\input{mainmacros_act}

% wavefield
\def\W{\mathcal{U}}
% laplacian
\def\LAP{\Delta}
\def\dd {\Delta}

% partial derivatives
\def\de#1{  \frac{\partial}{\partial #1} }
\def\dtwo#1#2{  \frac{\partial^2 #1}{\partial #2^2}   }
\def\done#1#2{  \frac{\partial   #1}{\partial #2  }   }
\def\eone#1#2{  \frac{\partial   }  {\partial #2  } #1}
\def\mtwo#1#2#3{\frac{\partial^2 #1}{\partial #2\partial #3}   }

\def\mmm#1#2{m^{#1#2}}
\def\ii{i}
\def\jj{j}
\def\z{z}
\def\x{x}
\def\y{y}

\def\qx{\xi_1}
\def\qy{\xi_2}
\def\qz{\xi_3}
\def\qi{\xi_i}
\def\qj{\xi_j}

\def\kz{k_\qz}
\def\kx{k_\qx}
\def\ky{k_\qy}
\def\ki{k_\qi}
\def\kj{k_\qj}

\def\xone{x_1}
\def\xtwo{x_2}
\def\xthr{x_3}

\def\DF#1#2{h_{#1#2}}
%%\def\hxx{\DF{\qx}{\qx}}
%%\def\hyy{\DF{\qy}{\qy}}
%%\def\hzz{\DF{\qz}{\qz}}
%%\def\hxy{\DF{\qx}{\qy}}

\def\EE{g_{11}}
\def\FF{g_{12}}
\def\GG{g_{22}}
\def\JJ{(\EE\GG-\FF^2)}
\def\HH{g_{13}}
\def\LL{g_{23}}
\def\PP{\Phi}
\def\AA{g_{33}}

\def\ww{\omega}
\def\ss{s}
\def\vv{v}

\def\xvec{\bf{x}}

\def\dxdex{ \frac{\partial x_k}{\partial \qx} }
\def\dxdey{ \frac{\partial x_k}{\partial \qy} }
\def\dxdez{ \frac{\partial x_k}{\partial \qz} }

% Partials
\def\ddex{ \frac{\partial}{\partial \qx} }
\def\ddey{ \frac{\partial}{\partial \qy} }
\def\ddez{ \frac{\partial}{\partial \qz} }
\def\ddexx{ \frac{\partial^2}{\partial \qx \partial \qx} }
\def\ddeyy{ \frac{\partial^2}{\partial \qy \partial \qy} }
\def\ddezz{ \frac{\partial^2}{\partial \qz \partiql \qz} }
\def\ddexy{ \frac{\partial^2}{\partial \qx \partial \qy} }
\def\ddexz{ \frac{\partial^2}{\partial \qx \partial \qz} }
\def\ddeyz{ \frac{\partial^2}{\partial \qy \partiql \qz} }

\def\gdet{ \left| \mathbf{g} \right| }
\def\gdetf{ \sqrt{\gdet} }

\def\hxxdef{\dxdex \dxdex}
\def\hyydef{\dxdey \dxdey}
\def\hzzdef{\dxdez \dxdez}
\def\hxydef{\dxdex \dxdey}
\def\hxzdef{\dxdex \dxdez}
\def\hyzdef{\dxdey \dxdez}

\def\c{c}
\def\cxx{\c_{\qx\qx}}
\def\cx {\c_{\qx   }}
\def\cyy{\c_{\qy\qy}}
\def\cy {\c_{\qy   }}
\def\czz{\c_{\qz\qz}}
\def\cz {\c_{\qz   }}
\def\cxy{\c_{\qx\qy}}

\def\ko{\; k_o}
\def\ofpo{ \lp \qz,\qx,\qy \rp}
\def\ofzo{ \lp \z ,\x ,\y  \rp}

% ray coordinates
\def\g{\gamma}
\def\t{\tau}
\def\hgg{\DF{\g}{\g}}
\def\htt{\DF{\t}{\t}}

\def\ofto{ \lp \t ,\g \rp}
\def\ctt{\c_{\t\t}}
\def\ct {\c_{\t  }}
\def\cgg{\c_{\g\g}}
\def\cg {\c_{\g  }}

\def\kt{k_\t}
\def\kg{k_\g}
\def\kn{k_{\nu}}
% discretization
\def\Wpo{\W^{\qx+1}_{\qz}}
\def\Woo{\W^{\qx}  _{\qz}}
\def\Wmo{\W^{\qx-1}_{\qz}}

\def\Wp {\W^{\qx+1}_{\qz+1}}
\def\Wo {\W^{\qx}  _{\qz+1}}
\def\Wm {\W^{\qx-1}_{\qz+1}}