CN-121997560-A - Moon giant weathering layer thickness estimation method based on gravity and topographic data

CN121997560ACN 121997560 ACN121997560 ACN 121997560ACN-121997560-A

Abstract

The invention discloses a moon giant weathering layer thickness estimation method based on gravity and topographic data, which comprises the steps of 1, collecting gravity data and topographic data, sequentially carrying out spherical harmonic analysis and pretreatment on the gravity data and the topographic data respectively to obtain pretreated gravity data and topographic data, 2, calculating an effective density spectrum of each node on the surface of a moon, namely an observed local effective density spectrum, 3, constructing an underground double-layer density structure model comprising a giant weathering layer and a shell layer, calculating predicted effective density, randomly sampling to inversion parameter combinations by using a Markov chain Monte Carlo algorithm, carrying out Bayesian inversion to obtain posterior distribution of parameter combinations on each grid point, and simultaneously, calculating fitting degree between the observed local effective density spectrum and the predicted effective density spectrum, and 4, determining the parameter combinations to be inverted according to the fitting degree value, thereby obtaining space distribution of the thickness of the moon giant weathering layer, and having good continuity and higher resolution.

Inventors

ZHANG WENSONG
LI KEZHAO
WANG YONG
YAN JIANGUO
QIU DENGGAO
CHEN LIN
LIANG NAN

Assignees

河南省科学院空天信息研究所
河南省科学院
河南理工大学

Dates

Publication Date: 20260508
Application Date: 20251229

Claims (7)

1. The moon giant weathering layer thickness estimation method based on gravity and topography data is characterized by comprising the following steps: Step 1, acquiring original gravity data and topographic data, and respectively performing spherical harmonic analysis on the gravity data and the topographic data to obtain gravity data with different orders And topographic data Then will And Cutting off the data into data with the same order to obtain preprocessed gravity data and topographic data; Step 2, dividing the lunar surface into a plurality of discrete grid nodes, for each grid node, adopting a Slepian window method to locally process the unit density modified Bragg gravity data and the preprocessed gravity data, acquiring an effective density value of each node in a space domain, converting the effective density value into a spherical harmonic domain, and calculating an effective density spectrum of each node, namely an observed local effective density spectrum ; Step 3, constructing an underground double-layer density structure model and performing Bayesian inversion, wherein the specific process is as follows: Step 3.1, constructing an underground double-layer density structure model comprising a giant weathering layer and a shell layer, and expressing the effective density spectrum predicted by the model as: Wherein: Is the density of the giant weathering layer; Is the density difference between the giant weathering layer and the shell layer; is the density gradient when the shell layer changes linearly with the depth; r is the radius of moon; Is the first The radius of the shell layer of the layer, First, the Radius of the shell layer of the layer; step 3.2, combining the parameters to be inverted by using a Markov chain Monte Carlo algorithm 、 And Random sampling is carried out, and then Bayesian inversion is utilized to obtain parameter combinations on each grid node 、 And Posterior distribution of (2); step 3.3, calculating the observed local effective density spectrum And predicted effective density spectrum Degree of fit between Expressed as: Wherein: The standard deviation, which represents the local effective density spectrum, is expressed as: Wherein: representing the sensitivity of each noise source to the local effective density spectrum; Representing each noise source Is a standard of (2); And 4, evaluating uncertainty of the parameter combination according to the fitting degree value, and screening out the parameter combination M with the fitting degree value smaller than 20, so that spatial distribution of the thickness of the huge lunar weathering layer of the moon is obtained.
2. The method for estimating the thickness of the huge lunar weathering layer based on the gravity and the topographic data according to claim 1, wherein the specific process of the step1 is as follows: Step 1.1, acquiring original gravity data, namely acquiring full-moon gravity data of moon gravity recovery and internal laboratory tasks from a planetary data system, and performing spherical harmonic analysis on the gravity data to obtain gravity data of different orders Expressed as: Wherein: spherical harmonic coefficients of gravitational data; is a spherical harmonic function; is spherical coordinates; And Respectively representing the order and the order of the spherical harmonics; Step 1.2, acquiring original topographic data, namely acquiring global topographic data of the moon by utilizing a lunar orbit laser altimeter, and performing spherical harmonic analysis on the global topographic data to obtain topographic data of different orders Expressed as: Wherein: spherical harmonic coefficients that are topographic data; is a spherical harmonic function; is spherical coordinates; And Respectively representing the order and the order of the spherical harmonics; step 1.3, preprocessing data, namely respectively preprocessing gravity data of different orders through SHTools And topographic data Pretreatment is carried out, and And And cutting off the data into data of the same order to obtain preprocessed gravity data and topographic data.
3. The method for estimating the thickness of the lunar giant weathering layer based on gravity and topographic data according to claim 1, wherein the resolution of the raw gravity data and topographic data of step 1 is 1200 order and 2600 order, respectively.
4. The method for estimating a thickness of a huge lunar weathering layer based on gravity and topographic data according to claim 2, wherein the step 1.3 will be And Truncated to 660 order data.
5. The method for estimating a thickness of a lunar giant weathering layer based on gravity and topographic data according to claim 2, wherein the local effective density spectrum of step 2 Expressed as: Wherein: The pre-processed gravity data and the unit density of the Bragg correction cross power spectrum; is a Bragg correction power spectrum, expressed as: Wherein: is a gravity signal, which is the gravity data after pretreatment At spherical coordinate point A value at; Is unit density corrected Bragg gravity data expressed as: Wherein: Is the reference radius of the moon; is the surface topography height of the lunar, expressed as: Wherein: Representing the preprocessed topographic data; representing spherical harmonics; Spherical coordinates, wherein: And Corresponding to latitude and longitude, respectively.
6. The method for estimating the thickness of the lunar giant weathering layer based on gravity and topographic data according to claim 1, wherein the shell layer of the step 3.1 is divided into 400 layers, each layer having a thickness of 0.1 km.
7. The method for estimating the thickness of the lunar giant weathering layer based on the gravity and the topographic data according to claim 1, wherein the posterior distribution of the step 3.2 is expressed as: Wherein: Is posterior distribution; is a likelihood function; Is a priori distribution, M is the parameter combination of a double-layer density structure model, and comprises 、 And 。

Description

Moon giant weathering layer thickness estimation method based on gravity and topographic data Technical Field The invention belongs to the technical field of astrophysics, and particularly relates to a method for estimating the thickness of a lunar giant weathering layer based on gravity and topographic data. Background The moon giant weathering layer is a thick fracture layer formed at the early stage of strong impact bombardment, records the accumulated effect of early large impact, controls the porosity, heat insulation and crust rheological property of the moon surface, plays an important role in researching the geological evolution and heat history of the moon, and therefore has important significance in estimating the thickness of the moon giant weathering layer. However, the conventional method for estimating the thickness of the giant lunar layer has no better constraint on the thickness distribution of the giant lunar layer, can only estimate the thickness of the regional giant lunar layer, lacks global or local continuity, and has low estimation accuracy, so that a global high-resolution giant lunar layer thickness distribution map is difficult to obtain. Disclosure of Invention The invention aims to provide a method for estimating the thickness of a lunar giant weathering layer based on gravity and topographic data, which is used for constructing a double-layer density structure model by constructing gravity-topographic data, improving the accuracy of lunar giant weathering layer thickness estimation and the continuity of spatial distribution and being beneficial to obtaining a global high-resolution giant weathering layer thickness distribution map. The invention is realized by the following technical scheme: a moon giant weathering layer thickness estimation method based on gravity and topography data comprises the following steps: Step 1, acquiring original gravity data and topographic data, and respectively performing spherical harmonic analysis on the gravity data and the topographic data to obtain gravity data with different orders And topographic dataThen willAndCutting off the data into data with the same order to obtain preprocessed gravity data and topographic data; Step 2, dividing the lunar surface into a plurality of discrete grid nodes, for each grid node, adopting a Slepian window method to locally process the unit density modified Bragg gravity data and the preprocessed gravity data, acquiring an effective density value of each node in a space domain, converting the effective density value into a spherical harmonic domain, and calculating an effective density spectrum of each node, namely an observed local effective density spectrum; step 3, constructing an underground double-layer density structure model and performing Bayesian inversion, wherein the specific process is as follows: Step 3.1, constructing an underground double-layer density structure model comprising a giant weathering layer and a shell layer, and expressing the effective density spectrum predicted by the model as: Wherein: Is the density of the giant weathering layer; Is the density difference between the giant weathering layer and the shell layer; is the density gradient when the shell layer changes linearly with the depth; r is the radius of moon; Is the first The radius of the shell layer of the layer,First, theRadius of the shell layer of the layer; step 3.2, combining the parameters to be inverted by using a Markov chain Monte Carlo algorithm 、AndRandom sampling is carried out, and then Bayesian inversion is utilized to obtain parameter combinations on each grid node、AndPosterior distribution of (2); step 3.3, calculating the observed local effective density spectrum And predicted effective density spectrumDegree of fit betweenExpressed as: Wherein: The standard deviation, which represents the local effective density spectrum, is expressed as: Wherein: representing the sensitivity of each noise source to the local effective density spectrum; Representing each noise source Is a standard of (2); And 4, evaluating uncertainty of the parameter combination according to the fitting degree value, and screening out the parameter combination M with the fitting degree value smaller than 20, so that spatial distribution of the thickness of the huge lunar weathering layer of the moon is obtained. Further, the specific process of the step 1 is as follows: Step 1.1, acquiring original gravity data, namely acquiring full-moon gravity data of moon gravity recovery and internal laboratory tasks from a planetary data system, and performing spherical harmonic analysis on the gravity data to obtain gravity data of different orders Expressed as: Wherein: spherical harmonic coefficients of gravitational data; is a spherical harmonic function; is spherical coordinates; And Respectively representing the order and the order of the spherical harmonics; Step 1.2, acquiring original topographic data, namely acquiring global