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 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.