CN-118939953-B - Five-dimensional seismic data interpolation method and system based on coordinates

CN118939953BCN 118939953 BCN118939953 BCN 118939953BCN-118939953-B

Abstract

The invention discloses a coordinate-based five-dimensional seismic data interpolation method and system, which are used for constructing a point-by-point seismic data interpolation model based on NeRF theory, modifying an MLP (multi-level plate) frame by combining an additional convolution layer on the basis of the point-by-point interpolation model to construct a seismic data section-by-section interpolation model, introducing nuclear norm regularization to construct an objective function, reading an original five-dimensional seismic data D obs , and inputting the five-dimensional seismic data with a defect lost on the way into a network to realize reconstruction of the five-dimensional seismic data. The invention eliminates the need for additional marking data, utilizes the unique characteristic of the seismic data, enables a convolution network decoder to output the data section by section, can obviously improve the data processing efficiency by 40 times, increases the nuclear norm regularization in the objective function, and can effectively improve the noise resistance and the robustness of the model.

Inventors

CHEN WENCHAO
GAO WENBIN
WANG QINGFANG
LIU DAWEI
WANG XIAOKAI

Assignees

西安交通大学

Dates

Publication Date: 20260508
Application Date: 20240716

Claims (6)

1. The five-dimensional seismic data interpolation method based on the coordinates is characterized by comprising the following steps of: S1, constructing an unsupervised seismic data point-by-point interpolation model based on NeRF theory, wherein the objective function of the unsupervised seismic data point-by-point interpolation model is as follows: Wherein, the Is a five-dimensional coordinate of the seismic data, For the five-dimensional seismic data to be solved, For the parameter weights of the MLP, Mapping coordinates to functions of the complete seismic data for the MLP, Representing the mean square error of the matrix; s2, combining additional convolution layers to modify the MLP framework, and constructing a section-by-section interpolation model on the basis of the constructed point-by-point interpolation model of the unsupervised seismic data, wherein the section-by-section interpolation model comprises an encoder and a decoder, and the encoder comprises a predefined single FFM layer And an encoder using MLP as prototype, the encoder converting coordinates Conversion to the corresponding latent variable Then, a decoder slave variable based on a convolutional network Reconstructing a complete seismic section using Representing a combination of encoder and decoder, a single FFM layer The method comprises the following steps: Wherein, the Representing the total number of components, the ith frequency component being obtained by linear sampling The representation is made of a combination of a first and a second color, Representing arbitrary coordinates normalized within [0,1 ]; S3, introducing nuclear norm regularization, and constructing an objective function of a section-by-section interpolation model, wherein the objective function of the section-by-section interpolation model is as follows: Wherein, the For the super-parameters used to balance the fidelity and regularization terms in the objective function, In order to be a core norm, And The maximum lengths of the inner coupling and the cross spool, Mapping coordinates to functions of the complete seismic data for the MLP, In order to be a tensor expansion mode, For a particular portion selected in the sampling matrix, Is the object of the corresponding study and, Is the Frobenius norm; s4, reading the original five-dimensional seismic data Five-dimensional seismic data with a gap lost on the way are input into a section-by-section interpolation model, so that the reconstruction of the five-dimensional seismic data is realized.
2. The coordinate-based five-dimensional seismic data interpolation method of claim 1, wherein the five-dimensional seismic data The method comprises the following steps: Wherein, the In the form of the hadamard product, In order to sample the matrix of samples, Is complete seismic data.
3. The coordinate-based five-dimensional seismic data interpolation method according to claim 2, wherein the matrix is sampled The medium elements meet the following conditions: Wherein, the Is five-dimensional seismic data Index in middle is Is an element of (a).
4. The coordinate-based five-dimensional seismic data interpolation method according to claim 1, wherein the objective function is defined for seismic data that does not use conventional moveout correction as: Wherein, the And The total length of the shaft coupling and the cross spool in the seismic source, For the total length of the coupling in the receiver, For indexing of the receiver on the inner coupling, Is a sampling matrix; for common midpoint seismic data using NMO techniques, the objective function is defined as: Wherein, the And The maximum lengths of the inner coupling and the cross spool, In order to be a tensor expansion mode, Is the object of the corresponding study and, The coordinates are mapped to functions of the complete seismic data for the MLP.
5. The coordinate-based five-dimensional seismic data interpolation method of claim 1, wherein the kernel norms The following are provided: Wherein, the Is that Is used to determine the (i) th singular value of (c), Is the total number of singular values.
6. A coordinate-based five-dimensional seismic data interpolation system, comprising: The construction module is used for constructing an unsupervised seismic data point-by-point interpolation model based on NeRF theory, and the objective function of the unsupervised seismic data point-by-point interpolation model is as follows: Wherein, the Is a five-dimensional coordinate of the seismic data, For the five-dimensional seismic data to be solved, For the parameter weights of the MLP, Mapping coordinates to functions of the complete seismic data for the MLP, Representing the mean square error of the matrix; Interpolation module, combining additional convolution layer to modify MLP frame to build section interpolation model based on point interpolation model of constructed unsupervised seismic data, section interpolation model including encoder and decoder, encoder including predefined single FFM layer And an encoder using MLP as prototype, the encoder converting coordinates Conversion to the corresponding latent variable Then, a decoder slave variable based on a convolutional network Reconstructing a complete seismic section using Representing a combination of encoder and decoder, a single FFM layer The method comprises the following steps: Wherein, the Representing the total number of components, the ith frequency component being obtained by linear sampling The representation is made of a combination of a first and a second color, Representing arbitrary coordinates normalized within [0,1 ]; The function module introduces nuclear norm regularization to construct an objective function of the section-by-section interpolation model, and the objective function of the section-by-section interpolation model is as follows: Wherein, the For the super-parameters used to balance the fidelity and regularization terms in the objective function, In order to be a core norm, And The maximum lengths of the inner coupling and the cross spool, Mapping coordinates to functions of the complete seismic data for the MLP, In order to be a tensor expansion mode, For a particular portion selected in the sampling matrix, Is the object of the corresponding study and, Is the Frobenius norm; reconstruction module for reading original five-dimensional seismic data Five-dimensional seismic data with a gap lost on the way are input into a section-by-section interpolation model, so that the reconstruction of the five-dimensional seismic data is realized.

Description

Five-dimensional seismic data interpolation method and system based on coordinates Technical Field The invention belongs to the technical field of seismic signal processing, and particularly relates to a coordinate-based five-dimensional seismic data interpolation method and system. Background In exploration seismology, fully sampled seismic data lays a solid foundation for subsequent tasks such as deconvolution, simultaneous source separation, and fault detection. However, in actual seismic data acquisition, trace loss often occurs in the observed data due to physical or economic constraints. These missing traces carry valuable geological information that may adversely affect subsequent data processing and interpretation. Therefore, reconstruction of seismic data has attracted considerable attention in both academia and industry. At present, the deep learning technology has demonstrated significant potential in various fields, and seismic data interpolation is no exception. Compared with the traditional method, the deep learning method reduces the requirement of a large amount of manual parameter adjustment. In addition, since deep learning utilizes nonlinear activation functions, the neural network model can more effectively capture nonlinear features in data, thereby enhancing information extraction and representation capabilities. Various types of neural networks have been applied to seismic data interpolation, including automatic encoder-based methods, generation of countermeasure networks, deep intra networks, and model driven networks. However, existing work has focused primarily on low dimensional data, such as two-dimensional or three-dimensional seismic data. Five-dimensional seismic data is better able to represent the directionality of geologic features, as well as the variation of seismic response for different offsets and azimuth angles, than these data, so that subsurface properties are more fully understood. However, characterizing complex geological environments in five dimensions using deep learning presents unique challenges because five-dimensional convolution requires more computational resources than three-dimensional convolution. The existing method utilizes the characteristic of three-dimensional convolution operation to construct a five-dimensional convolution neural network. The method adopts the synthesized five-dimensional seismic data as a tag training network so as to enable the data interpolation capability. However, in order to more widely apply the method, further improvement in the calculation efficiency is necessary. In recent years, the field of computer vision has generated a great deal of interest in coordinate-based neural representations and neural radiation field (NeRF) approaches have been proposed. The method requires building a model comprising a Fourier Feature Map (FFM) module and a multi-layer perceptron (MLP) that is capable of encoding the wavefield in a point-mode. The FFM module may convert the spatial coordinates to fourier domain codes, while the MLP maps the fourier codes to pixel values, such as color, density, or occupancy. By training the model using the observed data points, complete and continuous wave field information will be encoded in the weighting parameters of the MLP. Thus, missing data can be reconstructed by querying the values corresponding to the respective coordinates. The existing coordinate-based seismic shot interpolation method adopts an MLP network to encode a seismic wave field, queries the network at unobserved shot positions to recover lost shot sets, however, the method still has the defects, mainly solves the problem of incomplete shot sets, but does not solve the challenge of irregular track deletion in high-dimensional data. Disclosure of Invention The invention aims to solve the technical problems of the prior art, and provides a coordinate-based five-dimensional seismic data interpolation method and system, which are used for solving the technical problems that the prior method needs additional marking data. The invention adopts the following technical scheme: a five-dimensional seismic data interpolation method based on coordinates comprises the following steps: S1, constructing an unsupervised seismic data point-by-point interpolation model based on NeRF theory; s2, combining an additional convolution layer to modify the MLP framework, and constructing a section-by-section interpolation model on the basis of the constructed point-by-point interpolation model of the unsupervised seismic data; s3, introducing nuclear norm regularization, and constructing an objective function of the section-by-section interpolation model; S4, reading the original five-dimensional seismic data D obs, and inputting the five-dimensional seismic data with the defect lost on the way into a section-by-section interpolation model to realize reconstruction of the five-dimensional seismic data. Preferably, the objective function of the point-by-poin