Joint estimate of the co-seismic 2011 Tohoku earthquake fault slip and post-seismic viscoelastic relaxation by GRACE data inversion

SUMMARY Satellite-derived gravity data offer a novel perspective for understanding the physics of megathrust earthquakes at subduction zones. Nonetheless, their temporal resolution and observational errors make it difficult to discern the different phases of the seismic cycle, as the elastostatic deformation (co-seismic) and the stress relaxation by viscous flow (post-seismic). To overcome these difficulties and to take advantage of the physical constraints on the temporal evolution and on the spatial pattern of the earthquake-induced gravity disturbances, we have jointly estimated the fault slip of the 2011 Tohoku earthquake and the rheological stratification by means of a Bayesian inversion of GRACE data time series and within the framework of spherically symmetric self-gravitating compressible viscoelastic Earth models. This approach, in addition to improve the exploitation of satellite-derived gravity data, allows us (i) to constrain the fault slip taking advantage of information from both the co- and post-seismic signatures and (ii) to investigate the trade-off between the fault slip and the shallow rheological stratification. In this respect, it can be used to improve the modelling of crustal displacements from GPS data, even if their higher accuracy and temporal resolution allow to discriminate well the co-seismic signature from the others

MODELLING THE EARTH: COMPRESSIBLE VISCOELASTODYNAMICS, GRAVITATIONAL SEISMOLOGY AND TRUE POLAR WANDER

This thesis reviews and sheds new light on compressible Earth models and theories for the modelling of megathrust earthquakes and rotational instabilities caused by glacial isostatic adjustments and mantle convection. The basic theory is outlined in the first chapter, where we discuss the response of a self-gravitating Earth to external forces and loads seated at its surface or interior and we focus on elastic static perturbations and the transition between the elastic and fluid behaviours of the Earth that occurs on thousand and million years time scales. In the first part of this thesis, we derive the analytical solution of the momentum and Poisson equations for a spherically symmetric viscoelastic Earth model that accounts for compressibility both at the initial state of hydrostatic equilibrium and during the perturbations. This constitutes a step ahead with respect to all previous analytical solutions, which actually neglect compressibility in some aspects, and allows to gain deep insight into the relaxation spectrum of compressible viscoelastic Earth models. In the second part, we discuss long-wavelength gravity anomalies caused by the 2004 Sumatra earthquake and detected by the Gravity Recovery And Climate Experiment (GRACE) space mission. We extend the classic theory in order to interpret gravity anomalies in terms of volume changes within the solid Earth, advection of the initial density field and ocean water redistribution caused by perturbations of the ocean floor and surface topographies. This physics is then exploited in order to develop a novel procedure for the inversion of the principal seismic source parameters (hypocentre and moment tensor) of large earthquakes relying solely on space gravity data. This procedure, which complements traditional seismology and which we shall name Gravitational Centroid Moment Tensor (GCMT) analysis, is applied for the first time to the 2011 Tohoku earthquake. In the third part of the thesis, we discuss issues related to long time scale instabilities of the Earth's rotation. The slow motion of the rotation axis with respect to the mantle, called True Polar Wander (TPW), has continuously been debated after the pioneering works in the sixties by Munk, MacDonald and Gold. We thus discuss TPW due to variations of surface loading from ice ages on hundreds of thousand year time scales, its sensitivity to the elastic or viscoelastic rheologies of the lithosphere and the stabilizing role of mantle density heterogeneities. Also, we face the problem of TPW driven by mantle convection on the million years time scale. Most studies have assumed that on this long time scale the planet readjusts without delay and that the Earth's rotation axis and the maximum inertia direction of mantle convection coincide. We herein overcome this approximation and we provide a novel treatment of the Earth's rotation, which clearly explains the interaction between mantle convection and rotational bulge readjustments, and the physical laws for the characteristic times controlling the polar motion in the directions of the intermediate and minimum principal axes of the mantle convection inertia tensor. We thus clarify a fundamental issue related to mantle mass heterogeneities and TPW dynamics

Incompressible analytical models for spinning-down pulsars

We study a class of Newtonian models for the deformations of non-magnetized neutron stars duringtheir spin-down. The models have all an analytical solution, and thus allow to understand easily thedependence of the strain on the star\u2019s main physical quantities, such as radius, mass and crust thickness.In the first \u201chistorical\u201d model the star is assumed to be comprised of a fluid core and an elastic crustwith the same density. We compare the response of stars with different masses and equations of stateto a decreasing centrifugal force, finding smaller deformations for heavier stars: the strain angle ispeaked at the equator and turns out to be a decreasing function of the mass.We introduce a second,more refined, model in which the core and the crust have different densities and the gravitationalpotential of the deformed body is self-consistently accounted for. Also in this case the strain angle isa decreasing function of the stellar mass, but its maximum value is at the poles and is always largerthan the corresponding one in the one-density model by a factor of two. Finally, within the presentanalytic approach, it is possible to estimate easily the impact of the Cowling approximation: neglectingthe perturbations of the gravitational potential, the strain angle is 40% of the one obtained with thecomplete model

the coseismic slip distribution of a shallow subduction fault constrained by prior information the example of 2011 tohoku mw 9 0 megathrust earthquake

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On the response of the Earth to a fault system : its evaluation beyond the epicentral reference frame

Previous formalisms for determining the static perturbation of spherically symmetric selfgravitating elastic Earth models due to displacement dislocations deal with each infinitesimal element of the fault system in its epicentral reference frame. In this work, we overcome this restriction and present novel and compact formulas for obtaining the perturbation due to the whole fault system in an arbitrary and common reference frame. Furthermore, we show that, even in an arbitrary reference frame, it is still possible to discriminate the contributions associated with the polar, bipolar and quadrupolar patterns of the seismic source response, as well as their relationwith the along strike, along dip and tensile components of the displacement dislocation. These results allow a better understanding of the relation between the static perturbation and the whole fault system, and find direct applications in geodetic problems, like the modelling of long- wavelength geoid or gravity data from GRACE and GOCE space missions and of the perturbation of the deviatoric inertia tensor of the Earth

Time-dependent geoid anomalies at subduction zones due to the seismic cycle

We model the geoid anomalies excited during a megathrust earthquake cycle at subduction zones, including the interseismic phase and the contribution from the infinite series of previous earthquakes, within the frame of self-gravitating, spherically symmetric, compressible, viscoelastic Earth models. The fault cuts the whole 50 km lithosphere, dips 20\ub0, and the slip amplitude, together with the length of the fault, are chosen in order to simulate an Mw = 9.0 earthquake,while the viscosity of the 170 km thick asthenosphere ranges from 1017 to 1020 Pa s. On the basis of a new analysis from the Correspondence Principle, we show that the geoid anomaly is characterized by a periodic anomaly due to the elastic and viscous contribution from past earthquakes and to the back-slip of the interseismic phase, and by a smaller static contribution from the steady-state response to the previous infinite earthquake cycles. For asthenospheric viscosities from 1017-1018 to 1019-1020 Pa s, the characteristic relaxation times of the Earth model change from shorter to longer timescales compared to the 400 yr earthquake recurrence time, which dampen the geoid anomaly for the higher asthenospheric viscosities, since the slower relaxation cannot contribute its whole strength within the interseismic cycle. The geoid anomaly pattern is characterized by a global, time-dependent positive upwarping of the geoid topography, involving the whole hanging wall and partially the footwall compared to the sharper elastic contribution, attaining, for a moment magnitude Mw = 9.0, amplitudes as high as 6.6 cm for the lowermost asthenospheric viscosities during the viscoelastic response compared to the elastic maximum of 3.8 cm. The geoid anomaly vanishes due to the back-slip of the interseismic phase, leading to its disappearance at the end of the cycle before the next earthquake. Our results are of importance for understanding the post-seismic and interseismic geoid patterns at subduction zones

Residual polar motion caused by coseismic and interseismic deformations from 1900 to present

We challenge the perspective that seismicity could contribute to polar motion by arguing quantitatively that, in first approximation and on the average, interseismic deformations can compensate for it. This point is important because what we must simulate and observe in Earth Orientation Parameter time-series over intermediate timescales of decades or centuries is the residual polar motion resulting from the two opposing processes of coseismic and interseismic deformations. In this framework, we first simulate the polar motion caused by only coseismic deformations during the longest period available of instrumental seismicity, from 1900 to present, using both the CMT and ISC-GEM catalogues. The instrumental seismicity covering a little longer than one century does not represent yet the average seismicity that we should expect on the long term. Indeed, although the simulation shows a tendency to move the Earth rotation pole towards 133\ub0E at the average rate of 16.5mmyr-1, this trend is still sensitive to individual megathrust earthquakes, particularly to the 1960 Chile and 1964 Alaska earthquakes. In order to further investigate this issue, we develop a global seismicity model (GSM) that is independent from any earthquake catalogue and that describes the average seismicity along plate boundaries on the long term by combining information about presentday plate kinematics with the Anderson theory of faulting, the seismic moment conservation principle and a few other assumptions. Within this framework, we obtain a secular polar motion of 8mmyr-1 towards 112.5\ub0E that is comparable with that estimated from 1900 to present using the earthquake catalogues, although smaller by a factor of 2 in amplitude and different by 20\ub0 in direction. Afterwards, in order to reconcile the idea of a secular polar motion caused by earthquakes with our simplest understanding of the seismic cycle, we adapt the GSM in order to account for interseismic deformations and we use it to quantify, for the first time ever, their contribution to polar motion. Taken together, coseismic and interseismic deformations make the rotation pole wander around the north pole with maximum polar excursions of about 1 m. In particular, the rotation pole moves towards about Newfoundland when the interseismic contribution dominates over the coseismic ones (i.e. during phases of low seismicity or, equivalently, when most of the fault system associated with plate boundaries is locked). When megathrust earthquakes occur, instead, the rotation pole is suddenly shifted in an almost opposite direction, towards about 133\ub0E

Joint estimate of the rupture area and slip distribution of the 2009 L’Aquila earthquake by a Bayesian inversion of GPS data

Usually, when inverting geodetic data to estimate the slip distributions on a fault, the area is made large enough to more than cover the rupture zone, with regularization producing regions of large slip with very small slip over the rest of the surface.We have developed a new inverse method which assumes that nonzero slip is confined to a rectangular region, and which jointly estimates, using Bayesian methods, the boundaries of this region as well as the slip distribution within it, using a smoothing parameter also determined as part of the inversion. Synthetic tests show that our method can successfully image deeper slip regions not resolved by previous methods, and does not produce spurious regions of nonzero slip. We apply our method to coseismic displacements measured by GPS for the 2009 L'Aquila earthquake, first determining the orientation of the fault assuming a simplified model with uniform slip, and then determining probability density functions for the location, length, and width of the rupture area and for the slip distribution. The standard deviation of slip is about 10 cm and describes a normal-faulting earthquake with a maximum slip of 88 \ub1 11 cm and seismic moment of 3.32+0.30 -0.29 7 1018 Nm

Self-gravitating compressible Maxwell Earth models: the role of the self compression and the compositional initial density gradient

We analyse a new class of self-gravitating Maxwell Earth models that takes the compressibility into account both at the initial state of hydrostatic equilibrium and during the deformations. By resorting to the Correspondence Principle we derive the analytical solution for a particular model with an inviscid core, a Darwin law density profile in the mantle and a continuous compositional initial density gradient. It allows to gain deep insight into the global dynamics of the Earth showing that the compressional stratification is responsible only for stable modes, namely the C0 and M0 buoyancy modes, the D-modes and the transient modes, while the compositional stratification triggers new transient modes and a denumerably set of buoyancy modes, of which the RT-modes are a particular case. We show that the model is unstable only when the square of the Brunt-V{"a}i{"a}sala frequency is positive and the solely unstable modes are the new compositional ones. By resorting to a numerical algorithm we extend our analysis to more general self-compressed compressible models with specific Darwin law density profiles in each layer and a compositional initial density gradient describing the density contrasts at the main Earth interfaces. We show that no buoyancy modes are due to the continuous variation of the initial density but they arise because of the density contrasts while the D-modes are substitute by a non-modal contribution always associated with the compressional relaxation times. Such results shed light on the role of the compositional stratification on the relaxation processes and allow us to deal with the issue of the Earth stability in a more consistent way compared to the past. Besides this they are relevant to model the Post-Glacial rebound and the post seismic deformations

A source model for the great 2011 Tohoku earthquake (Mw=9.1) from inversion of GRACE gravity data

The co-seismic slip distribution of the 2011 Tohoku megathrust earthquake is constrained from GeoForschungsZentrum (GFZ) Gravity Recovery and Climate Experiment (GRACE) Level 2 data time series and our self-gravitating, compressible 1-D Earth model. After spatial localization of space gravity data in the surrounding of the U.S. Geological Survey (USGS) epicenter by means of orthogonal Slepian functions, we estimate the long-wavelength co-seismic gravity signature. The pattern is bipolar: the positive pole off-shore in the Pacific ocean (+3.6\u3bcGal) and the negative pole in the northern Japan and Japan sea (-8.6\u3bcGal). Inversion of the GRACE data resolves average features of finite fault models: the total seismic moment (5.3\ub11 710 22Nm, corresponding to M W=9.1 in agreement with the centroid-moment-tensor solution), the rake angle (87\ub0\ub19\ub0), and the mean position of the slip distribution on the fault plane. We obtain that the mean depth of the rupture is 17.1\ub15km, just below the Moho discontinuity, although we cannot exclude that the rupture also extended to shallower crustal layers and deeper within the lithospheric mantle due to the poor resolution of the along-dip dimension of the fault