Seismic source spectral properties of crack‐like and pulse‐like modes of dynamic rupture

Abstract

Earthquake source properties such as seismic moment and stress drop are routinely estimated from far‐field body wave amplitude spectra. Some quantitative but model‐dependent relations have been established between seismic spectra and source parameters. However, large variability is seen in the parameter estimates, and it is uncertain how the variability is partitioned among real variability in the source parameters, observational error, and modeling error due to complexity of earthquake behaviors. Earthquake models with dynamic weakening have been found to exhibit two different modes of rupture: expanding‐crack and self‐healing pulse modes. Four representative models are generated to model the transition from crack‐like to pulse‐like. Pulse‐like rupture leads to development of a second corner frequency, and the intermediate spectral slope is approximately 2 in most cases. The focal‐sphere‐averaged lower P and S wave corner frequencies are systematically higher for pulse‐like models than crack models of comparable rupture velocity. The slip‐weighted stress drop ΔσE exceeds the moment‐based stress drop ΔσM for pulse‐like ruptures, with the ratio ranging from about 1.3 to 1.65, while they are equal for the crack‐like case. The variations in rupture mode introduce variability of the order of a factor of 2 in standard (i.e., crack model‐based) spectral estimates of stress drop. The transition from arresting‐ to growing‐pulse rupture is accompanied by a large (factor of ∼1.6) increase in the radiation ratio. Thus, variations in rupture mode may account for the portion of the scatter in observational spectral estimates of source parameters.

Geometric Controls on Pulse‐Like Rupture in a Dynamic Model of the 2015 Gorkha Earthquake

“…We move the U.S. Geological Survey hypocenter (within its uncertainty bounds) closer to the western pinch point, because that adjustment reduces the level and spatial extent of the stress perturbation required to initiate a sustained rupture in our model (this is only a computational device to which we attribute no physical significance). Rupture is initiated on the ramp by imposing a Gaussian‐shaped shear overstress within a 7,500‐m radius of the hypocenter (the red circular overstress patch in Figure a), with peak amplitude 1.5 times the local initial shear stress τ b (details can be found in Equation 11 in Wang and Day, ). The overstress in initiation zone results in a maximum ratio of shear to normal stress of 0.6.…”

“…The fault friction law is one of rate‐dependent dynamic weakening, within a rate and state framework, that has its basis in laboratory experiments (e.g., Dieterich, ; Marone, ; Ruina, ). Here we use the regularized formulation of the friction coefficient proposed by Lapusta et al (), and the steady state friction coefficient is formulated following Dunham et al (), Shi and Day (), and Wang and Day (). Details of the formulation are given by Equations 6 to 10 in Wang and Day (), and the numerical treatment is outlined in Rojas et al ().…”

“…Here we use the regularized formulation of the friction coefficient proposed by Lapusta et al (), and the steady state friction coefficient is formulated following Dunham et al (), Shi and Day (), and Wang and Day (). Details of the formulation are given by Equations 6 to 10 in Wang and Day (), and the numerical treatment is outlined in Rojas et al (). The evolution‐effect parameter b , the reference slip rate V 0 , and the weakening slip rate V w are constant over the fault (see Table ).…”

Microseismicity Simulated on Asperity‐Like Fault Patches: On Scaling of Seismic Moment With Duration and Seismological Estimates of Stress Drops

“…We determine the corner frequency f c for the P and SH waves by applying the spectral fitting method. The approach is the current state-of-art technique for estimating source parameters of observable small earthquakes (Abercrombie, 1995;Allmann & Shearer, 2009;Goebel et al, 2015Goebel et al, , 2017Lin et al, 2012;Shearer et al, 2006;Uchide et al, 2014) as well as for investigating characteristics of seismic signals from simulated source models (Kaneko & Shearer, 2014, 2015Madariaga, 1976;Sato & Hirasawa, 1973;Wang & Day, 2017). The spectrum of the displacement amplitude is fit by…”

Energetic Onset of Earthquakes

“…The early dynamic stage of rupture (EDSR) is commonly modeled as the accelerated growth of both slip and slip region (Lapusta & Rice, ; Ripperger et al, ; Ide et al, ). After accelerated growth, the earthquake evolves either as a crack (Madariaga, ), for instance seen during the M 9.0 2011 Tohoku earthquake; as a moving pulse (Haskell, ; Heaton, ; Nielsen & Madariaga, ; Wang & Day, ), for instance seen during the M 7.9 2015 Nepal earthquake; or as a combination of both. The arrest of earthquakes remains a particular unknown in seismology: Physical models predict that energetic stopping phases may heal the rupture when the arrest is abrupt (Madariaga, ), yet they remain challenging to observe (Kazutoshi & Minoru, , ; Meng et al, ; Savage, ).…”