Numerical inversion of deformation caused by pressure sources: application to Mount Etna (Italy)

The interpretation of geodetic data in volcanic areas is usually based on analytical deformation models. Although numerical finite element (FE) modelling allows realistic features such as topography and crustal heterogeneities to be included, the technique is not computationally convenient for solving inverse problems using classical methods. In this paper, we develop a general tool to perform inversions of geodetic data by means of 3-D FE models. The forward model is a library of numerical displacement solutions, where each entry of the library is the surface displacement due to a single stress component applied to an element of the grid. The final solution is a weighted combination of the six stress components applied to a single element-source. The pre-computed forward models are implemented in a global search algorithm, followed by an appraisal of the sampled solutions. After providing extended testing, we apply the method to model the 1993–1997 inflation phase at Mt Etna, documented by GPS and EDM measurements. We consider four different forward libraries, computed in models characterized by homogeneous/heterogeneous medium and flat/topographic free surface. Our results suggest that the elastic heterogeneities of the medium can significantly alter the position of the inferred source, while the topography has minor effect.     

Quasi-static analysis of strike fault growth in layered media

We study the effects of structural inhomogeneity on the quasi-static growth of strike-slip faults. A layered medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space with different elastic property. Mode III crack is employed as a mathematical model of strike-slip fault, which is nucleated in the lower half-space and then propagates towards the interface. We adopt FEM-β, newly proposed analysis method for failure, to simulate the quasi-statistic crack growth governed by the stress distribution in layered media. Our results show that along planar traces across interfaces a compliant upper layer has significant effects on promoting/suppressing crack growth before/after its extension into the layer and vice versa for a rigid one. This proposes a possibility that surface breaks due to strike-slip faulting could be arrested by deposit layers at the topmost part of the Earth's crust.     

Stable inversions for complete moment tensors

The seismic moment tensors for certain types of sources, such as volcanic earthquakes and nuclear explosions are expected to contain an isotropic component. Some earlier efforts to calculate the isotropic component of these sources are flawed due to an error in the method of Jost & Herrmann. We corrected the method after Herrmann & Hutchensen and found great improvement in the recovery of non-double-couple moment tensors that include an isotropic component. Tests with synthetic data demonstrate the stability of the corrected linear inversion method, and we recalculate the moment tensor solutions reported in Dreger et al. for Long Valley caldera events and Dreger & Woods for Nevada Test Site nuclear explosions. We confirm the findings of Dreger et al. that the Long Valley volcanic sources contain large statistically significant isotropic components. The nuclear explosions have strikingly anomalous source mechanisms, which contain very large isotropic components, making it evident that these events are not tectonic in origin. This indicates that moment tensor inversions could be an important tool for nuclear monitoring.     

Surface wave tomography for azimuthal anisotropy in a strongly reduced parameter space

Large scale seismic anisotropy in the Earth's mantle is likely dynamically supported by the mantle's deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for evaluation of dynamic models to allow more general axis orientation. In this study, we derive 3-D finite-frequency surface wave sensitivity kernels based on the Born approximation using a general expression for a hexagonal medium with an arbitrarily oriented symmetry axis. This results in kernels for two isotropic elastic coefficients, three coefficients that define the strength of anisotropy, and two angles that define the symmetry axis. The particular parametrization is chosen to allow for a physically meaningful method for reducing the number of parameters considered in an inversion, while allowing for straightforward integration with existing approaches for modelling body wave splitting intensity measurements. Example kernels calculated with this method reveal physical interpretations of how surface waveforms are affected by 3-D velocity perturbations, while also demonstrating the non-linearity of the problem as a function of symmetry axis orientation. The expressions are numerically validated using the spectral element method. While challenges remain in determining the best inversion scheme to appropriately handle the non-linearity, the approach derived here has great promise in allowing large scale models with resolution of both the strength and orientation of anisotropy.     

Instantaneous deformation from continuous GPS: contributions from quasi-periodic loads

Continuous GPS (CGPS) coordinate time-series are known to experience repeating deformation signals with seasonal and other periods. It is unlikely that these signals represent perfect sinusoids with temporally constant amplitude. We develop an analysis method that accommodates temporal variations in the amplitudes of sinusoidal signals. We apply the method to simulated coordinate time-series to numerically explore the potential consequences of neglecting decadal variation in amplitude of annual motions on the residual-error spectra of CGPS measurements, as well as potential bias in estimates for secular site velocity. We find that secular velocity bias can be appreciable for shorter time-series, and that residual-error time-series of longer duration may contain significant power in a broad band centred on semi-annual frequency if temporal variation in the amplitude of annual motions is not accounted for in the model used to reduce the observations to residuals. It may be difficult to differentiate the bandpass filtered signature of mismodelled loading signals from power-law noise, using residual-error spectra for shorter time-series. We provide an example application to a ∼9-yr coordinate time-series for a CGPS station located in southern California at Carbon Creek Control Structure (CCCS), which is known to experience large amplitude seasonal motions associated with the Santa Ana aquifer system.