On the resolution of the isotropic component in moment tensor inversion

Abstract

S U M M A R YIt is in theory possible to solve a full moment tensor from inversion of a few seismograms, using normal-mode data, surface waves or body waves. In fact, the isotropic component is usually set to zero in many inversions, in order to stabilize them. This approximation may be considered valid for tectonic earthquakes, but for other applications (such as the study of nuclear or volcanic explosions, deep earthquakes and induced seismicity), the determination of the volumetric component is a key point of the inversion. Our aim is to investigate under which practical conditions the determination of the isotropic component is feasible, and is mathematically and physically reliable. In the first part, we examine the question from a physical point of view and show that the classical interpretation of a full moment tensor for tectonic events implies rheological constraints that are not always realistic. We therefore propose an extended physical model which includes tectonic and non-tectonic volumetric variations. In the second part, we use the tools of inverse theory to infer mathematical constraints on the problem of full moment tensor inversions, from teleseimic surfacewave or body-wave spectra. In particular, we examine how much of the moment tensor can be solved, in relation to the eigenvalues, the condition number and the sampling of the inverse problem. In addition, the resolution and the correlation matrices show that, among a choice of possible constraints on the full tensor, a constraint on the isotropic component is most valuable. In the third part, we also show some applications of our theoretical developments to regional waveform inversions, using the 1992 April Roermond, the Netherlands, earthquake. In addition to physically reliable estimations of the tectonic and non-tectonic isotropic components in full moment tensor inversions, we finally propose extensions of the basic linear methods that can lead to particular models in subspaces of interest, such as tectonic models, or decompositions in a doublecouple plus a volumetric part. By revisiting carefully the determination and interpretation of moment tensors, we provide new perspectives in the estimation of the model and of its error, for a more flexible tectonic and physical interpretation of source mechanisms.

Source Mechanisms of Induced Earthquakes at The Geysers Geothermal Reservoir

“…A discussion of the isotropic part of the moment tensor must include the possibility that it is an artifact, because it appears to be the most poorly resolved part of the moment tensor. Discussions of this matter can be found in O' CONNELL and JOHNSON (1988), VASCO and JOHNSON (1989), KUGE and LAY (1994), Š ILENÝ et al (1996), (2009), DUFUMIER and RIVERA (1997), JULIAN et al (1998) andCOVELLONE andSAVAGE (2012). This possibility of a greater uncertainty in the isotropic part is supported by the results listed in Table 7, wherem iso is considerably smaller than m o , but sd½m iso is only slightly smaller than sd[m o ].…”

Moment Tensor Inversions of Icequakes on Gornergletscher, Switzerland

“…If the sources are located at shallow depths with respect to the wavelength used in the inversion, the isotropic part of the moment tensor cannot be fully recovered (Dufumier and Rivera, 1997;Julian et al, 1998). In the present study this likely introduced errors in isotropic moments such as artificial negative volumetric changes for the double-couple sources of surface cluster B.…”

A Systematic Analysis of Seismic Moment Tensor at The Geysers Geothermal Field, California

“…It has been shown that care is needed in evaluating the robustness and stability of non-DC and full moment tensor solutions (e.g., Dufumier and Rivera, 1997;Dreger et al, 2000;Vavrycuk, 2001Vavrycuk, , 2011Templeton and Dreger, 2006;Minson et al, 2007;Ford et al, 2008Ford et al, , 2009Ford et al, , 2010). We applied a systematic procedure for the evaluation of aleatoric and epistemic solution uncertainty of seismic moment tensor solutions, using bootstrap, jackknife, and NSS approaches to develop solutions that can be used to investigate the underlying mechanical and fluid-mechanical processes that result in the observed seismicity in The Geysers geothermal field.…”