Time-domain Modeling of Constant-Q Seismic Waves Using Fractional Derivatives

— Kjartansson's constant-Q model is solved in the time-domain using a new modeling algorithm based on fractional derivatives. Instead of time derivatives of order 2, Kjartansson's model requires derivatives of order 2γ, with 0 <γ< 1/2, in the dilatation-stress formulation. The derivatives are computed with the Grünwald-Letnikov and central-difference approximations, which are finite-difference extensions of the standard finite-difference operators for derivatives of integer order. The modeling uses the Fourier method to compute the spatial derivatives, and therefore can handle complex geometries. A synthetic cross-well seismic experiment illustrates the capabilities of this novel modeling algorithm.     

Attenuation and Shock Waves in Linear Hereditary Viscoelastic Media; Strick–Mainardi,Jeffreys–Lomnitz–Strick and Andrade Creep Compliances

Dispersion, attenuation and wavefronts in a class of linear viscoelastic media proposed by Strick and Mainardi (Geophys J R Astr Soc 69:415–429, 1982) and a related class of models due to Lomnitz, Jeffreys and Strick are studied by a new method due to the author. Unlike the previously studied explicit models of relaxation modulus or creep compliance, these two classes support propagation of discontinuities. Due to an extension made by Strick, either of these two classes of models comprise both viscoelastic solids and fluids. We also discuss the Andrade viscoelastic media. The Andrade media do not support discontinuity waves and exhibit the pedestal effect.     

An insight into the Bucaramanga nest

We used the local seismicity for the period of 1993 to 2001, in the northeast of Colombia to show the existence of two slabs in the north and south of the Bucaramanga nest. The northern slab has a dip angle of about 25° and the southern slab has a 50° dip angle, while the dip in the Bucaramanga nest is about 29°. In order to explain the nature of the Bucaramanga nest, we proposed the scenario of collision between these two slabs. Using a 3D Finite Element Model (FEM) we show that collision can concentrate, modify and perturb the stress field. The active process of dehydration embrittlement at intermediate depths and the concentrated stress field in the collision zone may explain the high rate of seismic activity inside the Bucaramanga nest. The perturbed and modified stress field resulting from the simultaneous effect of collision between two subducted slabs and subduction of the lithosphere under its own weight can explain the variation in the focal mechanism of micro-earthquakes and the complexity in the source of the moderate size earthquakes in the Bucaramanga nest.