MuRAT is a Matlab Package for Seismic Attenuation Tomography at multiple Earth scales using Body and Coda Waves.
MuRAT is a complete software package for measuring seismic attenuation, scattering, and absorption from passive and active data, and map 2D and 3D variations of these parameters in space.
MuRAT also comes in Python and C++ versions (under development) to provide a fully-integrated solution for seismic attenuation imaging.
MuRAT1.0 was first developed by Luca De Siena (Johannes Gutenberg University, Mainz, Germany) during his PhD at the INGV-Osservatorio Vesuviano, Italy, and published in 2014 while he was research assistant at the Westfälisches Wilhelms Universität, Münster.
MuRAT2.0 is the result of the activity of the Volcano Imaging group, led by De Siena during his stint as permanent Lecturer at the University of Aberdeen, UK.
The group of active users (providing questions, feedback, snippets of code) comprises De Siena’s PhD students at the University of Aberdeen. It includes PhD students he co-supervises internationally.
2006-2010: MuRAT (at the time named “Multi-scale reasonable attenuation tomography analysis”) is built using Matlab, c++, csh and Fortran codes mostly developed at INGV-Osservatorio.
2010-2013: MuRAT1.0 is developed as a 3D direct-wave attenuation imaging Matlab-only code with the contribution of Christine Thomas and Richard Aster.
2014: MuRAT1.0 is published in De Siena et al. 2014, JVGR, with two sample datasets (Mount St. Helens and Vesuvius) JVGR article
2019: MuRAT2.0 is released including 2D scattering/absorption mapping and kernel-based inversion and re-branded Multi-Resolution Seismic Attenuation Tomography. [GitHub Repository] (https://github.com/LucaDeSiena/MuRAT)
The full documentation for MuRAT2.0 is under construction. This README file and the linked internet sites are to be used as a reference.
SYSTEM: The program works on: 1) Macbook pro with High Sierra, Matlab R2017a; 2) Ubuntu 16.04.6 LTS, Matlab R2017a.
Necessary Toolboxes: Signal Processing, Curve Fitting, Image Processing (compulsory) and Mapping (optional, for geolocalisation - Romania example).
Two sample datasets (Mount St. Helens and Romania) can be downloaded at https://doi.pangaea.de/10.1594/PANGAEA.893893 to test the code. The third sample input (Pollino) in the working directory works with a dataset that may be requested to Luca De Siena.
The current version works following these steps:
Download the package at https://github.com/LucaDeSiena/MuRAT.
Download the two sample datasets at https://doi.pangaea.de/10.1594/PANGAEA.893893. Unzip the MSH (Mount St. Helens) and Romania datasets and put the folders in Murat-master folder. Delete the zipped files.
MuRAT works with a single input file in .xsl format (for now). Build the Input file starting from the samples (either Input_MSH.xsl or Input_Romania.xsl). Read the instructions presented in the next sections.
After the L-curve plots are visible, a prompt asks for the smoothing parameter. Input them based on the plot.
When applying MuRAT to your dataset, use one of the Excel Input files as a template. Read the comments attentively and edit only the required parameters. Start with a “pa=1” or “pa=2” analysis. “pa=3” only works with a suitable velocity model.
Available indexes: 1, 2, or 3 - Default -> 1
Analysis = 1 performs a pick-delay and Qc analysis without kernels, as De Siena et al. 2016 (EPSL)
Analysis = 2 performs a pick-delay and Qc analysis with kernels, as De Siena et al. 2017 (GRL)
Analysis = 3 performs a pick delay, Qc with kernels, and P/S wave attenuation with the coda normalisation method, as De Siena et al. 2017 (GRL) and 2017 (Scientific Reports) combined.
Name of the folder containing output files and figures. It will appear in the working directory
Directory where MuRAT.m is contained - Default = ./
Directory containing the SAC files - Default = ./sac_Label
Figures’ output format as per Matlab functions - Default -> jpeg
Set visibility during computation, set on or off - Default -> on
These are the coordinates of the sections in the 3D V and Q models. Only available for Analysis=3
P or S
Available indexes: 2 or 3 - Default -> 2
Index one in the time files contains the origin time of events. Index two in the time files contains the P-wave phase. Index three in the time files contains the S-wave phase.
Available indexes: 1, 2 or 3 - Default -> 1
MuRAT works with one vertical (1) or two horizontal (2) recordings, or with the three components(3) of motion.
Available indexes: 0 or any number n in the data range - Default -> 0
n corresponds to the SAC recording of the spectrogram that the user wants to plot.
This input is the frequency where the analyses will be carried on, depending on the data recordings.
Maximum Peak Delay Time
This input is the maximum time from picking where the maximum of the envelope will be searched for in the peak delay analysis.
Minimum Peak Delay Time
This input is the minimum time from picking where the maximum of the envelope will be searched for in the peak delay analysis.
Starting Lapse Time
This input is the starting time for the coda window, used for both the coda attenuation and the total-attenuation analyses.
Coda Window Length
This input is the length of the coda window for the coda attenuation analysis.
This input is the average velocity of the medium, in the case that the origin-time is absent from recordings or a velocity model is unavailable - Default -> 0
SAC Origin Time
This input is the origin-time of the event. The best practice is to save it in the SAC file as o variable -> SAChdr.time.o. If this is unavailable set it as Default -> 
SAC P Time
This input is the P-wave time of the event; this parameter is compulsory. The best practice is to save it in the SAC file as a variable -> SAChdr.time.a
SAC S Time
This input is the S-wave time of the event. The best practice is to save it in the SAC file as t0 variable -> SAChdr.time.t0. If this is unavailable set it as Default -> 
Length Window for Body Wave and Noise
This input is the window length that the user sets to compute the energy for P or S waves and noise. Only available for Analysis=3
Start Window Noise
This input sets the seconds before P-wave arrival where the window to compute noise starts. Only available for Analysis=3
Import Option for Events and Stations
Available indexes: 1 or 2 - Default -> 2
It is necessary to define source and station locations for mapping: the user can import event origin-time and coordinates of events and station from an external .txt file (1) or directly from the SAC files (2). Index one is the original format of MuRAT 1.0 and requires even.txt and staz.txt files as per sample files. Index two is the ideal format, storing event and station information as latitude and longitude in the SAC header. The user needs to fill the following variables in the header:
Event: Name of event - SAChdr.event.kevnm; Station latitude - SAChdr.event.evla; Station longitude- SAChdr.event.evlo; Station depth - SAChdr.event.evdp
Station: Name of station - SAChdr.station.kstnm; Station latitude - SAChdr.station.stla; Station longitude- SAChdr.station.stlo; Station elevation - SAChdr.station.stel
Origin of the Grid
The origin of the 2D or 3D grid for imaging is either in UTM or lat/long with depths in meters or kilometers.
Name Events File
The Name of the file containing events’ coordinates, for Import Option = 1. The format is:
even.txt: Column (1) = twelve numbers for the origin time of the event (date+time in seconds); Column (2) = UTM (WE) or latitude; Column (3) = UTM (SN) or longitude; Column (4) = Depth in meters or km
Name Stations File
Name of the file containing stations’ coordinates, for Import Option = 1. The format is:
staz.txt: Column (1) = Max four characters; Column (2) = UTM (WE) or latitude; Column (3) = UTM (SN) or longitude; Column (4) = Depth in meters or km
Number of X Nodes, Number of Y Nodes and Grid Step
The number of X and Y layers, and the step of the mapping grid. Must be defined by the user to include all events’ and stations’ locations.
Meters or Degrees
Can be set to either 1 (meters) or 111 (meters in degrees).
Set 1 to Create Rays - NOT RECOMMENDED
Can be set to either 0 (does not create) or 1 (creates) to build a unique variable containing all rays in 3D. The variable will become BIG for extensive tomographic datasets but can be useful as input for other programs.
Depth Synthetic Model Layer
This input sets the depth (negative) to create a two-layer synthetic test. Only available for Analysis=3.
Available indexes: 1 or 3
This input sets the dimension of the velocity model. In the case no 3D model is available, MuRAT uses iasp91. Only available for Analysis=3.
Name Velocity Model
The name of the file containing the 3D velocity model. Only available for Analysis=3.
Size Checkerboard Anomalies
Available indexes: 2 or 4
This input sets the dimension of the checkerboard anomalies to either twice or four times the step of the imaging grid.
Highs Checkerboard Anomalies and Lows Checkerboard Anomalies
This input sets the high-attenuation and low-attenuation values (as inverse Q and inverse Qc) for the checkerboard tests.
Linear or Nonlinear
Available indexes: 0 or 1 - Default -> 0
With this input, the user decides to inverts coda attenuation with either a linearised (0) or non-linear (1) approach.
Threshold Linear Fit
The maximum inverse-Qc uncertainty used to weight the coda attenuation data. To be set to an appropriate parameter for the linearised inversion.
Length Nonlinear Fit Window and Number Nonlinear Fit Window
These inputs correspond to the length and the number of windows used to compute coda energies for the inversion, respectively. E.g., for a total coda window of 15 seconds, the user can set either three windows of 5 seconds each or five windows of 3 seconds each. To be set to appropriate parameters for the non-linear inversion.
Minimum Nonlinear Inverse Qc, Maximum Nonlinear Inverse Qc, and Total Nonlinear Inverse Qc
With these inputs, the user searches for the Qc minimising the inversion from a minimum inverse Q (e.g. 0) to a maximum inverse Qc (e.g. 0.01). The total number of Qc are equally-spaced and defined between minimum and maximum. To be set to appropriate parameters for the non-linear inversion.
All the output files (.txt) and figures (in the format defined by the user) are stored in the Label folder, created in the Working Directory. The first three columns of the output files correspond to WE, SN, and depth. The fourth column is the mapped parameter.
The variations of Log10 Peak delay from the average - the parameter used to map scattering attenuation. The depth is set to -1000 m. Only four columns as the parameters are just regionalised, not inverted.
Variations of inverse Qc, alias coda attenuation - the parameter used to map absorption. The depth is set to -1000 m.
Analysis = 1: Only four columns as the parameters are just regionalised, not inverted.
Analyses = 2 or 3: The fifth and sixth columns correspond to the input and output of the checkerboard test, respectively. The seventh and eight columns are the first two 2D kernels.
Q3D.txt - Only for Analysis = 3
Variations of inverse Q used to map total attenuation. The fifth and sixth columns correspond to the input and output of the 3D checkerboard test, respectively. The seventh column provides the values of the resolution matrix. The eighth column is the result of a synthetic test using the actual result as input - this is improper, but used in some studies. The ninth and tenth columns are the input and output of the two-layer synthetic test, where the interface is at Depth Synthetic Model Layer.
All the figures (in the Figures Format defined by the user) are stored in the Label folder, created in the Working Directory. If the Mapping Toolbox is available and the coordinates are in latitude and longitude, the figures will show coastlines.
A figure to plot rays either in 2D (Analyses + 1 or 2) or 3D (Analysis = 3) - it will show rays in the reference system of the pre-defined grid with sources and stations used.
Qc_sensitivity.Figures format - Only available for Analyses = 2 or 3
A figure to plot the source-station normalised kernel for the first source-station pair. It will show the sensitivity in the reference system of the pre-defined grid.
Spectrogram.Figures format - Optional
A plot of the first spectrogram in the dataset. The plot can be used to set appropriate frequency, peak delay, and coda inputs.
A figure to evaluate the appropriate peak-delay and coda inputs. The upper panel should show a constant inverse Qc with travel time. The lower panel should show an increasing peak delay with travel time. Red dots correspond to outliers. For Qc, the maximum uncertainty to define outliers is set as Threshold Linear Fit, for the non-linear it is pre-defined. For the peak-delay, we define as outliers all the values over twice the standard deviation from the average.
CN_plot.Figures format - Optional
A figure to evaluate if the direct-energy decrease with travel time follows the assumption of the coda-normalisation method (upper panel). MuRAT2.0 inputs the Qc measurements obtained in previous steps in the equation. This operation removes the effect of coda attenuation variations, improving the fit for the direct wave attenuation. The lower panel shows the effect of a residual geometrical spreading on coda attenuation, with the eventual presence of outliers.
Lc_Qc.Figures format (for Analyses = 2 or 3) and Lc_CN.Figures format (for Analyses = 2 or 3)
These are the only plots appearing if Figures Visibility = 0 during computation. They show the L-curves corresponding to the coda-attenuation and total-attenuation inversion. After they appear, a prompt asks which damping parameter the user wants to pick.
Picard_Qc..Figures format (for Analyses = 2 or 3) and Picard_CN.Figures format (for Analysis = 3)
These plots show the result of the Picard analysis, necessary to evaluate how many of the inversion parameters are correctively solved in the coda-attenuation and total-attenuation inversions, respectively. The two figures do not appear during computation.
Peak_delay_map.Figures format and Qc_map.Figures format
These plots show the result of the peak-delay and Qc mapping in the grid’s reference system.
Qc_checkerboard_input.Figures format and Qc_checkerboard_output.Figures format - Only for Analyses = 2 or 3
These plots show the result of the checkerboard test for the Qc mapping in the grid’s reference system.
The plot shows the separation of the scattering and absorption parameters in their parameter space. Grey dots correspond to parameters too near to the average to be interpreted as scattering or absorption variations - the threshold is pre-defined at 5% of the maximum variation of each parameter. Red = High scattering and absorption; Cyan = High scattering and low absorption; Orange = Low scattering and high absorption; Green = Low scattering and absorption.
Q_model.fig; V_model.fig; 3DQ_check_input.fig; 3DQ_check_output.fig - Only for Analysis = 3
The 3D velocity model, the total attenuation model, and the checkerboard test input and output are available as 3D figures in Matlab format. They can be loaded in Matlab and will show the vertical and horizontal slices defined in Figures Sections.
If you use MuRAT for your research and publications, please consider mentioning the GitHub internet site and citing the first release of the code, published as:
De Siena, L., C. Thomas, and R. Aster. “Multi-scale reasonable attenuation tomography analysis (MuRAT): An imaging algorithm designed for volcanic regions.” Journal of Volcanology and Geothermal Research 277 (2014): 22-35.
Although we have cross-checked the whole code, we cannot warranty it is exempt of bugs. The package is provided as-is, we will neither be held responsible for any use you make of it nor for the results and conclusions you may derive using MuRAT.
MuRAT is released under EUPL v1.1