Synthetic data generating parameters. The table summarizes the generating parameters for synthetic networks showing the corresponding symbol, name and range after the application of the constraints in Section e.2.

Data set to "Synthetic inversions for density using seismic and gravity data" by Nienke Blom, Christian Boehm and Andreas Fichtner

This data set relates to our paper "Synthetic inversions for density using seismic and gravity data", in which we discuss the imaging of density variations inside the Earth as a separate, independent parameter using seismic waveform tomography and gravity measurements. The research consists of synthetic experiments conducted using a home-written MATLAB wave propagation code. The data set contains the code itself, the input files and output files for each of the experiments described in the manuscript and its supplementary material, all the figures, some extra material (such as a video of Figure 1 in the manuscript) and some scripts.

Below I'll give a description of the contents of this data set and how they are structured, followed by an overview of the experiments conducted for the paper.

In this data set, the following things can be found:

There is a directory with all the figures: FIGURES. This contains the figures in *.pdf, *.eps and *.png formats.

There is a directory FD2D_ADJOINT_CODE with in it the MATLAB code fd2d-adjoint. If you plan on using our code, it would be awfully kind if you'd make a reference both to the code and to this paper. It was a lot of work to develop the code and the experiments. NOTE: the code supplied here is a snapshot of the code taken in February 2017. A more up-to-date version might be found on github (www.github.com/Phlos/fd2d-adjoint)

For each (series of) experiment(s) described in the paper, there is a directory T1, T2, …, Tn. This also holds for the supplementary tests, the folders for which are designated with the suffix .SUPPLEMENTARY.

For Figure 1 in the manuscript, there is a directory Fig1.snapshots. In this directory, everything pertaining to the snapshots figure and its corresponding video can be found.

There is a separate directory SCRIPTS with a couple of useful scripts that might be used in addition to the ones in the fd2d-adjoint code.

In each of the test directories T1...Tn, there are subdirectories for each experiment conducted within that test framework. Each of the subdirectories has a name Systematic.test-[xxx]. Within those Systematic.. directories, the following can be found:

an input file Systematic….input_parameters.m that can be copied to [fd2d-adjoint]/input/input_parameters.m in order to re-run the experiment. As the code has been under development while the tests were run, it may be that some input parameters are missing from the earlier experiments.

A mat-file obs.all-vars.mat. If this file is copied to [fd2d-adjoint]/output/Systematic.test… , this saves the recalculation of the 'obs' data when the code is run.

A mat-file initial_misfits.mat. If this file is copied to [fd2d-adjoint]/output/Systematic.test… , this saves the recomputation of the initial misfits with respect to the obs data when the code is run.

A file lbfgs_output_log.txt which monitors the misfit and gradient development across the iterations. If the inversion was restarted a couple of times, all of this remains in the logfile.

For each iteration of the inversion iter[xxx], an iter[xxx].all-vars.mat file, which contains most of the matlab output files for this iteration.

For each iteration of the inversion iter[xxx], some figures:

a model plot of the current model anomalies with respect to the background model iter[xxx].model-diff.rhovsvp.png.

a gravity plot of the gravity vector difference between the current model and the background model iter[xxx].gravity_difference.png.

a kernel plot of the total relative kernels (whether seis only or seis+grav) of the current model in rho-mu-lambda parametrisation: iter[xxx].rho-mu-lambda.png.

Now follows a brief description of each of the (series of) tests conducted for the paper. The test numbers are mostly chronological, and so are the Systematic.test… subdirectories.

Figure 1: shows snapshots of wave propagation past a density anomaly. The full data for this and the full video are given in the Fig1.snapshots. Discussed in: Figure 1 of the manuscript.

T1: reference. A reference test in which we assess to which density can be recovered as an independent parameter. Discussed in: Figure 4

Reference experiment: Systematic.test-033

T2: ignored density. A test in which the effect is explored if density is ignored, i.e. if it is kept fixed to the starting model. Discussed in: Figure 4

Fixing density: Systematic.test-040

T3: starting model. A series of test in which is explored to what extent the starting models of P and S seismic velocity influence the recovery of density. In the different sub-tests, different levels of information on P and S velocity are already present. Discussed in: Figure 6

vs, vp 100% correct: Systematic.test-029

vs, vp 75% correct: Systematic.test-037

vs,vp 50% correct: Systematic.test-036

T4: fixed velocities. A series of tests in which is explored to what extent one can "get away with" only updating density, assuming that the models for P and S velocity are already sufficiently accurate. Discussed in: Figure 7

vs,vp fixed at 50% correct: Systematic.test-038

vs, vp fixed at 75% correct: Systematic.test-041

vs, vp fixed at 100% correct: Systematic.test-039

T5: gravity. A set of tests in which the addition of gravity data to the (up until here purely) seismic inversion. Both the full gravity vector and its potential are used as gravity data. Discussed in: Figure 8

seismic + full gravity vector (x,z) data: Systematic.test-045

seismic + gravity potential data ('geoid'): Systematic.test-046

T6: noise. A series of tests in which the addition of noise to the seismic data is explored. Both correlated and uncorrelated noise are explored. Noise levels vary across frequencies. Discussed in: Figure 9

correlated noise: Systematic.test-050

uncorrelated noise: Systematic.test-052

T7: impedance. A test in which the impedance contrast across anomaly boundaries are set to zero. It is explored to what extent the recovery of density relies on the presence of an impedance contrast. Discussed in: Figure 10

no impedance contrast: Systematic.test-055

T8: parametrisation (supplementary). A test in which it is explored to what extent the inversion is affected if an inversion parametrisation using density and the elastic parameters mu and lambda is used, instead of the otherwise used parametrisation density-S velocity-P velocity. Discussed in: Supplementary Figure 1,2 @ Supplementary_material.pdf

inversion parametrisation rho-mu-lambda (reference target model): Systematic.test-032

inversion parametrisation rho-mu-lambda with 'scaling' target model: Systematic.test-062a

T9: scaling relations. A set of tests in which it is explored to what extent the recovery of density and seismic velocities is influenced if density is scaled to S velocity using a fixed scaling. Discussed in: Figure 5

target model with density scaled to S velocity in different ways; all parameters free: Systematic.test-063

same target model, but now density is scaled to S velocity with a fixed relationship: Systematic.test-067

T10: anomaly strength (supplementary). A set of tests in which the effect of the strength of the anomalies on the recovery of density and the other parameters is investigated. Discussed in: Supplementary Figure 3-5 @ Supplementary_material.pdf

target model like reference case, but the anomalies 10% of PREM instead of 1%: Systematic.test-065

target model like reference case, but the anomalies in the upper mantle only 10% of PREM instead of 1%: Systematic.test-064

If you have any further questions, feel free to contact me.

All the best,

Nienke Blom, Utrecht University n.a.blom@uu.nl nienke.blom@posteo.net