% beamer version of chapter 1 "Introduction" in "Computational Seismology, A Practical Introduction" (H. Igel)

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\title[Computational Seismology] % (optional, use only with long paper titles)
{Computational Seismology: Introduction}

%\subtitle{Introduction} 

\author[Heiner Igel]{Heiner Igel}


\institute[] 
  {Department of Earth and Environmental Sciences \\ Ludwig-Maximilians-University Munich} 



\date[] % (optional)
{}

\subject{Talks}


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\begin{document}

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\begin{frame}
  \titlepage
\end{frame}

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%\begin{frame}{Outline}
%\fs
%  \tableofcontents
%  % You might wish to add the option [pausesections]
%\end{frame}

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\section{Scope}

	\begin{frame}{Introduction}
	%\vspace{-2cm}
		\begin{figure}
			\includegraphics[width=.85\textwidth]{\figpath/newgrid2.jpg}
		\end{figure}
	\end{frame}

% ---------------------------------------------------------

	\begin{frame}{Goals of the course}
	\footnotesize
		\begin{itemize}
			\item Understand methods that allow the calculation of \textbf{seismic wavefields in  heterogeneous media}
			\item Prepare you to be able to understand Earth science papers that are based on \textbf{3-D wave simulation tools} (e.g., seismic exploration, full waveform imaging, shaking hazard, volcano seismology)
			\item Know \textbf{the dangers, traps, and risks of using simulation tools} (as black boxes -> turning black boxes into white boxes)
			\item Providing you with basic knowledge about common \textbf{numerical methods}:
			\item Knowing \textbf{application  domains} of the various methods and guidelines what method works best for various problems	
			\item ... and having fun simulating waves ... 
		\end{itemize}
	\end{frame}

% ---------------------------------------------------------

	\begin{frame}{Course structure}
	\footnotesize
		\begin{itemize}
			\item \textbf{Introduction}
				\begin{itemize}	\footnotesize
					\item[-] What is computational seismology?
					\item[-] When and why do we need numerical maths?
				\end{itemize}
			\item \textbf{Elastic waves in the Earth}
				\begin{itemize}	\footnotesize
					\item[-] What to expect when simulating seismic wave fields?
					\item[-] Wave equations
					\item[-] Seismic waves in simple media (benchmarks)
					\item[-] Seismic sources and radiation patterns
					\item[-] Green's functions, linear systems
				\end{itemize}	
			\item \textbf{Numerical approximations of the 1 (2, 3) -D wave equation}
				\begin{itemize}	\footnotesize
					\item[-] Finite-difference method
					\item[-] Pseudospectral method
					\item[-] Spectral-element method
					\item[-] Discontinuous Galerkin method
				\end{itemize}
			\item \textbf{Applications in the Earth Sciences}								
		\end{itemize}
	\end{frame}

% ---------------------------------------------------------

	\begin{frame}{Who needs Computational Seismology}
	\footnotesize
		Many problems rely on the analysis of \textbf{elastic wavefields}
		\begin{itemize}
			\item \textbf{Global seismology} and tomography of the Earth's interior
			\item The quantification of \textbf{strong ground motion - seismic hazard}
			\item The understanding of the \textbf{earthquake source process}
			\item The monitoring of \textbf{volcanic processes} and the forecasting of eruptions
			\item \textbf{Earthquake early warning} systems 
			\item \textbf{Tsunami early warning} systems
			\item Local, regional, and global \textbf{earthquake services}
			\item Global monitoring of \textbf{nuclear tests}
			\item \textbf{Laboratory scale analysis} of seismic events
		
		\end{itemize}
	\end{frame}
	
	% ---------------------------------------------------------

	\begin{frame}{Who needs Computational Seismology (cont'd)}
	\footnotesize
(...)
		\begin{itemize}
			\item Ocean generated \textbf{noise measurements} and cross-correlation techniques
			\item \textbf{Planetary seismology}
			\item \textbf{Exploration geophysics}, reservoir scale seismics
			\item \textbf{Geotechnical engineering} (non-destructive testing, small scale tomography
			\item \textbf{Medical applications}, breast cancer detection, reverse acoustics
		\end{itemize}
	\end{frame}


% ---------------------------------------------------------

	\begin{frame}{Literature}
	\footnotesize
		\begin{minipage}{0.6\textwidth}
			\begin{itemize}
				\item Computational Seismology: A Practical Introduction (Oxford University Press, 2016) 
				\item Shearer: Introduction to Seismology (2nd edition, 2009,Chapter 3.7-3.9)
				\item Aki and Richards, Quantitative Seismology (1st edition, 1980)
				\item Mozco, The Finite-Difference Method for Seismologists. An Introduction. (pdf available at spice-rtn.org), also as book Cambridge University Press
				\item Fichtner, Full Seismic Waveform Modelling and Inversion, Springer Verlag, 2010. 
			\end{itemize}
		\end{minipage}
	\mbox{}		
	\hfill	
		\begin{minipage}{0.35\textwidth}
			\includegraphics[width=0.95\textwidth]{\figpath/titlepage.jpg}
		\end{minipage}
	\end{frame}
	
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\section{What is Computational Seismology?}

	\begin{frame}{What is Computational Seismology?}
		\begin{block}{}
			We define \textbf{computational seismology} such that it \textbf{involves the complete solution of the seismic wave propagation (and rupture) problem for arbitrary 3-D models by numerical means}.
		\end{block}
	\end{frame}
	
	% ---------------------------------------------------------

	\begin{frame}{What is not covered ...}
	\footnotesize
		\begin{minipage}{0.6\textwidth}
			\begin{itemize}
				\item Ray-theoretical methods
				\item Quasi-analytical methods (e.g., normal modes, reflectivity method)
				\item Frequency-domain solutions
				\item Boundary integral equation methods
				\item Discrete particle methods
				\vskip1truecm
				These methods are important for benchmarking numerical solutions!
			\end{itemize}
		\end{minipage}
	\mbox{}		
	\hfill	
		\begin{minipage}{0.35\textwidth}
			\includegraphics[width=0.95\textwidth]{\figpatha/fig_raydensity.png}
		\end{minipage}
	\end{frame}

% ---------------------------------------------------------

\section{Why numerical methods?}


	\begin{frame}{Why numerical methods?}
		\begin{figure}
			\includegraphics[width=0.65\textwidth]{\figpath/Seismo.png}
		\end{figure}
	\end{frame}

% ---------------------------------------------------------

	\begin{frame}{Why numerical methods?}
		\begin{figure}
			\includegraphics[width=0.7\textwidth]{\figpath/Seismo2.png}
		\end{figure}
	\end{frame}
	
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	\begin{frame}{Why numerical methods?}
		\begin{figure}
			\includegraphics[width=0.7\textwidth]{\figpath/Seismo3.png}
		\end{figure}
	\end{frame}
	
% ---------------------------------------------------------

	\begin{frame}{Why numerical methods?}
		\begin{figure}
			\includegraphics[width=0.7\textwidth]{\figpath/Seismo4.png}
		\end{figure}
	\end{frame}


% ---------------------------------------------------------

\section{Waves and Computers}


	\begin{frame}{Computational Seismology, Memory, and Compute Power}
	
	\footnotesize
		\begin{minipage}{0.6\textwidth}
			Numerical solutions necessitate the discretization of Earth models. Estimate how much memory is required to store the Earth model and the required displacement fields.\\
		\vskip 2true cm
		\textbf{Are we talking laptop or supercomputer?}
		\end{minipage}
	\mbox{}		
	\hfill	
		\begin{minipage}{0.35\textwidth}
			\includegraphics[width=0.95\textwidth]{\figpatha/fig_about_schuberth.png}
		\end{minipage}
	\end{frame}
	
	% ---------------------------------------------------------

	\begin{frame}{Seismic Wavefield Observations}
	
	\footnotesize
		\begin{minipage}{0.49\textwidth}
		\begin{center}
			\includegraphics[width=0.45\textwidth]{\figpath/fig_waves_seismogram.png}
			\end{center}
		\end{minipage}
	\mbox{}		
	\hfill	
		\begin{minipage}{0.49\textwidth}
		\begin{center}
			\includegraphics[width=0.85\textwidth]{\figpath/fig_waves_spectrum.png}
		\end{center}
		\end{minipage}
	\end{frame}
	
		% ---------------------------------------------------------

	
	\begin{frame}{Matching Wavefield Observations}
	
	\footnotesize
	
		\begin{center}
			\includegraphics[width=0.8\textwidth]{\figpath/fig_misfit.png}
		\end{center}
	
	\end{frame}

% ---------------------------------------------------------

	\begin{frame}{Exercise: Sampling a global seismic wavefield}
		\begin{minipage}{0.6\textwidth}
			\footnotesize
			%\vskip 1 truecm
			\begin{itemize}
			\item The highest frequencies that we observe for global wave fields is 1Hz. 
			\item We assume a homogeneous Earth (radius 6371km). 
			\item P velocity $v_p = 10km/s$ and the $v_p/v_s$ ratio is $\sqrt{3}$
			\item We want to use 20 \textbf{grid points (cells) per wavelength} 
			\item How many grid cells would you need (assume cubic cells). 
			\item What would be their size? 
			\item How much memory would you need to store one such field (e.g., density in single precision).
			\end{itemize}
		\end{minipage}
	\mbox{}		
	\hfill			
		\begin{minipage}{0.35\textwidth}
		\footnotesize
					\begin{figure}
				\includegraphics[width=0.5\textwidth]{\figpath/Earth.png}
			\end{figure}
			
		You may want to make use of 
		$$
		c = \frac{\lambda}{T} \ = \ \lambda f \ = \frac{\omega}{k}
		$$

			\begin{figure}
				\includegraphics[width=0.5\textwidth]{\figpath/fig_waves_npl.png}
			\end{figure}
		\end{minipage}
	\end{frame}
	
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	\begin{frame}{Exercise: Solution (Matlab)}

	\begin{minipage}{0.55\textwidth}

\begin{block}{}
\tiny
\% Earth volume \\
$v_e = 4/3 * pi * 6371^3;$ \\
\% smallest velocity (ie, wavelength) \\
vp=10; % km/s \\
vs=vp/sqrt(3); \\
\% Shortest Period \\
T=10;   \\
\% Shortest Wavelength \\
lam=vs*T; \\
\% Number of points per wavelength and \\ 
\% required grid spacing \\
$nplambda=20;$ \\
$dx=lam/nplambda;$ \\
\% Required number of grid cells \\
$nc = v_e/(dx^3);$ \\
\% Memory requirement (TBytes) \\
$mem = nc * 8 /1000 /1000 /1000 /1000;$ \\
\end{block}

	\end{minipage}
	\mbox{}		
	\hfill
	\begin{minipage}{0.39\textwidth}

\begin{center}
\footnotesize
Results ($@T=1s$) : $ \ $ 360 TBytes  

Results ($@T=10s$) :$ \  $ 360 GBytes  

Results ($@T=100s$) : $ \ $ 360 MBytes  
\end{center}  

\end{minipage}

	\end{frame}
		
	
	
% ---------------------------------------------------------

	\begin{frame}{Computational Seismology, Memory, and Compute Power}
	
		\begin{minipage}{0.3\textwidth}
		\vskip1truecm
			\begin{itemize}
			\footnotesize
				\item[] 1960:  1 MFlops
				\item[] 1970: 10MFlops
				\item[] 1980: 100MFlops
				\item[] 1990: 1 GFlops
				\item[] 1998: 1 TFlops
				\item[] 2008: 1 Pflops
				\item[] 20??: 1 EFlops
			\end{itemize}			
		\end{minipage}
	\mbox{}		
	\hfill			
		\begin{minipage}{0.65\textwidth}
			\begin{figure}
				\includegraphics[width=0.99\textwidth]{\figpath/Moore.png}
			\end{figure}
		\end{minipage}
	\end{frame}
	
% ---------------------------------------------------------

	\begin{frame}{Computational Seismology, Parallel Computing}
	
		\begin{minipage}{0.49\textwidth}
			\begin{figure}
				\includegraphics[width=0.95\textwidth]{\figpath/fig_fund_supermuc.png}
			\end{figure}			
		\end{minipage}
	\mbox{}		
	\hfill			
		\begin{minipage}{0.49\textwidth}
			\begin{figure}
				\includegraphics[width=0.99\textwidth]{\figpath/fig_fund_merapi.png}
			\end{figure}
		\end{minipage}
	\end{frame}
	

% ---------------------------------------------------------

	\begin{frame}{Computational Seismology, Practical Exercises, Jupyter Notebooks}
	
		\begin{minipage}{0.49\textwidth}
		\footnotesize
			\begin{itemize}
			\item \textit{Jupyter notebooks} are interactive documents that work in any browser
			\item Simple text editing
			\item Inclusion of graphics
			\item Equations with Latex
			\item Executable code cells with Python (or else)
      \item The coolest thing since ...
			\item Many examples on: \textit{www.seismo-live.org}
			\end{itemize}			
		\end{minipage}
	\mbox{}		
	\hfill			
		\begin{minipage}{0.49\textwidth}
			\begin{figure}
				\includegraphics[width=0.99\textwidth]{\figpath/fig_app_jupyter.png}
			\end{figure}
		\end{minipage}
	\end{frame}	
	
	
	
% ---------------------------------------------------------

	\begin{frame}{Summary}
	\footnotesize
		\begin{itemize}
			\item Computational wave propagation (as defined here) is turning more and more into a routine tool for many fields of Earth sciences
			\item There is a zoo of methods and in many cases it is not clear which method works best for a specific problem
			\item For single researchers (groups, institutions) it is no longer possible to code, implement, maintain an algorithm efficiently
			\item More and more well engineered community codes become available (e.g., sofi3d, specfem, seissol)
			\item Community platforms (e.g., verce.eu) are developing facilitating simulation tasks 
		\end{itemize}
		This course aims at understanding the theory behind these methods and understanding their domains of application.
	\end{frame}

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\end{document}
