Approximation of seismic velocities from the spectrum of weighted graphs

Extracting seismic velocities from recorded seismic data requires converting the shot gathers to mid-point gathers, calculating the velocity spectrum, and picking the velocity values. In this paper, we propose to use graph theory to extract the seismic velocity values directly from the mid-point gathers. We use spectral data of a weighted graph model for approximating the seismic velocity. We develop a regression model to predict the seismic velocity from the largest eigenvalue of the graph representing the physical system. The approach is tested on a synthetic seismic data that represent a typical near-surface geological situation. The method was able to predict the seismic velocity of the second layer with 99.4% accuracy.