Analysis of Multiple Seismic Wave Scattering in Random Media using the FOLDY Method in Geophysics

In geophysical research, the propagation behavior of seismic waves in random media represents a significant topic, particularly when addressing multiple scattering problems. The Foldy method offers an efficient analytical solution for simulating these scenarios. This approach treats scatterers within the medium as randomly distributed point scatterers and establishes a statistically averaged wave field model, thereby circumventing the need for direct solution of complex wave equations. The core of the Foldy method lies in introducing concepts such as effective wavenumber and scattering cross-section, describing coherent wave propagation through solutions of the mean field equation. This method proves particularly suitable for analyzing multiple scattering effects under weak scattering conditions. The analytical solution not only significantly reduces computational costs but also intuitively reflects how scattering affects wave field amplitude and phase characteristics, providing theoretical support for understanding seismic wave propagation in complex media. From a code implementation perspective, the Foldy method typically involves: - Generating random scatterer distributions using statistical functions - Calculating effective medium parameters through ensemble averaging algorithms - Solving the mean field equation using iterative numerical methods - Implementing scattering cross-section calculations based on Born approximation Key functions would include scatterer positioning algorithms, wave number correction routines, and phase compensation modules for coherent wave field reconstruction.