Seismic Refraction Modeling Using Time-Terms Inversion Based on Linear Programming: A Study on Synthetic Data

Abstract

Seismic refraction is a geophysical method widely used to model the distribution of subsurface velocity. The main challenge of this method is the instability of the inversion that often arises due to noise and inaccuracies in determining the first arrival time (first arrival picking). In general, the inversion is carried out using the Least-Squares method, which tends to be unstable under non-ideal data conditions. To overcome this, this study develops a Time-Terms Inversion (TTI) approach utilizing Linear Programming. The linear formulation of TTI allows the inversion process to be expressed as an optimization problem with a clearly defined objective function, so that the resulting solution is more stable and resistant to data errors. Numerical tests on synthetic data show that this approach can reduce the influence of picking errors while maintaining the accuracy of the velocity model. These results show that the combination of TTI and Linear Programming is effective for seismic refraction modeling under synthetic data conditions affected by noise and picking inaccuracies.