Computing F-K Spectrum for Seismic Sequences

To compute the F-K spectrum of an earthquake sequence, follow this structured approach. Begin by gathering seismic event data including timestamped coordinates and magnitudes. Preprocess the data by converting temporal and spatial information into numerical arrays compatible with spectral analysis libraries. The core algorithm involves applying a 2D Fourier transform to the spatial-temporal distribution matrix. Key implementation steps include: 1. Organizing earthquake epicenters into a grid-based spatial matrix 2. Applying windowing functions (e.g., Hanning window) to reduce spectral leakage 3. Executing Fast Fourier Transform (FFT) along both temporal and spatial dimensions using functions like numpy.fft.fft2() in Python The resulting F-K spectrum reveals frequency-wave number characteristics, enabling identification of seismic wave propagation patterns and dominant vibration modes. This analysis assists in detecting seismic clusters, migration trends, and potential foreshock/main shock relationships. The computed spectrum can be visualized through contour plots or surface maps using matplotlib.pyplot.contourf() for geological interpretation. This methodology provides quantitative insights into seismic sequence dynamics, supporting earthquake hazard assessment and tectonic studies. The workflow can be integrated with seismic monitoring systems through Python/Matlab scripts with modular functions for data loading, spectrum calculation, and visualization.