsequent lunar resource development and scientific exploration. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the dual-layer density structure model of the present invention. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0015] A method for estimating the thickness of a giant lunar regolith based on gravity and topographic data includes the following steps: Step 1: Data Acquisition and Preprocessing Step 1.1: Acquire high-resolution raw gravity data: Obtain full-moon gravity data (GRGM1200B) from the Planetary Data System (PDS) for the Lunar Gravity Recovery and Interior Laboratory (GRAIL) mission. The gravity data has a resolution of 1200th order, accurately reflecting gravity variations on the lunar surface. Perform spherical harmonic analysis on the gravity data to obtain gravity data of different orders. , is represented as: In the formula: The spherical harmonic coefficients of gravity data; It is a spherical harmonic function; Spherical coordinates; and These represent the order and degree of the spherical harmonics, respectively. Step 1.2: Acquire high-resolution raw terrain data: Use the Lunar Orbiting Laser Altimeter (LOLA) to acquire global terrain data of the Moon at a resolution of 2600th order. Perform spherical harmonic analysis on the global terrain data to obtain terrain data of different orders. , is represented as: In the formula: The spherical harmonic coefficients of the terrain data; These are spherical harmonic functions, serving as orthogonal basis functions on a sphere to represent spatial modes of different frequencies; Spherical coordinates; and These represent the order and degree of the spherical harmonics, respectively. Step 1.3, Data Preprocessing: SHTools is used to preprocess gravity and terrain data of different orders, respectively, to preprocess the gravity data... and terrain data All data were truncated to the 660th order to obtain preprocessed gravity and topographic data, providing a basic data source for obtaining the effective density spectrum of each point on the Moon. Step 2: Calculate the local effective density spectrum The lunar surface is divided into several discrete grid nodes. For each grid node, the Slepian window method is used to localize the unit density corrected Bouguer gravity data and the preprocessed gravity data, obtaining the effective density value of each node in the spatial domain. Then, the effective density value is transformed into the spherical harmonic domain to obtain the effective density spectrum of each node. The observed local effective density spectrum is expressed as: In the formula: It consists of preprocessed gravity data and Bouguer-corrected cross-power spectra per unit density; The Bouguer-corrected power spectra are expressed as follows: In the formula: It is a gravity signal, representing gravity data. At spherical coordinate points The value at; These are the Bouguer gravity data corrected for unit density, expressed as: In the formula: This is the reference radius for the Moon; This represents the elevation of the lunar surface terrain, expressed as: In the formula: This represents the preprocessed terrain data; Represents spherical harmonic functions; Let be spherical coordinates, where: and Corresponding to latitude and longitude respectively; Step 3: Construct a two-layer underground density structure model and perform Bayesian inversion. Step 3.1: Constructing a two-layer density structure model: To characterize the density difference between the upper giant regolith layer of the lunar surface and the lower bedrock layer (the bedrock is mainly the lunar crust, referred to as the crust layer), a model is constructed based on the effective density distribution and surface geological features, consisting of the giant regolith layer and the crust layer. Figure 1The underground double-layer density structure model shown in (a) is as follows: Figure 1 As shown in (b), the bilayer density structure model constructs a piecewise density function that varies with depth by setting the density difference between the giant weathering layer and the crust and the interface depth, thus representing the effective density spectrum predicted by the bilayer density structure model as follows: In the formula: The density of the giant weathering layer; The density difference between the giant weathered layer and the crust; This represents the density gradient of the shell as it changes linearly with depth. R is the thickness of the giant regolith; R is the lunar radius; the crust is divided into layers every 0.1 km along the depth direction. layer, For the first The radius of the shell layer, No. The radius of the shell layer; Step 3.2, Bayesian Inversion: Use the Markov Chain Monte Carlo (MCMC) algorithm to combine the parameters to be inverted. , and Random sampling is performed, and then Bayesian inversion is used to explore the parameter space of the two-layer density structure model, eliminate potential biases in the estimation of the lunar subsurface structure using the two-layer density structure model, and obtain the parameter combination at each grid node. , and posterior distribution , is represented as: In the formula: It is the likelihood function; It is the prior distribution; M The parameter combination for the two-layer density structure model includes , and ; Step 3.3: Calculate the observed local effective density spectrum With the predicted effective density spectrum degree of fit between , is represented as: In the formula: The standard deviation of the local effective density spectrum is expressed as: In the formula: This indicates the sensitivity of each noise source to the local effective density spectrum; Represent each noise source The standard, by introducing a noise term This effectively reduces the impact of changes in the local effective density spectrum on the inversion results; Step 4: Evaluate the uncertainty of parameter combinations based on the goodness-of-fit values, and then select parameter combinations with a goodness-of-fit value of less than 20. M This allows us to obtain a high-resolution spatial distribution of the thickness of the giant lunar regolith.

Claims

1. A method for estimating the thickness of a giant lunar regolith based on gravity and topographic data, characterized in that, Includes the following steps: Step 1: Collect raw gravity and terrain data, and perform spherical harmonic analysis on the gravity and terrain data respectively to obtain gravity data of different orders. and terrain data Then and Data is truncated to the same order to obtain preprocessed gravity and terrain data; Step 2: Divide the lunar surface into several discrete grid nodes. For each grid node, use the Slepian window method to localize the unit density corrected Bouguer gravity data and the preprocessed gravity data, obtaining the effective density value of each node in the spatial domain. Then, transform the effective density value to the spherical harmonic domain and calculate the effective density spectrum of each node, i.e., the observed local effective density spectrum. ; Step 3: Construct a two-layer underground density structure model and perform Bayesian inversion. The specific process is as follows: Step 3.1: Construct a subsurface two-layer density structure model including a giant weathered layer and a crust, and express the effective density spectrum predicted by the model as: In the formula: The density of the giant weathering layer; The density difference between the giant weathered layer and the crust; This represents the density gradient of the shell as it changes linearly with depth. R is the thickness of the giant regolith; R is the radius of the moon. For the first The radius of the shell layer, No. The radius of the shell layer; Step 3.2: Use the Markov chain Monte Carlo algorithm to combine the parameters to be inverted. , and Random sampling is performed, and then Bayesian inversion is used to obtain the parameter combination at each grid node. , and The posterior distribution of; Step 3.3: Calculate the observed local effective density spectrum With the predicted effective density spectrum degree of fit between , is represented as: In the formula: The standard deviation of the local effective density spectrum is expressed as: In the formula: This indicates the sensitivity of each noise source to the local effective density spectrum; Represent each noise source Standards; Step 4: Evaluate the uncertainty of parameter combinations based on the goodness-of-fit values, and then select parameter combinations with a goodness-of-fit value of less than 20. M This allows us to obtain the spatial distribution of the thickness of the giant regolith on the moon.

2. The method for estimating the thickness of the lunar giant regolith based on gravity and topographic data according to claim 1, characterized in that, The specific process of step 1 is as follows: Step 1.1: Acquire raw gravity data: Obtain full-moon gravity data from the Lunar Gravity Recovery and Interior Laboratory mission from the Planetary Data System, perform spherical harmonic analysis on the gravity data, and obtain gravity data of different orders. , is represented as: In the formula: The spherical harmonic coefficients of gravity data; It is a spherical harmonic function; Spherical coordinates; and These represent the order and degree of the spherical harmonics, respectively. Step 1.2: Acquire raw terrain data: Use a lunar orbital laser altimeter to acquire global terrain data of the Moon, perform spherical harmonic analysis on the global terrain data, and obtain terrain data of different orders. , is represented as: In the formula: The spherical harmonic coefficients of the terrain data; It is a spherical harmonic function; Spherical coordinates; and These represent the order and degree of the spherical harmonics, respectively. Step 1.3, Data Preprocessing: SHTools is used to preprocess gravity data of different orders. and terrain data Preprocessing is performed to... and Data is truncated to the same order to obtain preprocessed gravity and terrain data.

3. The method for estimating the thickness of the lunar giant regolith based on gravity and topographic data according to claim 1, characterized in that, The resolutions of the raw gravity data and terrain data in step 1 are 1200th order and 2600th order, respectively.

4. The method for estimating the thickness of the giant lunar regolith based on gravity and topographic data according to claim 2, characterized in that, Step 1.3 will and The data is truncated to order 660.

5. The method for estimating the thickness of the lunar giant regolith based on gravity and topographic data according to claim 2, characterized in that, The local effective density spectrum in step 2 , is represented as: In the formula: It consists of preprocessed gravity data and Bouguer-corrected cross-power spectra per unit density; The Bouguer-corrected power spectra are expressed as follows: In the formula: This is a gravity signal, specifically preprocessed gravity data. At spherical coordinate points The value at; These are the Bouguer gravity data corrected for unit density, expressed as: In the formula: This is the reference radius for the Moon; This represents the elevation of the lunar surface terrain, expressed as: In the formula: This represents the preprocessed terrain data; Represents spherical harmonic functions; Let be spherical coordinates, where: and These correspond to latitude and longitude, respectively.

6. The method for estimating the thickness of the giant lunar regolith based on gravity and topographic data according to claim 1, characterized in that, The shell in step 3.1 is divided into 400 layers, each with a thickness of 0.1 km.

7. The method for estimating the thickness of the lunar giant regolith based on gravity and topographic data according to claim 1, characterized in that, The posterior distribution of step 3.2 is expressed as: In the formula: It is a posterior distribution; It is the likelihood function; It is the prior distribution; M The parameter combination for the two-layer density structure model includes , and .

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