Enhancing the accuracy of seismic velocity in near-surface layers through Laplacian spectra analysis of weighted graphs

Shallow seismic surveys can play an important role in sustainable urban planning as well as monitoring of geological changes, contributing to climate resilience and the sustainable management of terrestrial ecosystems. A typical seismic layout involves devices (essentially senders and receivers) that transmit signals among themselves. Such layouts can be modeled by a graph using the notions of vertices and edges. In this paper, we propose a regression model to estimate seismic velocity in common near surface settings from spectra data of the normalized Laplacian matrix of the graph representing the seismic layout. The method is validated through tests on both synthetic and real seismic datasets, demonstrating exceptional accuracy. For the synthetic dataset, our model achieved about 99 % accuracy in velocity estimation. Remarkably, when applied to a real dataset acquired over a sabkha (salty soil) in eastern Saudi Arabia, it estimated the second layer's velocity within 0.3% of the value determined by traditional methods, performed by an experienced geophysicist. In comparison to conventional velocity analysis approaches, the proposed method requires only one or few traces. In addition, it does not require picking of first arrivals, which can be costly and often inaccurate.