AM13 Gaussian, Linear least squares tomography

A Matlab script for the following example is available at sippi_AM13_least_squares.m.

sippi_least_squares.m allow solving a linear inverse problem with Gaussian prior and noise model. The tomographic problem can be considered linear in case any of the linear forward models are chosen, and the prior parameterized in slowness.

Load the data

clear all;close all
D=load('AM13_data.mat');
txt='AM13';

Define a Gaussian noise model using e.g.:

%% THE DATA
id=1;
data{id}.d_obs=D.d_obs;
data{id}.d_std=D.d_std;

Define a Gaussiain type prior model, using(for example) the FFTMA method, using slowness (inverse velocity):

im=1;
prior{im}.type='FFTMA';
prior{im}.name='Slowness (ns/m)';
prior{im}.m0=7.0035;
prior{im}.Va='0.7728 Exp(6)';
prior{im}.x=[-1:dx:6];
prior{im}.y=[0:dx:13];
prior{im}.cax=1./[.18 .1];

Finally, define a linear forward model

forward.forward_function='sippi_forward_traveltime';
forward.type='ray';forward.linear=1;
% forward.type='fat';forward.linear=1; % alternative forward model
% forward.type='born';forward.linear=1; % alternative forward model
forward.sources=D.S;
forward.receivers=D.R;
forward.is_slowness=1; % USE SLOWNESS PARAMETERIZATION

The above represents a linear Gaussian inverse problem. This can be solved using sampling methods, or it can be solved using linear least squares inversion.

[m_est,Cm_est,m_reals,options]=sippi_least_squares(data,prior,forward,options);