Diffuse wave-field correlation in space: An instantaneous time-reversal mirror for Green's function retrieval

Spectral element simulations of a diffuse linear elastic wavefield in 2D using 30000 Dirac Delta sources (A Dirac pulse emitted at the first time step of the simulation).The time-domain wave propagation simulation was performed using the SALVUS package by Mondaic. Details on the software can be found in Afanasiev 2019 [1]. The diffuse field is achieved by 30000 randomly distributed elastic point forces with random orientation and strength.  The time-series of wave propagation is used for the numerical experiment in 'Diffuse wave-field correlation in space: An instantaneous time-reversal mirror for Green's function retrieval' - Aichele, Müller, van-Manen.The medium closely mimics soft tissue, with a compression wave velocity of 1500 m/s, shear wave velocities of 1 and 2 m/s and a density of 1000 kg/m3. The repository also contains the results of a simulation with a single Delta source for pedagogic purposes. The source positions for the diffuse field are saved in the file SrcList. csv which  can be loaded with:

import pandas as pd

# Load CSV into Pandas DataFrameSrcListLoad = pd.read_csv("SrcList.csv")

The simulation configuration for Salvus is free from attenuation and defined in the following: 

mc = sn.ModelConfiguration(    background_model=None, volume_models="noAtt")

center_frequency = 300.0

p += sn.SimulationConfiguration(    name=simulation_name,    max_frequency_in_hertz=center_frequency * 2.0,    elements_per_wavelength=2.5,    model_configuration=mc,    event_configuration=sn.EventConfiguration(        wavelet=sn.simple_config.stf.Delta(            #center_frequency=center_frequency        ),        waveform_simulation_configuration=sn.WaveformSimulationConfiguration(            end_time_in_seconds=0.025,            receiver_sampling_rate_in_time_steps=10000, # output every xth for receivers            time_step_in_seconds=2.5e-8, # fix the timestep -- > 0.25 ms            # This is to tell the simulation to actually            # simulate with attenuation or not.        ),    ),    )

The results are saved as displacements in m at a time sampling of dt=2.5e-4 s. 

You can load the time-series of displacement in Matlab: load('Deltaevent_030000.mat').The displacements are saved in vz_vx with the dimensions: space, space, polarization of displacement, time. A small Matlab example script to load and show the data can be found under LoadAndShowExampleScript.m

[1]Afanasiev, Michael, Christian Boehm, Martin van Driel, Lion Krischer, Max Rietmann, Dave A May, Matthew G Knepley, and Andreas Fichtner. “Modular and Flexible Spectral-Element Waveform Modelling in Two and Three Dimensions.” Geophysical Journal International 216, no. 3 (March 1, 2019): 1675–92. https://doi.org/10.1093/gji/ggy469.