. (2006): PSGRN/PSCMP -a new code for calculating co-and post-seismic deformation, geoid and gravity changes based on the viscoelasticgravitational dislocation theory.

Deformation models used for explaining the triggering mechanism often assume pure elastic behaviour for the crust and upper mantle. In reality however, the mantle and possibly the lower crust behave viscoelastically, particularly at long-term scale. Consequently, the stress field of an earthquake is in general time dependent. In addition, if the elastic stress increase were enough to trigger a later earthquake, this triggered event should occur instantaneously and not many years later. Hence, it is adequate to include inelastic behaviour when analysing stress transfer and earthquake interaction.In this work, we analyse a sequence of 10 magnitude M s > 6.5 events along the North Anatolian Fault between 1939 and 1999 to study the evolution of the Coulomb stress field.We investigate the triggering of events in the series by stress transfer, taking viscoelastic relaxation into account. We evaluate the contribution of elastic stress changes, of post-seismic viscoelastic relaxation in the lower crust and mantle, and of steady tectonic loading to the total Coulomb stress field. We analyse the evolution of stress in the region under study, as well as on the rupture surfaces of the considered events and their epicentres. We study the state of the Coulomb stress field before the 1999 Izmit and Düzce earthquakes, as well as in the Marmara Sea region.In general, the Coulomb stress failure criterion offers a plausible explanation for the timing and location of the events in this area and for this sequence of events. However, we show that using a purely elastic model disregards an important part of the actual stress increase/decrease. In several cases, post-seismic relaxation effects are important and greater in magnitude than the stress changes due to steady tectonic loading. Consequently, viscoelastic relaxation should be considered in any study dealing with Coulomb stress changes. of 39According to our study, and assuming that an important part of the rupture surface must be stressed for an earthquake to occur, the most likely value for the viscosity of the lower crust or mantle in this region is 5⋅10 17 -10 18 Pa⋅s. Our results also suggest that other time-dependent processes apart from viscoelastic relaxation might have been involved in the triggering of the 1999 Düzce event. Finally, we argue that the Marmara Sea region is currently being loaded with positive Coulomb stresses at a much faster rate than would arise exclusively due to steady tectonic loading on the North Anatolian Fault.

S U M M A R YData collected during two Global Positioning System campaigns in 1994 and 1996 across Chile and western Argentina (22 stations), in the area where the M w = 9.5 1960 May 22 Valdivia earthquake took place, shows ground motion velocities that cannot be fully explained by the elastic strain accumulation during the interseismic phase of an earthquake deformation cycle. We use dislocation models to reproduce the observed velocities, with a 3-D source in a medium with one elastic layer overlying a Maxwell viscoelastic half-space, and a planar rupture surface with uniform coseismic slip. The reason for avoiding a more detailed and elaborated model is that knowledge about the Valdivia earthquake source parameters and the area where the event took place is poorly constrained. We focus, therefore, on examining the first-order postseismic deformation, and ignore finer details about the heterogeneity of the Earth. By means of a grid search inversion over more than a million different models, we derived the most likely values for some of the medium and source parameters involved in the deformation process, namely viscosity (η), thickness of the elastic layer (D), average slip on the rupture surface (U 0 ) and the seismic coupling coefficient (χ ). According to our study, the optimum values are: η = 10 20 Pa · s, D = 46 km, U 0 = 15 m and χ = 96. A clear difference is seen between the surface deformation caused by silent-slip on the rupture surface and the one caused by postseismic relaxation processes, two possibilities proposed to explain the anomalous velocities. We find that the deformation associated with the 1960 Valdivia event can still be observed after several decades and it is the most likely explanation for the velocity component that cannot be explained by plate convergence. Our model also predicts that this deformation will still be measurable for several more decades. Our model reproduces the first-order pattern of the measured GPS velocities, showing good agreement with recent finite-element studies, with the advantage of simplicity and short computation time, allowing the extensive search for the best-fitting model.