Island of Misfit Toys

Welcome to the Island of Misfit Toys!

Our PyPI page and Documentation (work in progress).

This repository contains implementations of various misfit functions found in seismic inversion literature. Our goal is to create a comprehensive collection of these functions to aid researchers and practitioners of seismic inverse problems. We aim for a rapid prototyping environment built on top of deepwave, the primary dependency of our package. Deepwave represents acoustic and elastic forward solvers as a pytorch module and thus integrates pytorch's optimization packages seamlessly into an FWI workflow.

If you have interest in adding features, please add a pull request or contact me directly at tyler@oden.utexas.edu. If you have any trouble with our code or find bugs, please let us know by filling out an issue!

For those curious about our logo's inspiration, search "Misfit Toys" in Rudolph the Red-nosed Reindeer, see the Marmousi model, and the importance of misfits in inverse problems.

Table of Contents

• Getting Started
• Misfit Functions (roadmap for future)

Getting Started

To begin using the misfit functions in this repository, simply run

pip install IslandOfMisfitToys

and should should be ready to go on any linux or arm64 MacOS system. Please let us know if you have trouble with the installation.

Roadmap

(1) One-dimensional $W_1$ and $W_2$ (trace-by-trace)

• Yang et al. 2018

(2) Huber

• Guitton and Symes 2003

(3) $L^1$-$L^2$ hybrid

• Bube and Langan

(4) Normalized and unnormalized Sobolev norms

• Zhu et al. 2021

(5) Fisher-Rao metric

• Zhou et al. 2018

(6) Graph-space OT

• Metivier et al. 2018

(7) Entropic regularization OT

• Cuturi 2013

(8) Misfits based on reduced-order models

• Borcea et al. 2023