{section_conclusion}
Layer-wise finite difference discretization of the 3D isotropic elastic wave propagation on staggered grids with nonconforming interfaces between layers is considered in this work.
It is shown that energy conserving simulation across the nonconforming layer interfaces can be achieved through the use of summation-by-parts finite difference operators, simultaneous approximation terms, and compatible interpolation operators, which ensure the stability of the simulation. 
Moreover, by examining the standard process of determining the discretization parameters for seismic wave simulations under the usual constraints, as presented in \ref{appendix_thought_experiment}, and by the numerical examples, it is demonstrated that, compared to finite difference discretization on uniform grids, significant reduction of computational resources can be achieved by employing the proposed layer-wise discretization approach, thus enabling more efficient processing of seismic data.



\section{Additional plots related to the example of Layered model}\label{supp_additional_plots}

\begin{figure}[H]
\captionsetup{font=small,labelfont=small}
\centering
\begin{subfigure}[b]{0.495\textwidth}
\captionsetup{width=1\textwidth, font=small,labelfont=small}
\centering\includegraphics[scale=0.125]{\string"./fig/layered_model/seismogram_small_segment\string".png}
\end{subfigure}
\begin{subfigure}[b]{0.495\textwidth}
\captionsetup{width=1\textwidth, font=small,labelfont=small}
\centering\includegraphics[scale=0.125]{\string"./fig/layered_model/seismogram_3x_small_segment\string".png}
\end{subfigure} 
\caption[]{
Segments of the seismograms between 3.05 s and 3.25 s. The left figure corresponds to Figures~\ref{fig_layered_seismogram} of the manuscript; the right figure corresponds to Figure~\ref{fig_layered_seismogram_3x} of the manuscript, which uses three times finer grid spacing. The improved agreement can be observed more easily here than by comparing Figures~\ref{fig_layered_seismogram} and~\ref{fig_layered_seismogram_3x} of the manuscript.}
\label{fig_seismograms_small_segment}
\end{figure}


\section{Additional expenditure information on computing resources}\label{supp_additional_tables}

\begin{table}[H]
\captionsetup{font=small,labelfont=small}
\caption[]{Expenditure on computing resources corresponding to Figure~\ref{fig_layered_seismogram_3x} of the manuscript. The expected ratio in total computational resources, i.e., core hours, is $\sim$$19.1$, based on the amount of spatial-temporal discretization points involved. The measured ratio is $\sim$$18.5$, which suggests a $\sim$$3\%$ overhead on a per core basis in our implementation.}
\label{computing_resources_figure_5}
\arraycolsep=2.pt\def1{1}
\centering
\small
\begin{tabular}{| r | c | c | c |}
\hline
	     	  & core count & elapsed time & total core hours \\ \hline
uniform 	  & 23328   &  63482 seconds  & $4.114 \times 10^5$  \\ \hline
nonuniform & 6785    &  11805 seconds &  $2.225 \times 10^4$  \\ \hline
\end{tabular}
\end{table}


\begin{table}[H]
\captionsetup{font=small,labelfont=small}
\caption[]{Expenditure on computing resources corresponding to Figure~\ref{fig_overthrust_seismogram} of the manuscript. The expected ratio in total computational resources, i.e., core hours, is $\sim$$3.153$, based on the amount of spatial-temporal discretization points involved. The measured ratio is $\sim$$3.095$, which suggests a $\sim$$2\%$ overhead on a per core basis in our implementation.}
\label{computing_resources_figure_9}
\arraycolsep=2.pt\def1{1}
\centering
\small
\begin{tabular}{| r | c | c | c |}
\hline
	     	  & core count & elapsed time & total core hours \\ \hline
uniform 	  & 19200   &  12787 seconds  & $6.820 \times 10^4$  \\ \hline
nonuniform & 7300    &  10860 seconds &  $2.202 \times 10^4$  \\ \hline
\end{tabular}
\end{table}



\section{Supplementary performance tests}\label{supp_performance_tests}

In the comparison of the elapsed wall clock times shown in section Numerical examples, each processor core is assigned the same number of grid points for both nonuniform and uniform simulations. 
This ensures that, on each processor core, the pressure on performance-critical resources are similar and that the comparison is fair on a per core basis.
However, this implies that the total number of processor cores used in the uniform simulation is larger, which may lead to an unfair comparison if a larger number of processor cores incurs considerable communication overhead.
(Such a situation would unfairly favor the proposed nonuniform simulation.) 
In the following, we provide some additional test results to further validate our algorithmic intuition that the nonuniform simulations incur little overhead. The setup of the physical problem is the same as in Example Layered model. 

First, we run the uniform simulation using a number of processor cores (6480 = $12 \times 15 \times 36$) similar to that used in the nonuniform case (6785 cores) presented in Example Layered model. 
Each processor core is assigned $90 \times 72 \times 30$ grid points.
The elapsed time (averaged over 5 runs) is $\sim$3363 s. 
In terms of the total resources consumed (i.e., number of processor cores multiplied by elapsed time), this simulation setting is actually $\sim$7\% more costly than the uniform simulation setting used in Example Layered model.
(Plausible explanations for the increase of consumed resources include heavier memory pressure on each processor core, longer runtime and therefore greater susceptibility to interference from the shared hardware environment, and finally, natural performance variances on modern large-scale computing systems.
Nevertheless, this test suggests that the performance comparison presented in Example Layered model did not unfairly favor the proposed nonuniform simulation due to the difference in core numbers.)

Additionally, some weak scaling results are provided in Tables~\ref{weak_scaling_nonuniform} and~\ref{weak_scaling_uniform}, where the number of cores in the $z$ direction doubles from column to column.
The grid points per processor core are kept the same at $60 \times 60 \times 15$. 
All simulations are performed for 2000 time steps.
The elapsed times shown in Tables~\ref{weak_scaling_nonuniform} and~\ref{weak_scaling_uniform} are averaged over 5 runs.
From both tables, we observe that increasing the number of cores does not lead to an increase in simulation time for both the nonuniform and uniform simulations, suggesting that both weak-scale well.

\begin{table}[H]
\caption[]{Weak scaling (nonuniform).}
\label{weak_scaling_nonuniform}
\setlength{\tabcolsep}{12pt}
\def1{1}
\centering
\small
\begin{tabular}{| c | c | c | c | c | c |}
\hline
Number of cores & 6785 & 13570 & 27140 & 54280 & 108560 \\ \hline
Elapsed time (seconds) & 45.7 & 45.4 & 44.2 & 43.5 & 43.2 \\ \hline
\end{tabular}
\end{table}
\begin{table}[H]
\caption[]{Weak scaling (uniform).}
\label{weak_scaling_uniform}
\setlength{\tabcolsep}{12pt}
\def1{1}
\centering
\small
\begin{tabular}{| c | c | c | c | c |}
\hline
Number of cores & 11664 & 23328 & 46656 & 93312 \\ \hline
Elapsed time (seconds) & 46.4 & 44.6 & 43.5 & 43.3 \\ \hline
\end{tabular}
\end{table}

Together, these tests suggest that for the comparison made in Example Layered model, difference in the sizes of the processor network 
is unlikely to be a major contributing factor.
Can we centrally manage SUMo in corporate environment?
Yes, that's exactly the purpose of the "Network supervisor" (SUMo Online) introduced with SUMo 5.9.
I'm using Sumo and from time to time and since its early start, have to say its carreer started bad with the adware thing (that's why I still only download.zip ) and you really made the right move.
