Investigating Spectral Estimates of Stress Drop for Small to Moderate Earthquakes With Heterogeneous Slip Distribution: Examples From the 2016–2017 Amatrice Earthquake Sequence

Estimates of spectral stress drop are fundamental to understanding the factors controlling
earthquake rupture and high frequency ground motion, but are known to include large, poorly-constrained
uncertainties. We use earthquakes from the 2016–2017 sequence in the Italian Appenines (largest event at
Norcia, Mw 6.3) to investigate these uncertainties and their causes. The similarly-sized events near Amatrice
(Mw 6.0) and Visso (Mw 5.9) enable better constrained relative analysis. We calculate S wave source spectra,
corner frequencies, and spectral stress drop for 30 of the larger events. We compare both empirical and
modeling approaches to isolate the source spectra and calculate source parameters; we also compare our
results with those from published studies. Both random and systematic inter-study variations are larger than
the standard errors reported by any individual study. The reported magnitude dependence of stress drop
varies between studies, being largest for generalized inversions and smallest for more individual event based
approaches. The relative spectral estimates of inter-event stress drop are more consistent; all approaches
estimated higher stress drop in the Amatrice earthquake than the similar-sized Visso earthquake. In contrast,
finite fault inversions of these two earthquakes found that the Visso earthquake had the larger region of
concentrated, higher slip, whereas the Amatrice earthquake had multiple, lower slip, subevents. The Amatrice
spectra contain more high frequency energy than those of the Visso earthquake. This comparison suggests that
consistent measurement of a higher spectral stress drop indicates greater high-frequency ground motion but
may correspond to greater rupture complexity rather than higher stress drop.

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The stress release (or stress drop) during an earthquake is an important
element of seismic hazard forecasting; high stress drop earthquakes radiate more high frequency energy,
causing stronger ground shaking. The stress drop also provides information about the energy budget, and the
size of fault ruptured, and consequently, earthquake triggering and rupture dynamics. Reliable estimates of
stress release are difficult to make, largely because of the ambiguity in removing the distorting propagation
effects experienced by waves traveling from earthquake to seismometer from recorded seismograms. Most
measurements are made using frequency amplitude spectra. We use two methods to estimate earthquake stress
drop for 30 of the larger earthquakes in central Italy (2016–2017) and compare them with the results of previous
studies. We find that the variation between absolute values estimated in different studies is much larger than
the reported formal inversion errors. The relative values are more reliable, with different studies consistently
finding a particular earthquake has relatively high or low stress drop. Direct comparison of the similar-sized,
damaging Amatrice and Visso earthquakes reveals that the relative spectral stress drop estimates reflect the
relative strength of high-frequency ground motion, but may indicate more complex rupture rather than higher
average stress release.