Optimal Path Constraints Minimize Noise in Seismic Generalized Inversion Analysis

Selecting the path bin with the most path attenuation terms as a constraint yields the minimum noise impact when applying the generalized inversion technique to seismic data, according to an evaluation of synthetic and real datasets. The study demonstrated that the choice of path constraint controls the noise robustness of inverted source and path terms, resulting in more stable estimates of physical parameters such as stress drop and corner frequency. In contrast, the site term remains highly robust across all evaluated path constraints.

The generalized inversion technique decomposes seismic Fourier amplitude spectra into source, path, and site terms to quantify key seismological parameters. However, the inversion method is susceptible to noise contamination in records, particularly for small-magnitude earthquake events, which can bias the resulting parameters. To explain how errors spread through the inversion, the researchers conducted a mathematical analysis of the technique’s linear system, elucidating the specific mechanism that governs noise propagation.

In addition to identifying optimal constraints, the investigation quantified the discrepancy between one-step and two-step generalized inversions, mathematically explaining why the difference between their path bin terms decreases when more attenuation terms are included in the constraint bin. The authors also adapted the Empirical Correction Function approach to enable flexible assessment of path constraints, offering a practical strategy to enhance inversion reliability in noisy data environments.

Subject of Research: Noise robustness and path constraints in seismic generalized inversion

Article Title: The influence of path constraint on the noise robustness of the generalized inversion technique

Article References: Zhou, T., & Xie, Z. (2026). The influence of path constraint on the noise robustness of the generalized inversion technique. Earthquake Engineering and Engineering Vibration, 25(4), 905-923. https://doi.org/10.1007/s11803-026-2412-2

Image Credits: AI Generated

DOI: 10.1007/s11803-026-2412-2

Keywords: generalized inversion technique, seismic Fourier amplitude spectra, path constraint, noise robustness, stress drop, corner frequency, attenuation, seismological parameters, influence, path, constraint, noise