CN-122020124-A - FNO deep learning model for gravity inversion, training method and gravity inversion method

CN122020124ACN 122020124 ACN122020124 ACN 122020124ACN-122020124-A

Abstract

The invention discloses an FNO deep learning model, a training method and a gravity inversion method for gravity inversion, which relate to the technical field of gravity inversion in geophysical exploration, wherein the model comprises a characteristic lifting layer, at least two spatial adaptive operator layers, a characteristic projection layer arranged behind the last spatial adaptive operator layer and at least one cross-layer residual jump connection which are sequentially connected; each spatial adaptive operator layer comprises a global Fourier branch, a local convolution branch, an adaptive fusion module, a spatial attention module and an activation module. The gravity data intelligent inversion method overcomes the defects that the traditional inversion method has strong dependence on an initial model, low calculation efficiency and weak generalization capability of a traditional deep learning model and is difficult to capture global features when gravity inversion is carried out, and realizes the gravity data intelligent inversion with high precision, high efficiency and strong generalization capability.

Inventors

XU YA
LU SHUPENG
HUANG SONG
WEI WEI
HAO TIANYAO

Assignees

中国科学院地质与地球物理研究所

Dates

Publication Date: 20260512
Application Date: 20260203

Claims (10)

1. The FNO deep learning model for gravity inversion is characterized by comprising a feature lifting layer, at least two layers of space self-adaptive operator layers, a feature projection layer arranged behind the last layer of space self-adaptive operator layer and at least one cross-layer residual jump connection which are sequentially connected, wherein each layer of space self-adaptive operator layer comprises a global Fourier branch, a local convolution branch, a self-adaptive fusion module, a space attention module and an activation module, and the feature lifting layer, the at least two layers of space self-adaptive operator layers are sequentially connected, wherein: The feature lifting layer is used for splicing the input scalar gravity field data with the coordinate grid representing the space position and projecting the coordinate grid into a high-dimensional feature space to obtain high-dimensional features corresponding to the gravity field data; A global Fourier branch, which is used for carrying out linear transformation on the high-dimensional characteristics corresponding to the gravitational field data in a frequency domain to capture a low-frequency trend and outputting the global Fourier characteristics corresponding to the gravitational field data; The local convolution branch is used for carrying out convolution operation on the high-dimensional features corresponding to the gravity field data to capture the high-frequency trend and outputting the local convolution features corresponding to the gravity field data; The self-adaptive fusion module is used for fusing the global Fourier features and the local convolution features corresponding to the gravitational field data and outputting fused features corresponding to the gravitational field data, wherein the fusion weight is self-adaptively adjusted according to the depth and the spatial position of the gravitational field; the spatial attention module is used for generating attention weights corresponding to the fused features through a spatial attention mechanism, multiplying the fused features by the corresponding attention weights and outputting the features for identifying the density abnormal body; the activating module is used for activating the output of the spatial attention module; The characteristic projection layer predicts a three-dimensional density model corresponding to gravitational field data by mapping the output of the activation module back to the output dimension of the target, and completes gravity inversion; The cross-layer residual is connected in a jumping manner and is used for fusing the input of the k-th layer space self-adaptive operator layer with the output of the p-th layer space self-adaptive operator layer, and taking the fusion result as the input of the next layer structure of the p-th layer space self-adaptive operator layer, wherein p-k is more than or equal to 1.
2. The FNO deep learning model for gravity inversion of claim 1, wherein in the global fourier branch, the specific method for capturing the low frequency trend by linear transformation of the high dimensional features corresponding to the gravity field data in the frequency domain by using the fast fourier transform comprises: The method comprises the steps of converting high-dimensional features corresponding to gravitational field data into a frequency domain through fast Fourier transform, performing point-by-point multiplication operation on partial feature data converted into the frequency domain and a group of leachable complex weight tensors, and converting a point-by-point multiplication operation result back into a space domain through inverse Fourier transform to obtain global Fourier features corresponding to the gravitational field data, wherein the partial feature data are 32 low-frequency Fourier patterns in an X direction and 17 low-frequency Fourier patterns in a Y direction.
3. The FNO depth learning model for gravity inversion of claim 1, wherein in the partial convolution branches, the convolution operation employed is a1 x1 convolution operation.
4. The FNO deep learning model for gravity inversion of claim 1, wherein in the adaptive fusion module, the specific method of fusing the global fourier features and the local convolution features corresponding to the gravity field data comprises: acquiring global Fourier feature weights and local convolution feature weights corresponding to the depth and the spatial position of the gravitational field; Carrying out softmax normalization on the global Fourier feature weight and the local convolution feature weight to enable the sum of the two weights to be 1, and obtaining the normalized global Fourier feature weight and the normalized local convolution feature weight; Multiplying the global Fourier feature by the normalized global Fourier feature weight, multiplying the local convolution feature by the normalized local convolution feature weight, and adding the two multiplication results to obtain the fused feature.
5. The FNO depth learning model for gravity inversion of claim 1, wherein the spatial attention module comprises a convolution layer with a convolution kernel size of 1, a gelu activation function layer, a convolution layer with a convolution kernel size of 1, and a Sigmoid activation function layer and a multiplication output layer connected in sequence, wherein: the first convolution layer with the convolution kernel size of 1 is used for compressing the channel number of the fused features to 1/4 of the original channel number; gelu activate a function layer for introducing nonlinearity for the output of the first convolution layer with a convolution kernel size of 1; A second convolution layer with a convolution kernel size of 1, configured to restore the output of the gelu activation function layer to the original channel dimension; a Sigmoid activation function layer for generating attention weights within a [0,1] interval based on the output of a convolution layer with a second convolution kernel size of 1; And the multiplication output layer is used for multiplying the fused characteristic with the attention weight output by the Sigmoid activation function layer and outputting the characteristic for identifying the density abnormal body.
6. The FNO depth learning model for gravity inversion of claim 1, wherein the activation module employs gelu nonlinear activation functions.
7. The FNO depth learning model for gravity inversion of claim 1, wherein the spatial adaptive operator layers are 11 layers in total, the cross-layer residual jump connection is 5 in total, and p corresponds to values of 3, 5, 7, 9, 11, and p-k=2.
8. A method of training the FNO deep learning model for gravity inversion of any one of claims 1 to 7, comprising the steps of: setting batch processing size, learning rate, optimizer and termination training conditions; taking scalar gravity field data of a known three-dimensional density model and a coordinate grid representing a space position as input of an FNO depth learning model for gravity inversion, and obtaining a corresponding output three-dimensional density model; Constructing a loss function, and calculating a loss value based on the real three-dimensional density model and the corresponding output three-dimensional density model; And optimizing the FNO deep learning model for gravity inversion by an optimizer based on the loss value until a training termination condition is reached, so that training of the FNO deep learning model for gravity inversion is completed.
9. The training method of claim 8, wherein the expression of the loss function is: Wherein the method comprises the steps of Representing a loss function; In order to achieve a loss of structural similarity, , , Is the first A predicted three-dimensional density model of the individual samples; is the first A true three-dimensional density model of the individual samples; N is the total number of the coordinate grids; is the first The first sample of True three-dimensional density values of the individual coordinate grids; is the first The first sample of Predicted three-dimensional density values for the individual coordinate grids; Is a weight coefficient; Representing a loss of consistency of the physical forward performance, The gravity forward abnormal data is the real three-dimensional density model; And forward modeling abnormal data for predicting the gravity of the three-dimensional density model.
10. A gravity inversion method based on the FNO deep learning model for gravity inversion according to any one of claims 1 to 7, comprising the steps of: And acquiring scalar gravity field data and coordinate grids representing the space positions, inputting the trained FNO deep learning model for gravity inversion, acquiring a three-dimensional density model output by the FNO deep learning model for gravity inversion, and finishing gravity inversion.

Description

FNO deep learning model for gravity inversion, training method and gravity inversion method Technical Field The invention relates to the technical field of gravity inversion in geophysical exploration, in particular to an FNO deep learning model for gravity inversion, a training method and a gravity inversion method. Background Gravity exploration is a geophysical method for deducing underground density distribution by measuring the change of a surface gravity field, and has wide application in the fields of mineral exploration, oil and gas resource evaluation, geological structure research and the like. Gravity inversion is a core link of gravity exploration, and aims to quantitatively estimate the density structure of underground medium according to observed gravity anomaly data. The traditional gravity inversion method is mainly divided into two main types of linear inversion and nonlinear inversion. Although the linear inversion method (such as a least square method and a conjugate gradient method) has higher calculation efficiency, the result is seriously dependent on the selection of an initial model and the construction of regularization constraint, is easy to sink into a local optimal solution, and is difficult to solve the problem of strong nonlinearity. The nonlinear inversion method (such as a genetic algorithm, a simulated annealing algorithm and a particle swarm algorithm) has global searching capability, overcomes the dependence on an initial model to a certain extent, but has extremely high calculation cost and slow iteration convergence speed, and is difficult to apply to the problem of large-scale three-dimensional inversion. In recent years, the deep learning technology provides a new idea for gravity inversion. Researchers learn the end-to-end mapping from gravity data to a density model by using architectures such as convolutional neural networks and U-Net, and obtain inversion speed faster than that of the traditional method. However, these grid-based deep learning models have the inherent limitations that the mapping on a specific discrete grid is learned, the generalization capability is limited by the grid resolution of training data, the receptive field is limited, the receptive field is slowly expanded mainly through stacked convolution layers, and critical global features in a gravitational field are difficult to effectively capture, so that the inversion precision of underground structures and complex geological boundaries is insufficient. Fourier nerve operators (Fourier Neural Operator, FNO) act as an emerging framework of nerve operators, the core of which is to learn the mapping between the infinite dimensional function spaces. The FNO utilizes the fast Fourier transform to efficiently process global information by parameterizing the integral kernel in the frequency domain, and has a global receptive field naturally. However, although the standard FNO has a global receptive field, the fixed frequency domain processing mode cannot fully consider the physical facts of the gravity field on the sensitivity difference of underground sources with different depths, so that the inversion precision of a shallow fine structure and a deep abnormal body is limited. Therefore, developing an intelligent inversion model or method which can capture global dependence and pay attention to local detail information and can be embedded into a physical rule becomes an urgent need in the current gravity exploration field. Disclosure of Invention Aiming at the defects in the prior art, the FNO depth learning model, the training method and the gravity inversion method for gravity inversion solve the problem that inversion precision of shallow fine structures and deep abnormal bodies is limited due to the fact that the sensitivity difference of gravity fields to underground different depth sources cannot be fully considered when the gravity inversion is carried out on the existing FNO depth learning model. In order to achieve the aim of the invention, the invention adopts the following technical scheme: The utility model provides an FNO deep learning model for gravity inversion, which comprises a feature lifting layer, at least two layers of space self-adaptive operator layers, a feature projection layer arranged behind the last layer of space self-adaptive operator layer and at least one cross-layer residual jump connection, wherein each layer of space self-adaptive operator layer comprises a global Fourier branch, a local convolution branch, a self-adaptive fusion module, a space attention module and an activation module, and the feature lifting layer, the at least two layers of space self-adaptive operator layers are sequentially connected, wherein: The feature lifting layer is used for splicing the input scalar gravity field data with the coordinate grid representing the space position and projecting the coordinate grid into a high-dimensional feature space to obtain high-dimensional features corr