Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

Propagating coupled elastic wavefields

Following Carcione (2007), we denote the spatial variables $x$ , $y$ and $z$ of a right-hand Cartesian system by the indices $i, j,$ ...$=1$ , $2$ and $3$ , respectively, the position vector by $\mathbf{x}$ , a partial derivative with respect to a variable $x_i$ with $\partial_i$ , and the first and second time derivatives with $\partial_t$ and $\partial_{tt}$ . Matrix transposition is denoted by the superscript $\lq\lq T''$ . We also denote $\sqrt{-1}$ by $i$ , the scalar and matrix products by the symbol $\lq\lq \cdot''$ , the dyadic product by the symbol $\lq\lq \otimes''$ . The Einstein convention of repeated indices is assumed unless otherwise specified.