A Direct Convergence Method for Computing Synthetic Seismograms for a Layered Half-Space with Sources and Receivers at Close Depths

ABSTRACT This study presents the direct convergence method (DCM), a novel numerical method for efficient computation of synthetic seismograms in a layered half-space when sources and receivers are at close depths. Conventional methods such as the discrete wavenumber method suffer from the slow convergence in such scenarios, which requires impractical wavenumber cutoffs. Although the semi-analytical method (SAM) and peak-trough averaging method (PTAM) offer improvements, SAM involves complex mathematical derivations, and PTAM demands an extra meticulous numerical implementation. DCM addresses these limitations by directly removing the slowly convergent component of the wavenumber-domain integrand over a finite interval and supplementing it with an analytically derived correction term. The method achieves higher accuracy and better stability than PTAM with minimal computational overhead—implementable in fewer than 20 lines of code in frameworks like PyGRT. Validation via the Sommerfeld integral and Lamb’s problem confirms DCM’s robustness and accuracy. Applications to soft sedimentary layers and far-field scenarios demonstrate its reliability. DCM provides a simple, efficient, and easily implementable solution for high-fidelity synthetic seismograms in challenging source–receiver configurations.