Assessing volumes of tephra fallout deposits: 
A simplified method for data scarcity cases 

Roberto Sulpizio (1,2,3), A. Costa (2), S. Massaro (1,2), J. Selva (4) and Elisabetta Billotta (1)
1 Dipartimento di Scienze della Terra e Geoambientali, Universitˆ degli Studi di BariÒAldo MoroÓ, via Orabona 4, 70125, Bari (Italy), roberto.sulpizio@uniba.it, silvia.massaro@uniba.it, elisabetta.billotta@uniba.it

2 Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Bologna, Viale Carlo Berti Pichat, 6/2, 40127, Bologna (Italy), antonio.costa@ingv.it

3 Istituto di Geologia Ambientale e Geoingegneria, Consiglio Nazionale delle Ricerche, via Mario Bianco 9, Milano (Italy)

4 Dipartimento di Scienze della Terra, dellÕAmbiente e delle Risorse, Universitˆ di Napoli ÒFederico IIÓ, Napoli (Italy), jacopo.selva@unina.it


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DISCLAIMER: This Python script is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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1. Description of "ESM6_run_using_distances.py" 

The ESM5_run_using_distances.py script is designed to determine the volume and magnitude of tephra deposits based on the geometric assumptions of elliptical shape for isopachs, a statistical characterization of their eccentricity, and an empirical relationship between their thinning length scale and volumes. The method can be applied for a pair of thickness data (T0, T1) whose distances from the vent (d0, d1) show a minimum distance ratio (d1/d0) larger than 2. The method has been tested against about 40 published volume data, from both equatorial belt and mid-latitude volcanoes.


The command line to launch the script is the following: 

python ESM6_run_using_distances.py --distances d0,d1 --thicknesses T0,T1 --eccentricity equatorial


The labels Ò--distancesÓ, Ò--thicknessesÓ and Ò--eccentricityÓ indicate the input parameters to run the case study. In particular, the user must set the couple of distances d0, d1 (in km) from the source where the fallout deposits data are located, the two thicknesses (in cm), and the type of eccentricity (ÒequatorialÓ or ÒmidlatitudeÓ) depending on which Beta distribution fits with the investigated volcano. The Beta distributions derived from a dataset of eccentricities calculated from isopach maps from about 50 volcanoes divided into equatorial (± 15¡ of latitude) and mid latitude (± 15¡ - 66¡ of latitude) belt. 

NB: It is important to note that, for each run, a single value of eccentricity is randomly sampled. In case of no solution, this means that the sampled eccentricity does not verify the boundary condition: d1 > d0/(1-eps2). To overcome this issue, you launch the command more times in order to select other combinations that can verify such a condition. 


2. Description of "ESM7_plotting.py" 

The ESM_6_plotting.py script is designed to provide the normalized uniform distribution and frequency histograms of the Magnitude obtained considering the two thickness data but varying the eccentricity (randomly sampled from the Beta distributions, mid-latitude or equatorial). In this case, the sample of eccentricity is set to 1000. 
 
The command line to launch the script is the following:

python ESM_7_plotting.py

Within the script, it is possible to set the input parameters (d0,d1,T0,T1) and to select the Beta distribution for the eccentricity. 


3:How to install and use the scripts
The script needs to be run using Python (https://www.python.org/) on your computer.