Time-domain 2D FWI with TTI anisotropy

The modeling operator is based on a star 1D stencil of order 2,4 or 6. It solves the system in parallel over sources . Source injection and receiver sampling is done via cubic interpolation and exponential damping over a 3x3 square around the source location. The Jacobian is derived by linearizing the discretized system and its forward.

Author: Mathias Louboutin, Philipp Witte

       September 2015
       Seismic Laboratory for Imaging and Modeling
       Department of Earch & Ocean Sciences
       The University of British Columbia

Dependencies
Running & Parallelism
Functions
Examples
References

Dependencies

The modeling code uses the following packages, found in the tools part of the software release.

SPOT - object oriented framework for matrix-free linear algebra.
pSPOT - parallel extension of SPOT.

Running & Parallelism

All the examples can be reproduced by running the scripts found in the software release under applications/Modeling/2DAcousticFreqModeling. Start matlab from that directory or run startup in that directory to add the appropriate paths.

The scripts can be run in serial mode but parallel mode is advised for the modeling and imaging examples. Use parpool to start parallel pool with the appropriate configuration and a divisor of 12 workers.

Functions

The modeling code consists of 3 distinct packages which can be found in the tools part of the software release. The main components are listed below

algorithms/TimeModeling

opF - modeling operator
opJ - Jacobian
Gen_data - Data generation function
Born - Born modelling and RTM function
GS - function that output [f,g] misfit and gradient for FWI

operators/misc

opLInterp1D - 1D cubic Lagrange interpolation
opExtension - Pads input with zeros or constant values
opSmooth - 1D smoothing by convolution with triangular kernel
opSaveSnapshot - save history of iterations operator

functions/misc

grid2odn, odn2grid - convert grid vectors to [origin, increment, size] triplet and vice versa

Examples

A few examples are included here

An examples of the 2D FWI capabilities are shown in FWI_TTI_2D.m.

References

.[1] Philipp Witte*, Mathias Louboutin and Felix J. Herrmann, Overview on anisotropic modeling and inversion, Technical report