FDM_1D_verticalコマンドで用いているアルゴリズム

1. 記号の定義

• \(x\), \(y\)軸を水平に、 \(z\)軸を鉛直上向きに取る。
  The \(x\) and \(y\) axes are taken horizontal, and the \(z\) axis is taken vertically upward.
  
  
• ボアホール観測点の標高を\(z=z_o\)、地表の標高を\(z=z_s\)とする。
  The altitudes of the borehole station and ground surface are represented by \(z=z_o\) and \(z=z_s\), respectively.
  
  
• 媒質のP波速度、S波速度、密度、ラメ定数を標高\(z\)の関数として \(V_p(z)\), \(V_s(z)\), \(\rho(z)\), \(\lambda(z)\), \(\mu(z)\) と表す。
  The P-wave velocity, S-wave velocity, density, and Lame constants are expressed as \(V_p(z)\), \(V_s(z)\), \(\rho(z)\), \(\lambda(z)\), and \(\mu(z)\), respectively, which are functions of the altitude \(z\).
  
  
• 速度場、応力場を標高\(z\)および時刻\(t\)の関数として \(V_p(z,t)\), \(\tau_{pq}(z,t)\)と表す。 ここで\(p,q=x,y,z\)である。
  The velocity and stress fields are expressed as \(V_p(z,t)\) and \(\tau_{pq}(z,t)\), respectively, which are functions of the altitude \(z\) and time \(z\), where \(p,q=x,y,z\).