Seismic radiation from dynamic coalescence, and the reconstruction of dynamic source parameters on a planar fault

The dynamic coalescence of two mode II cracks on a planar fault is simulated here using the elastodynamic boundary integral equation method. We focus on the complexity of the resultant slip rate and seismic radiation in the crack coalescence model (CCM) and on the reconstruction of a single crack model (SCM) that can reproduce the CCM waveforms from heterogeneous source parameters rather than coalescence. Simulation results reveal that localized higher slip rates are generated by coalescence as a result of stress interaction between the approaching crack tips. The synthesized seismic radiation exhibits a distinct coalescence phase that has striking similarities to stopping phases in the radiation and propagation properties. The corresponding SCM yields a singular increase in the stress drop distribution, which is accompanied by a sudden decrease in it across the point of coalescence in the CCM. This implies that the generation of high-frequency radiation is more efficient from coalescence than from stopping, although both phenomena exhibit the same strong  ω⁻²  -type displacement spectra.     

Numerical modelling of rise and fall of a dense layer in salt diapirs

Numerical models are used to study the entrainment of a dense anhydrite layer by a diapir. The anhydrite layer is initially horizontally embedded within a viscous salt layer. The diapir is down-built by aggradation of non-Newtonian sediments ( n = 4, constant temperature) placed on the top of the salt layer. Several parameters (sedimentation rate, salt viscosity, perturbation width and stratigraphic position of the anhydrite layer) are studied systematically to understand their role in governing the entrainment of the anhydrite layer. High sedimentation rates during the early stages of the diapir evolution bury the initial perturbation and, thus, no diapir forms. The anhydrite layer sinks within the buried salt layer. For the same sedimentation rate, increasing viscosity of the salt layer decreases the rise rate of the diapir and reduces the amount (volume) of the anhydrite layer transported into the diapir. Model results show that viscous salt is capable of carrying separate blocks of the anhydrite layer to relatively higher stratigraphic levels. Varying the width of the initial perturbation (in our calculations 400–800 m), from which a diapir triggers, shows that wider diapirs can more easily entrain an embedded anhydrite layer than the narrower diapirs. The anhydrite layer is entrained as long as rise rate of the diapir exceeds the descent rate of the denser anhydrite layer. We conclude that the four parameters mentioned above govern the ability of a salt diapir to entrain an embedded dense layer. However, the model results show that the entrained blocks inevitably sink back if the rise rate of the diapir is less than the rate of descent of the anhydrite layer or the diapir is permanently covered by a stiff overburden in case of high sedimentation rates.     

Note on rain-triggered earthquakes and their dependence on karst geology

Recently reported rain-triggered seismicity from three separate storms occurred exclusively in karst geology. In this paper, I discuss how the hydrogeology of karst controls rain-triggered seismicity by channeling of the watershed after intense rainfall directly into the karst network. Such channeling results in very large increases in hydraulic head, and more importantly, substantially increases the vertical stress acting on the underlying pore-elastic media. Rapid loading upon a pore-elastic media induces seismicity by increasing pore pressure at depth in a manner similar to that observed from reservoir impounding. Using a simple 1-D model of a pore-elastic medium, it is shown that the instantaneous fluid pressure increase at depth is a substantial fraction of the pressure step applied at the boundary, followed by time-dependent pore pressure increases associated with the typical linear diffusion problem. These results have implications for the change in fluid pressure necessary to trigger earthquakes, and leads to the following hypothesis to be tested: Unambiguous rain-triggered seismicity will only occur in karst regions.     

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.     

Scaling relations of earthquakes and aseismic deformation in a damage rheology model

We perform analytical and numerical studies of scaling relations of earthquakes and partition of elastic strain energy between seismic and aseismic components using a thermodynamically based continuum damage model. Brittle instabilities occur in the model at critical damage level associated with loss of convexity of the strain energy function. A new procedure is developed for calculating stress drop and plastic strain in regions sustaining brittle instabilities. The formulation connects the damage rheology parameters with dynamic friction of simpler frameworks, and the plastic strain accumulation is governed by a procedure that is equivalent to Drucker–Prager plasticity. The numerical simulations use variable boundary forces proportional to the slip-deficit between the assumed far field plate motion and displacement of the boundary nodes. These boundary conditions account for the evolution of elastic properties and plastic strain in the model region. 3-D simulations of earthquakes in a model with a large strike-slip fault produce scaling relations between the scalar seismic potency, rupture area, and stress drop values that are in good agreement with observations and other theoretical studies. The area and potency of the simulated earthquakes generally follow a linear log–log relation with a slope of 2/3, and are associated with stress drop values between 1 and 10 MPa. A parameter-space study shows that the area-potency scaling is shifted to higher stress drops in simulations with parameters corresponding to lower dynamic friction, more efficient healing, and higher degree of seismic coupling.     

Modelling deformation rates in the western Gulf of Corinth: rheological constraints

The Gulf of Corinth is one of the most active extensional regions in the Mediterranean area characterized by a high rate of seismicity. However, there are still open questions concerning the role and the geometry of the numerous active faults bordering the basin, as well as the mechanisms governing the seismicity. In this paper, we use a 2-D plane strain finite element analysis to constrain the upper crust rheology by modelling the available deformation data (GPS and geomorphology). We consider a SSW–NNE cross-section of the rift cutting the main active normal faults (Aigion, West Eliki and Off-Shore faults). The models run for 650 Kyr assuming an elasto-viscoplastic rheology and 1.3 cm yr⁻¹ horizontal extension as boundary condition (resulting from GPS data). We model the horizontal and vertical deformation rates and the accumulation of plastic strain at depth, and we compare them with GPS data, with long term uplift rates inferred from geomorphology and with the distribution of seismicity, respectively. Our modelling results demonstrate that dislocation on high-angle normal faults in a plastic crustal layer plays a key role in explaining the extremely localized strain within the Gulf of Corinth. Conversely, the contribution of structures such as the antithetic Trizonia fault or the buried hypothetical subhorizontal discontinuity are not necessary to model observed data.     

A multidisciplinary study of a slow-slipping fault for seismic hazard assessment: the example of the Middle Durance Fault (SE France)

Assessing seismic hazard in continental interiors is difficult because these regions are characterized by low strain rates and may be struck by infrequent destructive earthquakes. In this paper, we provide an example showing that interpretations of seismic cross sections combined with other kinds of studies such as analysis of microseismicity allow the whole seismogenic source area to be imaged in this type of region. The Middle Durance Fault (MDF) is an 80-km-long fault system located southeastern France that has a moderate but regular seismicity and some palaeoseismic evidence for larger events. It behaves as an oblique ramp with a left-lateral-reverse fault slip and has a low strain rate. MDF is one of the rare slow active fault system monitored by a dedicated dense velocimetric short period network. This study showed a fault system segmented in map and cross section views which consists of staircase basement faults topped by listric faults ramping off Triassic evaporitic beds. Seismic sections allowed the construction of a 3-D structural model used for accurate location of microseismicity. Southern part of MDF is mainly active in the sedimentary cover. In its northern part and in Alpine foreland, seismicity deeper than 8 km was also recorded meaning active faults within the crust cannot be excluded. Seismogenic potential of MDF was roughly assessed. Resulting source sizes and estimated slip rates imply that the magnitude upper limit ranges from 6.0 to 6.5 with a return period of a few thousand years. The present study shows that the coupling between 3-D fault geometry imaging and accurate location of microseismicity provides a robust approach to analyse active fault sources and consequently a more refined seismic hazard assessment.     

Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets

Planetary topography can either be modelled as a load supported by the lithosphere, or as a dynamic effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However, local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this paper, we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associated stress function. In order to include bottom loading generated by mantle convection, we extend the method of stress functions to include loads with a toroidal tangential component. We further show that toroidal tangential displacement always occurs if the shell thickness varies, even in the absence of toroidal loads. We finally prove that the degree-one harmonic components of the transverse deflection and of the toroidal tangential displacement are independent of the elastic properties of the shell and are associated with translational and rotational freedom. While being constrained by the static assumption, degree-one loads can deform the shell and generate stresses. The flexure equations for a shell of variable thickness are useful not only for the prediction of the gravity signal in local admittance studies, but also for the construction of stress maps in tectonic analysis.     

Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M= 9.2 Sumatra earthquake

The 2004 M = 9.2 Sumatra–Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ∼1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress–strain relation; an aspherical perturbation in viscoelastic structure; a 'static' mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra–Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation.