A Test Platform of Back-Projection Imaging with Stochastic Waveform Generation, Part I: The Role of Incoherent Green Functions
Abstract
Back-projection (BP) is a cornerstone method for imaging earthquake
ruptures, particularly effective at teleseismic distances for
deciphering large earthquake kinematics. Its superior resolution is
attributed to the ability to resolve high-frequency (>1 Hz)
seismic signals, where waveforms immediately following the first
coherent arrivals are composed of waves scattered by small-scale seismic
velocity heterogeneities. This scattering leads to waveform incoherence
between neighboring stations, a phenomenon not captured by synthetic
tests of BP using Green’s functions (GF) derived from oversimplified 1D
or smooth 3D velocity models. Addressing this gap, we introduce a novel
approach to generate synthetic Incoherent Green’s Functions (IGF) that
include scattered waves, accurately mimicking the observed inter-station
waveform coherence decay spatially and temporally. Our methodology
employs a waveform simulator that adheres to ray theory for the travel
times of scattered waves, aggregating them as incident plane waves to
simulate the high-frequency scattered wavefield across a seismic array.
Contrary to conventional views that scattered waves degrade BP imaging
quality by reducing array coherence, our synthetic tests reveal that
IGFs are indispensable for accurately imaging extensive ruptures.
Specifically, the rapid decay of IGF coherence prevents early rupture
segments from overshadowing subsequent ones, a critical flaw when using
coherent GFs. By leveraging IGFs, we delve into previously unexplored
aspects of BP imaging’s resolvability, sensitivity, fidelity, and
uncertainty. Our investigation not only highlights and explains the
commonly observed “tailing” and “shadowing” artefacts but also
proposes a robust framework for identifying different rupture stages and
quantifying their uncertainties, thereby significantly enhancing BP
imaging accuracy.