Seismic tomography

Definition

Let $\Omega$ be a region of the Earth. Let $m$ be a model of a seismic property on $\Omega$, such as the P-wave or S-wave speed. Let seismic waves from sources $s_1, \dots, s_J$ be recorded at receivers $r_1, \dots, r_K$. Let $d$ be the vector of observations derived from the records, such as travel times or waveforms. Let $G$ be the forward operator that predicts these observations from $m$ by seismic wave theory. Seismic tomography is the geophysical inversion that estimates $m$ on $\Omega$ from $d$ and $G$. Usually it seeks a perturbation $\delta m$ of a reference model $m_0$, such as a radial Earth model. It solves the linearised equation $d - G(m_0) \approx DG(m_0)\, \delta m$ by regularised least squares.