Shallow Crustal Defocusing of Near-Fault S-Waves: A physical Origin for Distance attenuation

Alex Marston, Chen Ji, Morgan P. Moschetti, & Jorge G. Crempien

Submitted August 30, 2026, SCEC Contribution #15576, 2026 SCEC Annual Meeting Poster #TBD

Conventionally, near-fault geometrical spreading (GS) of S waves is assumed to follow a 1/R decay, where R is hypocentral distance. While steeper apparent decay rates are occasionally reported for R<50-60 km, their physical origin remains difficult to interpret, presumably due to observational trade-offs with anelastic attenuation, site effects, and radiation pattern. To isolate pure GS, we calculate synthetic seismograms using a 1D crustal seismic velocity model that renders anelasticity negligible. We compute Fourier velocity spectra using 3-component seismograms. For each source depth (2–12 km) and hypocentral distance (15–60 km), we generate 20 random focal mechanisms and simulate 20 receiver azimuths for each mechanism, yielding 400 source–receiver realizations. We calculate the geometric mean of their Fourier velocity spectra to minimize bias associated with source radiation and azimuthal sampling. The resulting geometric-mean spectra have an uncertainty of approximately 0.02 in log10 units. We find that steep GS decay (R-k, k~1.5-2.0) occurs naturally for sources beneath the uppermost crust. This steep decay is driven by the defocusing of upgoing seismic waves entering the low-velocity uppermost crust, reducing direct S-wave amplitudes by a factor of two to three between 15 and 60 km. The GS decay of 1D earth structure is depth- and frequency-dependent. The high frequency Fourier response within the uppermost crust cannot be adequately modeled with the conventional ray-theoretical approximation. Additional tests show that the inferred GS exponent depends on spectral definition: horizontal spectra yield larger k at greater depths and higher frequencies, whereas the low frequency responses of windowed S-wave spectra are less sensitive to source depth. Our calculations further suggest that unmodeled deterministic GS can be mapped into inferred attenuation, producing biases large enough to mimic empirical Q models.

Key Words
Geometric Spreading, Defocusing

Citation
Marston, A., Ji, C., Moschetti, M. P., & Crempien, J. G. (2026, 08). Shallow Crustal Defocusing of Near-Fault S-Waves: A physical Origin for Distance attenuation. Poster Presentation at 2026 SCEC Annual Meeting.

Related Projects & Working Groups
Seismology