Numerical modeling of attenuation and non linear effects in computational seismology

We solve elastic waves equations in 2D/3D using a fourth order in time and space finite volume method based on exact Riemann solver and wave limiters and designed particularly to capture shock waves.  We validate our code by comparing our results with spectral elements solutions (SPECFEM). 

 

The goal is to detect the levels of fluid saturations in complex rheological media at different scales (near surface or crustal scale) by homogenizing the rheological laws for different frequency contents of the signal sources. For this purpose, at high frequencies, attenuation and/or non linear effects must be added to the stress-strain relations that affect the apparent/effective seismic wave velocities due to unconsolidated, granular or damaged and fractured nature of solid media.

 

In our present studies, we show first how we include the viscoelastic models using auxiliary differential equation approach as in Martin et al. 2019. Then, we show at two different scales (laboratory and natural near surface) how we are able to reproduce real seismic data for granular and porous media in the range of 300-4000 Hz for a 1m configuration experimental setup and how the attenuation and homogeneized seismic velocities of the porous matrix correlate to gravity laws and can explain the recorded signals. Recorded signals are compared to the numerical solutions for three different vertical pore pressure gradients due to the injection of gas.  

 

After validating the code on this controlled experiment we extend our methods at the scale of a 100m natural site in the Orgeval basin in the Parisian region/ France where we want to model the variations of the seismic velocities in the first tens of meters close to the near surface due to the presence of water contents. The idea is to be able to monitor the fluid contents of the ground in the neighborhood of the rivers and the fluid exchanges between nappes, rivers and the underground at the different periods of time (weekly, monthly and annualy). The Vp/Vs ratios reaching high values around 2 due to the water presence, and the Vp and Vs models being obtained by ray-tracing based first arrival time inversions.

The data are provided by the PIREN-Seine program in the last three years.

 

Complex non-linearity responses of the medium  can be modelled with our codes and also be extended to  damaged faults that can be activated and trigger earthquakes due to bulk and shear moduli decrease.