MATLAB Code Implementation for Seismic Data Inversion

Seismic data inversion is a crucial technique in geophysical exploration, used to infer subsurface physical parameters from observed data. Among various methods, ray tracing migration is a commonly used approach that reconstructs underground structures by simulating the propagation paths of seismic waves through subsurface media.

Implementing ray tracing migration in MATLAB typically involves the following key steps:

Data Preparation and Preprocessing: The process begins by loading seismic data, typically stored as time series. Preprocessing operations such as noise removal, filtering, or gain adjustment may be required to improve the signal-to-noise ratio. In MATLAB, this can be implemented using functions like audioread for data loading and filter or smoothdata for signal processing.

Velocity Model Construction: Ray tracing depends on the velocity distribution of subsurface media, requiring the establishment of a reasonable initial velocity model. This model can be uniform, layered, or complex based on known geological information. MATLAB's matrix operations make it efficient to create and manipulate 2D/3D velocity models using functions like meshgrid and array operations.

Ray Path Calculation: Using ray tracing methods (such as shortest path method or bending ray method) to compute the propagation paths of seismic waves from sources to receivers. This typically involves iterative optimization to adjust ray paths according to velocity model variations. Implementation may utilize MATLAB's optimization toolbox with algorithms like fmincon for path optimization.

Migration Imaging: After obtaining ray paths, seismic data needs to be mapped to corresponding positions in subsurface space. Common migration methods include Kirchhoff migration or reverse-time migration. The purpose is to convert time-domain seismic signals into depth-domain reflection coefficient distributions. MATLAB's powerful visualization capabilities (imagesc, surf) are particularly useful for displaying migration results.

Inversion Optimization: Initial inversion results may contain errors, requiring iterative optimization (such as least squares method or full waveform inversion) to adjust the velocity model for better matching between synthetic and observed data. MATLAB's optimization toolbox provides functions like lsqnonlin for implementing these inversion algorithms efficiently.

MATLAB's matrix computation capabilities make it particularly suitable for implementing such algorithms, especially for processing and visualizing large-scale seismic data. Additionally, MATLAB's optimization toolbox can be utilized for parameter tuning during the inversion process.

This method has wide applications in seismic exploration and hydrocarbon reservoir prediction, helping researchers interpret subsurface structures more accurately.