EikoNet: A deep neural networking approach for seismic ray tracing

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Introduction

EikoNet is a software package that allows the training of a neural network that satisfies the Factored Eikonal for the computation of travel-time from any source-reciever pair in a user defined velocity model.

This approach is outline in greater detail in the publication: Smith et al. (2020) - EikoNet: A deep neural networking approach for seismic ray tracing - link to paper

Colab Jupyter Notebook

We have provided a Colab notebook to allow uses to go through the examples outlined in the paper provided above. The Colab notebook is separated into a series of sections which are all standalone executable scripts, but require the download and build of the software given in the 'Introduction' section of the notebook. As the software develops we will include additional sections.

Link to the Colab can be found at: link

Installation

The EikoNet software can be installed by using

  python setup.py install

If you wish to also plot comparisons with the python finite-difference software scikit-fmm (link) then an additional packge is required.

  pip install scikit-fmm

Guide to Training and Setup

The software can be separated into the imports:

from EikoNet import database as db
from EikoNet import model as md
from EikoNet import plot as pt

Outlined below is some background information to each of these sections. Additional information and usage can be found at the Colab link.

• EikoNet database

  • This section contains the sampling methods and velocity model classes used in the training of the EikoNet. Outlined below are some of the key information of these functions and setting up your own velocity model class.

  • db.Database - Function called during training to create a random source-receiver database for a given velocity class. Inputs are a input velocity function with the optional arguments: create if you wish to create a new database on load an existing at path, Numsamples the number of samples to draw, randomDist whether to use a random distance sampling over the standard random location method.

  • db.ToyProblem_Homogeneous - A class describing how random sampling of point in the model space relates to the velocity. Inside this class you will have a __init__ that must contains the the xmin and xmax for the model dimension to sample. The function eval takes in an array of source receiver pairs and returns the observed velocity at the source and receiver locations.

  • The classes db.ToyProblem_Homogeneous,db.ToyProblem_1DGraded,db.ToyProblem_BlockModel,db.ToyProblem_Checkerboard and db.Graded1DVelocity all represent classes to evaluate for different velocity models. In all cases the class functions must have a xmin and xmax in the init, and a function eval. Additional functions and variables are optional depending on the use problem

• EikoNet Model

  • The model class contains all the information about the network architecture, model training , model validation, post training travel-time formulation for new points, post training velocity formulation for new points and stationary point formulation

  • md.model - Called initially to setup the structure required for the problem. Inputs are a Velocity model class, path and file names, device to run on and additional optional arguments.

  • md.model.train - Called in training the EikoNet for a specific Velocity model class. This function requires number of epochs to run over, the resampling bounds to run between (typical [0.1,0.9] representing a clamp between 10-90%) and the optional validation percentage.

  • md.model.load - Loading a pre-trained EikoNet model. Input is the path to the eikonet model.

  • md.model.TravelTime - Takes in a numpy array of shape [NumPoints,6] where the table is the source - receiver points in [Xsrc,Ysrc,Zsrc,Xrcv,Yrcv,Zrv] format. This function returns the travel-time between each of the source receiver pairs.

  • md.model.Velocity - Takes in a numpy array of shape [NumPoints,6] where the table is the source - receiver points in [Xsrc,Ysrc,Zsrc,Xrcv,Yrcv,Zrv] format. This function returns the velocity at the receiver location.

  • md.model.StationayPoints - Takes in a two source locations defined in the form [Xsrc1,Ysrc1,Zsrc1] and [Xsrc2,Ysrc2,Zsrc2] to try and determine stationary point values between each of these points. You can either compute for a series of random locations, with number specified by numPoints, or by defining the optimal argument Xpoints which takes an array of size [NumPoints,3] representing the point locations in space

• EikoNet Plot

  • A plotting class that is able to plot the recovered travel-time, recovered velocity model, observed velocity model and finite-difference travel-times (optional argument). This class function should only be used for the toy velocity model examples. However, the md.model.TravelTime and md.model.Velocity could be used with matplotlib to evaluate for a user defined plotting

Developers

Corresponding email - [email protected]

Jonathan Smith - California Institute of Technology
Kamyar Azizzadenesheli - California Institute of Technology
Zachary Ross - California Institute of Technology
Jack Muir - California Institute of Technology