Elastic TTI

This repository contains a simple implementation of the 2D elastic TTI wave equation. This is fully implemented with Devito. This is an experimental setup and only provides basic utilities needed for elastic TTI modeling. These basic utilities are:

• SeismicStiffness: That creates the 4th order elastic tensor from the TTI parameters epsilon, delta, theta, phi, rho. The additional gamma parameter isn't yet implemented. This implements the 3D elastic stiffness tensor as well. The implementation of the transformatin and tensor operation are not currently designed to be optimal but to be mathematically elegant and can therefore take some time to initialize the Stiffness tensor.

• divrot, gradrot: custom divergence and gradient operator using a combination of standard FD and 45 degree rotated FD for better accuracy and less dispersion.

Prerequisite

This codes requires a few packages to be installed: numpy, matplotlib, sympy and mostly Devito. You will need to install Devito with the examples since this uses some of the utilities in it. To do so you can follow the cnda install instructions or do the following:

git clone https://github.com/devitocodes/devito
cd devito
pip install -e .

Example

We provide a single simple example in examples/tti_modeling.py that can be run from the main directory as:

PYTHONPATH=$PWD python3 examples/tti_modeling.py

and will plot the wavefield after the simulation. This implements a simple two layer model.

: Elastic TTI wavefields

Author

Mathias Louboutinmlouboutin3@gatech.edu