How To Use

Contents

1. Input
2. Analyses
3. Peak Delays
4. Coda Attenuation
5. Body-wave Attenuation
6. Damping

Input

Building the input file requires an understanding of the theory underlying the three techniques. In the Official Documentation, chapters 2-4 are dedicated just to this theory. A detailed description of each input is inside each of the provided input files. A shortest descripion can be found in this wiki at the Input File page.

Analyses

After running, MuRAT produces a Tests folder. Inside, you will find several figures (files _analysis_f_Hz). They allow assessing the quality of the data and inversion (except for the peak delay, which is only regionalised).

Peak delays

The hypotheses behind peak-delay imaging is that peaks increase vs travel times. The figure PD_analysis_frequency allows you to compare the differences (and problems) coming from peak-delay analysis. The user needs to check the fit of the peak-delay behaviour to a line in order to apply the regionalization procedure.

Coda attenuation

Coda attenuation must be constant with increasing ray length to interpret values of Qc as absorption. MuRAT outputs this simple variation for a first-order check on the data. A constant Qc does not mean that the field is diffusive, but indicates that equipartition is likely taking place.

We perform the inversion using the external packages regtools and their evolution for iterative regularisation, the IRTools. The Picard condition gives a first glance at how many coda-attenuation parameters will be solved by the inversion in space.

Body-wave attenuation

The coda-normalisation method requires the use of direct waves that decay linearly with travel time (hypocentral distance). The coda-normalisation analysis figure shows how its normalised logarithm decays for increasing travel time (upper panel). The data (black circles) are compared to the analytical forward with average attenuation measured on the data (red stars). The middle panel shows the behaviour of direct energy Without normalisation and correction for the velocity model. The inversion is tested with the usual Picard condition, showing that, for the chosen parametrisation, more than half of the parameters is solved.

Damping

The inversion for Qc and Q requires to set damping and/or smoothing parameters for each frequency. The L_curve figures show the relation between residual and norm of the solution, if using the regtools. Nevertheless, it is more sensible to employ the IRTools , as they offer much better stability for large inversion problems and allow visualising a cost function considering both damping and smoothing.