ON THE RESOLUTION OF THE ISOTROPIC COMPONENT IN MOMENT TENSOR INVERSION

It is in theory possible to solve a full moment tensor from inversion of a few seismograms, using normal-mode data, surface waves or body wa ves. In fact, the isotropic component is usually set to zero in many i nversions, in order to stabilize them. This approximation may be consi dered 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 pr actical conditions the determination of the isotropic component is fea sible, and is mathematically and physically reliable. In the first par t, we examine the question from a physical point of view and show that the classical interpretation of a full moment tensor for tectonic eve nts implies rheological constraints that are not always realistic. We therefore propose an extended physical model which includes tectonic a nd non-tectonic volumetric variations. In the second part, we use the tools of inverse theory to infer mathematical constraints on the probl em of full moment tensor inversions, from teleseimic surface-wave or b ody-wave spectra. In particular, we examine how much of the moment ten sor can be solved, in relation to the eigenvalues, the condition numbe r and the sampling of the inverse problem. In addition, the resolution and the correlation matrices show that, among a choice of possible co nstraints 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 t he 1992 April Roermond, the Netherlands, earthquake. In addition to ph ysically reliable estimations of the tectonic and non-tectonic isotrop ic components in full moment tensor inversions, we finally propose ext ensions of the basic linear methods that can lead to particular models in subspaces of interest, such as tectonic models, or decompositions in a double-couple plus a volumetric part. By revisiting carefully the determination and interpretation of moment tensors, we provide new pe rspectives in the estimation of the model and of its error, for a more flexible tectonic and physical interpretation of source mechanisms.