MATLAB Demonstration of Split-Step Fourier Algorithm

The Split-Step Fourier Algorithm is a numerical method commonly used for seismic wavefield simulation and imaging. It efficiently solves wave propagation problems in complex media by decomposing them into multiple simpler computational steps. In this MATLAB demonstration, the main program ssf.m implements the core logic of the split-step algorithm. The program first loads input data including a demonstration pulse record file and a constant velocity model file. The pulse record represents the initial wavefield, while the constant velocity file defines the medium's velocity distribution. The data loading is typically handled using MATLAB's file I/O functions like load() or fread(). The algorithm follows three key computational stages: Frequency-wavenumber domain conversion: Utilizes Fast Fourier Transform (FFT) through MATLAB's fft2() function to transform the wavefield from spatial domain to frequency-wavenumber domain Phase shift calculation: Computes phase correction terms based on propagation characteristics of different velocity models using complex exponential operations Inverse transformation: Applies Inverse FFT (ifft2()) to reconstruct the corrected wavefield back to spatial domain This stepwise approach maintains computational efficiency (benefiting from FFT's O(N logN) complexity) while accurately simulating wave propagation effects in heterogeneous media. The constant velocity model serves as the simplest test case, allowing users to validate the algorithm's basic functionality before substituting with more complex velocity models for practical scenario simulations. This demonstration package is particularly suitable for two user groups: Seismic imaging beginners: Ready-to-use code helps understand numerical implementation of wavefield propagation Algorithm researchers: Uses constant velocity model as benchmark for testing modified split-step variant algorithms The implementation demonstrates proper handling of Fourier domain operations, including appropriate padding and shifting techniques to avoid wraparound errors, and efficient matrix operations characteristic of MATLAB's vectorized computing capabilities.