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\mode<handout>{\setbeamercolor{background canvas}{bg=black!3}}

\usepackage{epstopdf}

%3. From internet 
\usepackage{natbib}
\bibliographystyle{agsm}
\usepackage{amsmath,amsthm,amsfonts,amscd}  %CJ_added
\usepackage{eucal}                           %CJ_added   
\usepackage{algorithm}                     %CJ_added            
\usepackage{algorithmic}                   %CJ_added
\usepackage{color}                         %CJ_added
\usepackage{arydshln}                      %CJ_added

\usepackage{wrapfig} %CJ added. 
\usepackage{setspace}%


%PUT YOUR MACROS HERE
% The authors' macros %CJ_added
\newcommand{\bdm}[1]{\mbox{\boldmath $#1$}}
\newcommand{\noi}{\noindent}
\newcommand{\non}{\nonumber\\}
\newcommand{\del}{\partial}


% %% Jose Antonio Abell Mena provided this for DSL descriptions
% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% % This is added for listing FEI DSL
% %   since   he   customized   it,   it   needs   to   be   changed   (linked  to
% % /usr/share/texmf/tex/latex/misc)
% %\usepackage{myListings}
% \input{essi_listings_options.tex}

 

\usepackage[absolute,overlay]{textpos}


  
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\usetikzlibrary{tikzmark,calc}




 
\usepackage{threeparttable}

%\usepackage{MnSymbol}%
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% for inclusion of other PDF pages, in this case Frank's presentation
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%This is a macro to  convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
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% \else
% % we are running pdflatex, so convert .pdf files to .pdf
% \usepackage[pdftex]{graphicx}
% \usepackage{epstopdf}
% \fi
% %*****************************************


%% ovo je za cirilicu
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% % for not showing eq numbers unless eq is references
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{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}

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% {{\cyrjb \lower0.50ex\hbox{\uppercase{J}}\kern-.58em\hbox{\uppercase{B}}}}
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%  \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
%  \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
%  \usetheme{Singapore} % ima sadrzaj i tackice gore
%  \usetheme{Antibes}  % ima sadrzaj gore i kao graf ...
%  \usetheme{Berkeley} % ima sadrzaj desno
%  \usetheme{Berlin} % ima sadrzaj gore i tackice
%  \usetheme{Goettingen} % ima sadrzaj za desne strane
%  \usetheme{Montpellier} % ima graf sadrzaj gore
%  \usetheme{Warsaw}
%  \usetheme{Warsaw}
  \usetheme{Dresden}
    \usecolortheme[RGB={20,0,128}]{structure}

% or ...

  \setbeamercovered{transparent}

% or whatever (possibly just delete it)
%  \usecolortheme{albatross} % teget sa svetlim slovima
%  \usecolortheme{beetle} % siva pozadina (vrh plav)
  \usecolortheme{seagull} % sivo
%%%%%%%
%  \usecolortheme{BorisJeremic}
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\usepackage[greek,english]{babel}



\usepackage{amsmath}
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\usepackage{amsfonts}

\newcommand{\ud}{{\rm d}}


\usepackage{array}



%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
\definecolor{webgreen}{rgb}{0, 0.35, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.50} % less intense blue
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\usepackage{hyperref}
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             colorlinks=true,
             linkcolor=webblue,
             citecolor=webblue,
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}
% \usepackage[pdfauthor={Boris Jeremic},
%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
%             urlcolor=webblue,
%             linktocpage,
%             pdftex]{hyperref}


\usepackage{pause}
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\usepackage[latin1]{inputenc}
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\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.



%      Site Specific Dynamics of Structures: 
%From Seismic Source to 
%the Safety of Occupants and Content


\title[3Deconvolution]
        {3D-Deconvolution}
%        {Three Dimensional, Three Component \\
%         Seismic Wave Field Reconstruction from \\
%         Limited Surface Measurements}


%\subtitle
%{Include Only If Paper Has a Subtitle}

%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


\author[Jeremi{\'c}] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}, Han Yang
}

%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
\institute[\pgfuseimage{university-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA}
% \\
% %  and\\
% %  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
%   Lawrence Berkeley National Laboratory, Berkeley, CA}
% % - Use the \inst command only if there are several affiliations.
% % - Keep it simple, no one is interested in your street address.


\date[] % (optional, should be abbreviation of conference name)
{\small CompDyn2023}

\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}




% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
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% \AtBeginSection[]
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   \begin{scriptsize}
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     \frametitle{Outline}
     \tableofcontents[currentsection,currentsubsection]
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\begin{document}

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\begin{frame}
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\begin{frame}
  \frametitle{Outline}

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% You might wish to add the option [pausesections]
   \end{scriptsize}
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% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:

% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.



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\section{Introduction}




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%\subsection{Motivation}
\subsection{\ }



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% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{OVERVIEW}
%  
%  
%  
%  Lecture 1 - Advanced numerical analysis of dams - Modeling:
%  
%  
%  ** Seismic wave fields:
%  
%  - Influence of realistic seismic wave fields on dynamic Soil Structure Interacting (SSI) behavior
%  
%  - Realistic three component (3C) seismic wave fields, including 3 translations and 3 rotations, free
%  field observations,
%   
%  -  Differences between 1C and 3C wave propagations
%  
%  ** Inelastic/nonlinear behavior of:
%  
%  - Rock and soil
%  
%   - Concrete dams: interfaces/joints/contacts, concrete materials,
%  
%  -  Earth dams: soil material, large deformations
%  
%  
%  
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  


 

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\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



 

%\vspace*{0.3cm}
  \item[-]  Improve analysis and design for infrastructure
 

%\vspace*{1mm}
% \item[]  Expert numerical modeling and simulation tool
%% 
%% \vspace*{1mm}
%%   \item[]      Use of numerical models to
%%   analyze statics and dynamics of soil/rock-structure systems
%% 
%%  
%%  %%  \vspace*{1mm}
%%    \item[-]  Reduction  of modeling, epistemic  uncertainty
%%  
%%  %\vspace*{1mm}
%%  %  \item[]  Choice of analysis level of sophistication
%%  
%%  
%%  %%  \vspace*{1mm}
%%    \item[-] Propagation of parametric, aleatory uncertainty
%%  

\vspace*{4mm}
  \item[-]  Control modeling, epistemic uncertainty

%\vspace*{3mm}
%  \item[]  Choice of analysis level of sophistication

\vspace*{4mm}
  \item[-] Propagate parametric, aleatory  uncertainty



%\vspace*{1mm}
%  \item[] Goal: predict and inform

\vspace*{4mm}
  \item[-] Predict and inform, Engineer needs to know!

%
%\vspace*{2mm}
% \item[-] Credible numerical analysis
%% 
  
% %%  \vspace*{1mm}
% \vspace*{2mm}
%   \item[-] Design, build and maintain sustainable objects


 


\end{itemize}



% %\vspace*{6mm}
% %
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{-4mm}
% %\includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Kuca_Bajina_Basta-Drina.jpg}
% %%\hspace*{2mm}											 
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Ctesiphon_arch_Iraq.jpg}
% %%\hspace*{2mm}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Brooklyn_bridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Hoover_dam.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Diablo_Canyon_NPP.jpg}
% \hspace*{-10mm}
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% %  
% %  


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\section{Seismic Motions}







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\subsection{Realistic Wave Propagation}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Seismic Motions}

\begin{itemize}



 

%\vspace*{0.3cm}
  \item[-] Knowledge  about seismic motions (?)
 
\vspace*{4mm}
  \item[-] Uncertainty in  seismic motions (!)
 
 

\vspace*{4mm}
  \item[-]  Simplifying assumptions, 1D/2D/3D; 1C, 2C, 3C, 3$\times$1C, 6C 

\vspace*{4mm}
  \item[-] Seismic energy input and dissipation within ESSI systems

\vspace*{4mm}
  \item[-] Seismic motions have critical importance for ESSI analysis


% \vspace*{4mm}
%   \item[-]
% 
% \vspace*{4mm}
%   \item[-]
% 



\end{itemize}



% %\vspace*{6mm}
% %
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{-4mm}
% %\includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Kuca_Bajina_Basta-Drina.jpg}
% %%\hspace*{2mm}											 
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Ctesiphon_arch_Iraq.jpg}
% %%\hspace*{2mm}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/Classes/2022/Spring/ENG104/Presentation_Boris_Jeremic_interests_and_work/Brooklyn_bridge.jpg}
% %\hspace*{2mm}
% \includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Hoover_dam.jpg}
% %\includegraphics[height=1.3truecm]{/home/jeremic/tex/works/Conferences/2022/USBR_V_and_V_Mar-Apr-May_2022/present/Lecture01_Modeling/Diablo_Canyon_NPP.jpg}
% \hspace*{-10mm}
% %
% %\vspace*{3mm}
% \end{center}
% \end{figure}
% %\vspace*{3mm
% %  
% %  


\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{ESSI Analysis}

\begin{itemize}



 

%\vspace*{0.3cm}
  \item[-] Earthquake Soil Structure Interaction (ESSI) 
 
\vspace*{4mm}
  \item[-] Developments in last 50+ years
 
 

\vspace*{4mm}
  \item[-] ESSI: Nuclear Power Plants, Dams, Bridges, Buildings

\vspace*{4mm}
  \item[-] Domain Reduction Method, DRM (J.Bielak et al.) !


% \vspace*{4mm}
%   \item[-]
% 
% \vspace*{4mm}
%   \item[-]
% 



\end{itemize}




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



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\begin{frame}
\frametitle{DRM}

  \vspace*{-5mm}
\begin{flushleft}
      \begin{eqnarray*}
  \hspace*{-10mm}
\left[\begin{array}{ccc}M^{\Omega}_{ii} &  M^{\Omega}_{ib} &   0 \\
  M^\Omega_{bi} &   M^\Omega_{bb}+M^{\Omega+}_{bb} &   M^{\Omega+}_{be}
  \\ 0 &   M^{\Omega+}_{eb} &   M^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b \\  \ddot{w}_e\end{array}\right\}
+\\
\left[ \begin{array}{ccc}K^\Omega_{ii} &   K^{\Omega}_{ib}  &  0 \\
 K^{\Omega}_{bi} &   K^{\Omega}_{bb}+K^{\Omega+}_{bb} &  K^{\Omega+}_{be} \\
 0 & K^{\Omega+}_{eb} &   K^{\Omega+}_{ee} \end{array}\right]
  \left\{\begin{array}{c} u_i \\  u_b \\  w_e \end{array} \right\}
   = \nonumber \\ \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
   \\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
\label{DRMeq08}
\end{eqnarray*}
\end{flushleft}
   

\vspace*{-5mm}
\begin{figure}[!h]
\begin{flushright}
\includegraphics[width=40mm]{/home/jeremic/tex/works/psfigures/DRM_NPP_idea01.pdf}
\end{flushright}
\end{figure}


\end{frame}








 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{DRM}



%DRM features:

\vspace*{2mm}
\begin{itemize}
%\vspace*{-0.2cm}
  \item[-]  Seismic forces $P_e$  replaced by $P^{eff}$

%\vspace*{-0.2cm}
  \item[-] $P^{eff}$ applied only to a  single layer of elements next to  $\Gamma$
%\vspace*{-0.2cm}
  \item[-] Only outgoing waves from structural oscillations
%\vspace*{-0.2cm}
  \item[-] Material inside $\Omega$ can be elastic-plastic

  \item[-] Any wave field can be input/imposed

  \item[-] Neglect the outside ($\Omega^+$) problems

% \item[-]  The only input wave field is the one for the nodes of this layer of elements.
\end{itemize}

\vspace*{-3mm}
\begin{figure}[!h]
\begin{flushright}
%\vspace*{-0.50cm}
%\begin{center}
%\hspace*{1cm}
%\vspace*{-3.50cm}
%{\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
%
{\includegraphics[width=8.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/tex_works_psfigures_DRM_NPP_idea03_with_element.pdf}}
%\vspace*{-5.50cm}
%\hspace*{1cm}
%\vspace*{-2.50cm}
%\end{center}
%\vspace*{-0.3cm}
\end{flushright}
\end{figure}


\end{frame}







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% 
% 
% 
% \end{frame}
% 




 
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\begin{frame}
 \frametitle{Realistic Seismic Motions}

% \begin{itemize}
% 
%   \item[-] Free field seismic motion models
% 
% \end{itemize}

% local
% local
% local
\vspace*{-2mm}
\begin{center}
%\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
\hspace*{-12mm}
% %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% \movie[label=show3,width=6.0cm,poster]
%   {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% \hspace*{-2mm}
% %\hfill
\hspace*{5mm}
\movie[label=show3,width=100mm,poster,showcontrols]
%\movie[label=show3,width=90mm,poster]
%  {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_mp4_icon.jpeg}}
  {\includegraphics[width=90mm]{movie_input_mp4_icon.jpeg}}
%{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
{movie_input.mp4}
\hspace*{-12mm}
\end{center}
% local
% local
% local
%

% online
% online
% online
\vspace*{-10mm}
\hspace*{-7mm}
\begin{flushleft}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01Apr2015/movie_input.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
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%

\end{frame}


% ln -s /home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4 .


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\begin{frame}
 \frametitle{Development of Realistic Seismic Motions}

\begin{itemize}

  \item[-] Sources will send both P and S waves

\end{itemize}

% online
% online  \begin{center}
% online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
% online    {\includegraphics[width=55mm]{movie_input_mp4_icon.jpeg}}
% online  %
% online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% online    {\includegraphics[width=50mm]{movie_input_closeup_mp4_icon.jpeg}}
% online  \end{center}
% online

% local
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\vspace*{-2mm}
\begin{center}
%\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
\hspace*{-12mm}
% %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% \movie[label=show3,width=6.0cm,poster]
%   {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% \hspace*{-2mm}
% %\hfill
% %\hspace*{-7mm}
% %\movie[label=show3,width=5.3cm,poster,autostart,showcontrols]
\movie[label=show3,width=80mm,poster, showcontrols]
{\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.jpg}}
{movie_input_closeup.mp4}
\hspace*{-12mm}
\end{center}
%{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% local
% local
% local
%
% online

% online
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% online
\vspace*{-10mm}
\hspace*{-7mm}
\begin{flushleft}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01Apr2015/movie_input_closeup.mp4}
{\tiny (MP4)}
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%       online



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\begin{frame}
\frametitle{1C vs 6C Free Field Motions}



 
\begin{itemize}

  \item[-] One component of motions, 1C from  6C
%  or 3$\times$1D (it is done all the time!)

  \item[-]  Excellent fit, wrong physics
%  (goal is to predict and inform and not (force) fit)


\end{itemize}




% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}
  {movie_ff_3d.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}
  {movie_ff_1d.mp4}
\hspace*{-16mm}
\end{center}
% local
%  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}


% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
{\tiny (MP4)}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
 {\tiny (MP4)}
\end{center}
% online






% out      
% out  
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% 
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\begin{frame}
\frametitle{6C vs 1C NPP ESSI Response Comparison}

 
% local
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.8cm,poster, showcontrols]
  {\includegraphics[width=92mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
\end{center}
% local
%  \vspace*{-2mm}
%  \begin{center}
%  \hspace*{-7mm}
%  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
%  \end{center}


% online
\vspace*{-12mm}
\begin{flushleft}
%\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online



% out 
% out  \vspace*{-2mm}
% out  \begin{center}
% out  \hspace*{-7mm}
% out  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% out    {\includegraphics[width=69mm]{BJicon.png}}
% out    {movie_2_npps.mp4}
% out  \end{center}
% out  
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% out  \vspace*{-15mm}
% out  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
% out    {\tiny (MP4)}
% out  \end{flushleft}
% out  %
% out  


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\subsection{3Deconvolution}







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\begin{frame}
 \frametitle{3-Deconvolution}


\begin{itemize}

\vspace*{2mm}
\item[-] 1D/1C deconvolution developed long time ago

\vspace*{3mm}
\item[-] Develop 3D/3C seismic waves from limited number of motion measurements, surface, depth

\vspace*{3mm}
\item[-] 3D/3C deconvolution provides many analysis opportunities

\vspace*{3mm}
\item[-] Utilize DRM features and the PDE-constrained optimization to develop DRM forces $P_{eff}$


\vspace*{3mm}
\item[-] C.Jeong et al. recent work on inverse modeling


%\item[-]
%
%\item[-]
%
\end{itemize}




\end{frame}




% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{3Deconvolution Methodology}
%  
%  The PDE-constrained optimization scheme analytically evaluates the gradient of
%  a misfit between measured responses at sensors induced by a targeted {physical}
%  profile {(e.g., material properties or dynamic forces)} and computed wave
%  solutions induced by an estimated profile with respect to control parameters{,
%  which parameterize the estimated profile}. Because of such an analytical nature,
%  its computational efficiency of computing the gradient of a misfit with respect
%  to control parameters does not depend on the number of {control parameters}.
%  Thus, it can update a large set of control parameters very efficiently. Such
%  robustness has led to a wide range of studies on elastodynamic inverse
%  problems---e.g., full-waveform material inversion
%  
%  % \citep{kallivokas2013site,fathi2015full,fathi2016three,KUCUKCOBAN_2019_IJSS_Lame}, 
%  % inverse material design \citep{Goh_JEM_2019_Group_Velocity}, full-waveform
%  % inverse-scattering \citep{guzina2003stress,jeong2009near}, and full-waveform
%  % source inversion \citep{Aquino_2013_Sandia_report,binder_defect_2015}---based on
%  % the PDE-constrained optimization.
%  %
%  
%  
%  
%  
%  \end{frame}
%  
%  




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\begin{frame}
 \frametitle{3Deconvolution Methodology}


\begin{itemize}



% \vspace*{2mm}
% \item[-]
% PDE-constrained optimization for inverse problems 



\vspace*{2mm}
\item[-]
Full-waveform inversion

\vspace*{3mm}
\item[-]
Inversion modeling is a minimization process


\vspace*{3mm}
\item[-]
Minimize misfits between motions at sensors/nodes

  \begin{itemize}
  
\vspace*{2mm}
    \item[-]
    Measured, real motions and
    
\vspace*{2mm}
    \item[-]
    Motions induced by developed effective forces $P_{eff}$
  
  \end{itemize}


\end{itemize}
%
%%Lagrangian function $\mathcal{A}$
%
% To tackle the minimization problem, the following Lagrangian function
% $\mathcal{A}$ is built by imposing the discrete form of the forward wave
% problem, using a discrete Lagrange multiplier $\hat{\boldsymbol{\lambda}}$, onto
% a misfit function $\mathcal{L}$:
% %-----------------------------------------
% \begin{equation}
%     \mathcal{A} =
%     \underbrace{(\hat{\mathbf{s}}_{\text{m}}-\hat{\mathbf{s}})^\text{T}
%     \,\overline{\textbf{B}}\,
%     (\hat{\mathbf{s}}_{\text{m}}-\hat{\mathbf{s}})}_{\text{Misfit: }  \mathcal{L} }
%     + \hat{\boldsymbol{\lambda}}^T 
%      \underbrace{(\textbf{Q}\hat{\mathbf{s}}-\hat{\mathbf{F}}_{\text{estm}})}_{\text{0 
% 				 per \red{Eq.} (\ref{eq:forward_proposed})}},
%     \label{disc_lagrangian_functional_again}
% \end{equation}
% %
% where vectors are defined as: 
% \blue{
% \setcounter{MaxMatrixCols}{1}
% \begin{align}
% %
% \hspace{-5pt}
% \hat{\mathbf{s}} = 
% \begin{bmatrix}
% \mathbf{s}_0^T,
% \dot{\mathbf{s}}_0^T,
% \ddot{\mathbf{s}}_0^T,
% ..,
% \mathbf{s}_N^T,
% \dot{\mathbf{s}}_N^T,
% \ddot{\mathbf{s}}_N^T
% \end{bmatrix}^T\hspace{-5pt},
% %\hspace{-5pt}
% %
% %\quad 
% \hat{\boldsymbol{\lambda}} = 
% \begin{bmatrix}
% \boldsymbol{\lambda}_0^T,
% \dot{\boldsymbol{\lambda}}_0^T,
% \ddot{\boldsymbol{\lambda}}_0^T,
% .., 
% \boldsymbol{\lambda}_N^T,
% \dot{\boldsymbol{\lambda}}_N^T,
% \ddot{\boldsymbol{\lambda}}_N^T,
% \end{bmatrix}^T\hspace{-5pt},
% %\quad 
% \hat{\mathbf{F}} = 
% \begin{bmatrix}
% 0, 
% 0, 
% \mathbf{F}_0^T,
% ..,
% \mathbf{F}_N^T,
% 0,
% 0
% \end{bmatrix}^T.
%  \label{eq_disc_vectors}
% \end{align}}
% 


\end{frame}






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\begin{frame}
 \frametitle{3Deconvolution Methodology, Forward}

%In \red{Eq.}~(\ref{eq_disc_vectors}), $\hat{\mathbf{s}}$ corresponds to the space-time discretization of a forward simulation variable induced by $\hat{\mathbf{F}}_{\text{estm}}$: N is the number of time steps, and $\mathbf{s}_i$ are the spatial degrees of freedom at the $i$-th time step; 
%$\hat{\mathbf{s}}_{\text{m}}$ is the  space-time discretization of a forward simulation solution
%induced by $\hat{\mathbf{F}}_{\text{target}}$; and $\overline{\textbf{B}}$ is a block diagonal matrix, determined as $\overline{\textbf{B}} =\Delta t \mathbf{B}$ on the diagonal, where \textbf{B} is a square matrix that is zero everywhere except on the diagonals that correspond to a degree of freedom, for which measured data are available; 
% $\hat{\boldsymbol{\lambda}}$ is a discrete (space-time) Lagrange multiplier; 
%$\hat{\mathbf{F}}_{\text{estm}}$ is an estimated global force vector corresponding to all the time steps. 
%\blue{Namely, the misfit $\mathcal{L}$ quantifies the $L_2$ norm between $\hat{\mathbf{s}}_{\text{m}}$ (measured seismic motion data) due to $\hat{\mathbf{F}}_{\text{target}}$ (equivalent to targeted incident seismic wave fields)  and $\hat{\mathbf{s}}$ (computed counterparts) induced by $\hat{\mathbf{F}}_{\text{estm}}$ (equivalent to estimated incident seismic wave fields).}
%%

\begin{itemize}

\vspace*{3mm}
\item[-] 
State problem: $\mathbf{Q} \hat{\mathbf{u}} = \hat{\mathbf{F}}$


\vspace*{5mm}
\item[-] 
$\hat{\mathbf{u}}$  are DoFs in \underline{space and time}  

\vspace*{5mm}
\item[-] 
 $\hat{\mathbf{F}}$  are loads  in \underline{space and time}  


%\vspace*{3mm}
% \item[-] 


\end{itemize}

% 


\end{frame}




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\begin{frame}
 \frametitle{3Deconvolution, Discrete Forward Operator}

%In \red{Eq.}~(\ref{eq_disc_vectors}), $\hat{\mathbf{s}}$ corresponds to the space-time discretization of a forward simulation variable induced by $\hat{\mathbf{F}}_{\text{estm}}$: N is the number of time steps, and $\mathbf{s}_i$ are the spatial degrees of freedom at the $i$-th time step; 
%$\hat{\mathbf{s}}_{\text{m}}$ is the  space-time discretization of a forward simulation solution
%induced by $\hat{\mathbf{F}}_{\text{target}}$; and $\overline{\textbf{B}}$ is a block diagonal matrix, determined as $\overline{\textbf{B}} =\Delta t \mathbf{B}$ on the diagonal, where \textbf{B} is a square matrix that is zero everywhere except on the diagonals that correspond to a degree of freedom, for which measured data are available; 
% $\hat{\boldsymbol{\lambda}}$ is a discrete (space-time) Lagrange multiplier; 
%$\hat{\mathbf{F}}_{\text{estm}}$ is an estimated global force vector corresponding to all the time steps. 
%\blue{Namely, the misfit $\mathcal{L}$ quantifies the $L_2$ norm between $\hat{\mathbf{s}}_{\text{m}}$ (measured seismic motion data) due to $\hat{\mathbf{F}}_{\text{target}}$ (equivalent to targeted incident seismic wave fields)  and $\hat{\mathbf{s}}$ (computed counterparts) induced by $\hat{\mathbf{F}}_{\text{estm}}$ (equivalent to estimated incident seismic wave fields).}
%%

% Discrete forward operator
% $\mathbf{Q}$ 
%in {Eq.} 
%({disc_lagrangian_functional_again}) 
%is defined as:
%
\setcounter{MaxMatrixCols}{15}
\begin{align}
\mathbf{Q} & = 
\begin{bmatrix}
    \mathbf{I} & 0 & 0 & 0 & 0 & 0 & \dots  & 0 & 0 & 0 & 0 & 0 & 0 \\
    0 & \mathbf{I} & 0 & 0 & 0 & 0 & \dots  & 0 & 0 & 0 & 0 & 0 & 0 \\
    \mathbf{K}_{t_0} & \mathbf{C} & \mathbf{M} & 0 & 0 & 0 & \dots  & 0 & 0 & 0 & 0 & 0 & 0 \\
    %----
    \mathbf{L}_1 & \mathbf{L}_2 & \mathbf{L}_3 & \mathbf{Keff}_{t_1} & 0 & 0 & \dots  & 0 & 0 & 0 & 0 & 0 & 0 \\
    a_1\mathbf{I} & \mathbf{I} & 0 & -a_1\mathbf{I} & \mathbf{I} & 0 & \dots  & 0 & 0 & 0 & 0 & 0 & 0 \\
    a_0\mathbf{I} & a_2\mathbf{I} & \mathbf{I} & -a_0\mathbf{I} & 0 & \mathbf{I} & \dots  & 0 & 0 & 0 & 0 & 0 & 0 \\
    \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\
    0 & 0 & 0 & 0 & 0 & 0 & \dots  & \mathbf{L}_1 & \mathbf{L}_2 & \mathbf{L}_3 & \mathbf{Keff}_{t_{\text{N}}} & 0 & 0 \\
    0 & 0 & 0 & 0 & 0 & 0 & \dots  & a_1\mathbf{I} & \mathbf{I} & 0 & -a_1\mathbf{I} & \mathbf{I} & 0 \\
    0 & 0 & 0 & 0 & 0 & 0 & \dots  & a_0\mathbf{I} & a_2\mathbf{I} & \mathbf{I} & -a_0\mathbf{I} & 0 & \mathbf{I} \\
\end{bmatrix}
\label{eq:Q_proposed_plan},
\end{align}
%(\red{Boris: could check whether my argument is correct?})
% 


\end{frame}





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\begin{frame}
 \frametitle{3Deconvolution Methodology, Forward}

%In \red{Eq.}~(\ref{eq_disc_vectors}), $\hat{\mathbf{s}}$ corresponds to the space-time discretization of a forward simulation variable induced by $\hat{\mathbf{F}}_{\text{estm}}$: N is the number of time steps, and $\mathbf{s}_i$ are the spatial degrees of freedom at the $i$-th time step; 
%$\hat{\mathbf{s}}_{\text{m}}$ is the  space-time discretization of a forward simulation solution
%induced by $\hat{\mathbf{F}}_{\text{target}}$; and $\overline{\textbf{B}}$ is a block diagonal matrix, determined as $\overline{\textbf{B}} =\Delta t \mathbf{B}$ on the diagonal, where \textbf{B} is a square matrix that is zero everywhere except on the diagonals that correspond to a degree of freedom, for which measured data are available; 
% $\hat{\boldsymbol{\lambda}}$ is a discrete (space-time) Lagrange multiplier; 
%$\hat{\mathbf{F}}_{\text{estm}}$ is an estimated global force vector corresponding to all the time steps. 
%\blue{Namely, the misfit $\mathcal{L}$ quantifies the $L_2$ norm between $\hat{\mathbf{s}}_{\text{m}}$ (measured seismic motion data) due to $\hat{\mathbf{F}}_{\text{target}}$ (equivalent to targeted incident seismic wave fields)  and $\hat{\mathbf{s}}$ (computed counterparts) induced by $\hat{\mathbf{F}}_{\text{estm}}$ (equivalent to estimated incident seismic wave fields).}
%%




\begin{eqnarray*}
  \mathbf{Keff}_{t_i} = a_0\textbf{M} + a_1\textbf{C} + \textbf{K}_{t_i}
  \\
    \mathbf{L}_1 = -a_0\textbf{M} - a_1\textbf{C}
    \\
    \mathbf{L}_2 = -a_2\textbf{M} - \textbf{C}
    \\
    \mathbf{L}_3 = -\textbf{M}
    \\
a_0 = \frac{4}{(\Delta t)^2} 
\\
 a_1 = \frac{2}{\Delta t} 
 \\
  a_2 = \frac{4}{\Delta t},  
\nonumber\\
\end{eqnarray*}

% Here, $\textbf{K}_{t_i}$ and $\mathbf{Keff}_{t_i}$ are the stiffness  and
% effective stiffness matrices, respectively, updated at the $i$-th time step in
% consideration of  {mild} 
% nonlinearity of {the stiffness of materials (i.e., either linear
% or secant, equivalent elastic stiffness)}.
% %\blue{We note that, because the strong nonlinearity is not considered in the proposed project, our forward wave solver does not need to employ Newton-Raphson method at each $i$-th time step.} 
% %(\red{Boris: could check whether my argument is correct?})
% 


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\begin{frame}
 \frametitle{3Deconvolution Methodology, Inverse}



\begin{itemize}

%

\vspace{2mm}
\item[-]
Objective functional
\begin{equation}
%{\cal L} = \frac{1}{2} (\hat{\bf{u}}_{esti} 
%                      - \hat{\bf{u}}_{targ})^{T}
%                      \mathbf{B}     
%                       (\hat{\bf{u}}_{esti} 
%                      - \hat{\bf{u}}_{targ})
%\cal{L} = \frac{1}{2} (\bf{{u}}_{esti} 
%                      - \bf{{u}}_{targ})^{T}
%                      \mathbf{B}     
%                       (\bf{{u}}_{esti} 
%                      - \bf{{u}}_{targ})
%{\cal L} = \frac{1}{2} (\hat{u}_{esti} - \hat{u}_{targ})^{T}
{\bf L} = \frac{1}{2} (\hat{\bf u}_{esti} - \hat{\bf u}_{targ})^{T}
                      {\bf B}     
                       (\hat{\bf u}_{esti} - \hat{\bf u}_{targ})
\nonumber
\end{equation}

${\mathbf B}$ is a square matrix, pairing sensor locations





\vspace{4mm}
\item[-]
Lagrangian functional to solve minimization problem


\vspace{4mm}
\item[-]
Forward step, predictor

\vspace{4mm}
\item[-]
Backward step, checker, corrector




\end{itemize}



\end{frame}

















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\begin{frame}
 \frametitle{3Deconvolution Methodology, Benefits}



\begin{itemize}

%

\vspace{4mm}
\item[-]
Leveraging DRM features ($\mathbf{w}=0$) to improve accuracy 


\vspace{4mm}
\item[-]
HPC/parallel implementation in the Real-ESSI Simulator





\vspace{4mm}
\item[-]
Still working on improving efficiency and accuracy



\vspace{4mm}
\item[-]
Large computational cost in 3D/3C


\vspace{4mm}
\item[-]
Wirth's law/observation and Moore's law/observation




\end{itemize}



\end{frame}













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\begin{frame}
 \frametitle{3Deconvolution Methodology, Trials}


% local
% local
% local
\vspace*{-2mm}
\begin{center}
% %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% \hspace*{-12mm}
% % %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% % \movie[label=show3,width=6.0cm,poster]
% %   {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% % \hspace*{-2mm}
% % %\hfill
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%\movie[label=show3,width=150mm,showcontrols]
\movie[height=60mm,showcontrols]
%\movie[label=show3,width=90mm,poster]
%  {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_mp4_icon.jpeg}}
%{\includegraphics[width=100mm]{/home/jeremic/tex/works/Thesis/HanYang/Inverse_model_comparison_May2023/compare_inverse.jpg}}
{\includegraphics[width=120mm]{/home/jeremic/tex/works/Thesis/HanYang/Inverse_model_comparison_May2023/compare_inverse.jpg}}
%{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
{/home/jeremic/tex/works/Thesis/HanYang/Inverse_model_comparison_May2023/compare.mpg}
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Accurate seismic energy input into the ESSI system

\begin{itemize}

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  \item[] 3Deconvolution
  
  
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  \item[] DRM

\end{itemize}


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\item[-]
Analysis of energy dissipation with ESSI system



\vspace{4mm}
\item[-]
Application: buildings, bridges, tunnels, dams, NPPs...




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\section{Summary}


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\begin{frame}
  \frametitle{Summary}

    \begin{itemize}



\vspace*{2mm}
      \item[-] 
      Improve analysis of ESSI systems

%for numerical analysis
       


\vspace*{4mm}
      \item[-] 
      3D/3C deconvolution $\rightarrow$ 3Deconvolution

\vspace*{4mm}
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      Realistic dynamic motions, seismic, etc.



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      Accurate energy input and dissipation analysis




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      3Deconvolution available within 
%      the Real-ESSI Simulator \\
       \href{http://real-essi.us}{http://real-essi.us}



\vspace*{4mm}
      \item[-]
      NSF project with Prof. Jeong CMichUniv.



%     \item[-] Importance of using proper models correctly (verification, validation, level of sophistication)
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%  \includegraphics[width=2.0cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/steel_frame2.pdf}
%  \includegraphics[width=2.0cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Tall_building_model_cut.pdf}
%  \includegraphics[width=2.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_A_Vertical_Stress.png}
%  % \caption{Fourier spectrum comparison at  different depths}\label{Fourier_Spectrum}
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\end{itemize}



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%   \frametitle{Summary}
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% %    \item[-] Importance   of   using  proper  models  correctly  (verification,
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% %
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%     \item[-]  Sophisticated inelastic/nonlinear modeling and simulations need to be
%     done carefully and in phases
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%     \item[-] Education and Training is the key!
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%    \item[-]     Collaborators:    Feng,  Yang,  Behbehani,  Sinha,  Wang, Wang,
%    Pisan{\'o}, Abell, Tafazzoli, Jie, Preisig, Tasiopoulou, Watanabe, Luo, 
%    Cheng, Yang.
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% \vspace*{1mm}
%   \item[-]  Funding  from  and  collaboration  with the ATC/US-FEMA, US-DOE, US-NRC, US-NSF, 
%   CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,
% 
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% \vspace*{1mm}
%   \item[-]  
%     \url{http://sokocalo.engr.ucdavis.edu/~jeremic}
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