Rayleigh Wave Dispersion Curve Inversion: Occam Versus the L1-Norm

We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam\u27s Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam\u27s Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. The use of such a regularization scheme for such an overparameterized inverse problem means blocky subsurface models can be obtained without fixing the layer boundaries in advance. This represents an entirely new philosophy for surface wave inversion

FEM-based linear inverse modeling using a 3D source array to image magma chambers with free geometry. Application to InSAR data from Rabaul Caldera (PNG).

This article is subject to a CC Attribution 3.0 License.In this study, we present a method to fully integrate a family of finite element models (FEMs) into the regularized linear inversion of InSAR data collected at Rabaul caldera (PNG) between February 2007 and December 2010. During this period the caldera experienced a long-term steady subsidence that characterized surface movement both inside the caldera and outside, on its western side. The inversion is based on an array of FEM sources in the sense that the Green’s function matrix is a library of forward numerical displacement solutions generated by the sources of an array common to all FEMs. Each entry of the library is the LOS surface displacement generated by injecting a unity mass of fluid, of known density and bulk modulus, into a different source cavity of the array for each FEM. By using FEMs, we are taking advantage of their capability of including topography and heterogeneous distribution of elastic material properties. All FEMs of the family share the same mesh in which only one source is activated at the time by removing the corresponding elements and applying the unity fluid flux. The domain therefore only needs to be discretized once. This precludes remeshing for each activated source, thus reducing computational requirements, often a downside of FEM-based inversions. Without imposing an a-priori source, the method allows us to identify, from a least-squares standpoint, a complex distribution of fluid flux (or change in pressure) with a 3D free geometry within the source array, as dictated by the data. The results of applying the proposed inversion to Rabaul InSAR data show a shallow magmatic system under the caldera made of two interconnected lobes located at the two opposite sides of the caldera. These lobes could be consistent with feeding reservoirs of the ongoing Tavuvur volcano eruption of andesitic products, on the eastern side, and of the past Vulcan volcano eruptions of more evolved materials, on the western side. The interconnection and spatial distribution of sources find correspondence in the petrography of the volcanic products described in literature and in the dynamics of the single and twin eruptions that characterize the caldera. As many other volcanoes, Rabaul caldera is an active and dangerous volcanic system whose dynamics still need to be understood to effectively predict the behavior of future eruptions. The good results obtained from the application of the method to Rabaul caldera show that the proposed linear inversion based on the FEM array of sources is suitable to generate models of magmatic systems. The method can image in space and time the complex free geometry of the source that generates the deformation, widening our understanding of deformational sources and their dynamics. This takes source modeling a step towards more realistic source models.Peer Reviewe

Homogeneous vs heterogeneous subduction zone models: Coseismic and postseismic deformation

A finite-element model (FEM) incorporating geologic properties characteristic of a subduction zone is compared with FEMs approximating homogeneous elastic half-spaces (HEHS)s to investigate the effect of heterogeneity on coseismic and postseismic deformation predictions for the 1995 Colima-Jalisco M_w =8.0 earthquake. The FEMs are used to compute a coefficient matrix relating displacements at observation points due to unit dislocations of contact-node pairs on the fault surface. The Green's function responses are used to solve the inverse problem of estimating dislocation distributions from coseismic GPS displacements. Predictions from the FEM with heterogeneous material properties, loaded with either of the HEHS dislocation distributions, significantly overestimate coseismic displacements. Postseismic deformation predictions are also sensitive to the coseismic dislocation distribution, which drives poroelastic and viscoelastic relaxation. FEM-generated Green's functions, which allow for spatial variations in material properties, are thus preferable to those that assume a simple HEHS because the latter leads to dislocation distributions unsuitable for predicting the postseismic response

Did a submarine landslide contribute to the 2011 Tohoku tsunami?

Many studies have modeled the Tohoku tsunami of March 11, 2011 as being due entirely to slip on an earthquake fault, but the following discrepancies suggest that further research is warranted. (1) Published models of tsunami propagation and coastal impact underpredict the observed runup heights of up to 40 m measured along the coast of the Sanriku district in the northeast part of Honshu Island. (2) Published models cannot reproduce the timing and high-frequency content of tsunami waves recorded at three nearshore buoys off Sanriku, nor the timing and dispersion properties of the waveforms at offshore DART buoy #21418. (3) The rupture centroids obtained by tsunami inversions are biased about 60 km NNE of that obtained by the Global CMT Project. Based on an analysis of seismic and geodetic data, together with recorded tsunami waveforms, we propose that, while the primary source of the tsunami was the vertical displacement of the seafloor due to the earthquake, an additional tsunami source is also required. We infer the location of the proposed additional source based on an analysis of the travel times of higher-frequency tsunami waves observed at nearshore buoys. We further propose that the most likely additional tsunami source was a submarine mass failure (SMF—i.e., a submarine landslide). A comparison of pre- and post-tsunami bathymetric surveys reveals tens of meters of vertical seafloor movement at the proposed SMF location, and a slope stability analysis confirms that the horizontal acceleration from the earthquake was sufficient to trigger an SMF. Forward modeling of the tsunami generated by a combination of the earthquake and the SMF reproduces the recorded on-, near- and offshore tsunami observations well, particularly the high-frequency component of the tsunami waves off Sanriku, which were not well simulated by previous models. The conclusion that a significant part of the 2011 Tohoku tsunami was generated by an SMF source has important implications for estimates of tsunami hazard in the Tohoku region as well as in other tectonically similar regions

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.Comment: 41 pages, 13 figures. Accepted for publication in a book: "Tsunami and Nonlinear Waves", Kundu, Anjan (Editor), Springer 2007, Approx. 325 p., 170 illus., Hardcover, ISBN: 978-3-540-71255-8, available: May 200

Magma plumbing systems: a geophysical perspective

Over the last few decades, significant advances in using geophysical techniques to image the structure of magma plumbing systems have enabled the identification of zones of melt accumulation, crystal mush development, and magma migration. Combining advanced geophysical observations with petrological and geochemical data has arguably revolutionised our understanding of, and afforded exciting new insights into, the development of entire magma plumbing systems. However, divisions between the scales and physical settings over which these geophysical, petrological, and geochemical methods are applied still remain. To characterise some of these differences and promote the benefits of further integration between these methodologies, we provide a review of geophysical techniques and discuss how they can be utilised to provide a structural context for and place physical limits on the chemical evolution of magma plumbing systems. For example, we examine how Interferometric Synthetic Aperture Radar (InSAR), coupled with Global Positioning System (GPS) and Global Navigation Satellite System (GNSS) data, and seismicity may be used to track magma migration in near real-time. We also discuss how seismic imaging, gravimetry and electromagnetic data can identify contemporary melt zones, magma reservoirs and/or crystal mushes. These techniques complement seismic reflection data and rock magnetic analyses that delimit the structure and emplacement of ancient magma plumbing systems. For each of these techniques, with the addition of full-waveform inversion (FWI), the use of Unmanned Aerial Vehicles (UAVs) and the integration of geophysics with numerical modelling, we discuss potential future directions. We show that approaching problems concerning magma plumbing systems from an integrated petrological, geochemical, and geophysical perspective will undoubtedly yield important scientific advances, providing exciting future opportunities for the volcanological community

Strong interseismic coupling, fault afterslip, and viscoelastic flow before and after the Oct. 9, 1995 Colima-Jalisco earthquake: Continuous GPS measurements from Colima, Mexico

Continuous GPS measurements from Colima, Mexico during 4/93-6/01, bracketing the Oct. 9, 1995 M = 8.0 Colima-Jalisco earthquake, provide new constraints on Rivera plate subduction mechanics. Modeling of margin-normal strain accumulation before the earthquake suggests the Rivera-North America subduction interface was fully locked. Transient postseismic motion from 10/ 95-6/97 is well fit by a model that includes logarithmically-decaying fault afterslip, elastic strain from shallow fault relocking, and possibly a minor viscoelastic response, but is fit poorly by models that assume a dominant Maxwell viscoelastic response of the lower crust and upper mantle, independent of the assumed viscosities. Landward, margin-normal motion since mid-1997 is parallel to but ? 75% slower than the pre-seismic velocity. Afterslip alone fails to account for this slowdown. The viscoelastic response predicted by a FEM correctly resolves the remaining velocity difference within the uncertainties. Both processes thus offset elastic strain accumulating from the relocked subduction interface