Reducing nonuniqueness in finite source inversion using rotational ground motions

Abstract

We assess the potential of rotational ground motion recordings to reduce nonuniqueness in kinematic source inversions, with emphasis on the required measurement accuracy of currently developed rotation sensors. Our analysis is based on synthetic Bayesian finite source inversions that avoid linearizations and provide a comprehensive quantification of uncertainties and trade-offs. Using the fault and receiver geometry of the Tottori 2000 earthquake as a test bed, we perform inversions for two scenarios: In scenario I, we use translational velocity recordings only. In scenario II, we randomly replace half of the velocity recordings by rotation recordings, thus keeping the total amount of data constant. To quantify the noise-dependent impact of rotation recordings, we perform a sequence of inversions with varying noise levels of rotations relative to translations. Our results indicate that the incorporation of rotational ground motion recordings can significantly reduce nonuniqueness in finite source inversions, provided that measurement uncertainties are similar to or below the uncertainties of translational velocity recordings. When this condition is met, rupture velocity and rise time benefit most from rotation data. The trade-offs between both parameters are then strongly reduced, and the information gain nearly doubles. This suggests that rotational ground motion recordings may improve secondary inferences that rely on accurate information about rise time and rupture velocity. These include frictional properties of the fault, radiation directivity, and ground motion in general.

Improved finite-source inversion through joint measurements of rotational and translational ground motions: a numerical study

“…It seems like the bottom row of the subfaults does not show any improvement by the incorporation of rotational ground motion data. This agrees with several studies (e.g., Bernauer et al, 2014;Cotton and Campillo, 1995;Semmane et al, 2005;Monelli and Mai, 2008;Mendoza and Hartzell, 1989). The total cumulative information gain over all 24 sub- Figure 3.…”

“…One major advantage of this method is the possible comparison between results of very different experiments by quantification of the inversion quality. For further details on the method we refer to the publications of Bernauer et al (2014) and Tarantola (2005).…”

“…At this point we want to emphasize that, due to the theoretical nature of this study, the geographical location of fault and receivers are in no way related to real data of past earthquakes or geographical areas. The parametrization of the fault and the rupture itself is used in the same manner as in Bernauer et al (2014): we break up the fault plane into 8 × 3 = 24 quadratic subfaults. Each subfault is filled by 8 × 8 = 64 moment tensor point sources with a regular spacing of 500 m between the point sources.…”

“…Following the approach by Bernauer et al (2014), we employ a Bayesian, i.e., probabilistic, inversion algorithm and compare the inversions with different data types and different earthquake source mechanisms. Our data consist of wave-field seismograms calculated at receiver positions at the Earth's surface by numerical simulations in six components (three translational and three rotational components).…”

“…Because rotations around the horizontal axes (i.e., ω x and ω y in Eq. 2) carry information about vertical gradients, which is not possible to resolve with common arrays on the Earth's surface (Bernauer et al, 2014), we expect to see an even greater benefit for inversions for the dip-slip scenario due to the higher energy in the horizontal rotation components.…”