The method of interlineation of vector functions \vec{w} (x, y, z, t) on a system of vertical straight lines and its application in crosshole seismic tomography

The authors propose a method to construct interlineation operators for vector functions $ \vec{w} $ (x, y, z, t) on a system of arbitrarily located vertical straight lines. The method allows calculating the vector $ \vec{w} $ at each point (x, y, z) between straight lines Γ _k for any instant of time t ≥ 0. They are proposed to be used to construct a crosshole accelerometer to model Earth’s crust on the basis of seismic sounding data $ {{\vec{w}}_k}\left( {z,t} \right),\,k=\overline{1,M} $ , about the vector of acceleration $ \vec{w} $ (x, y, z, t) received by accelerometers at each chink Γ _k .