Conventions

Vector conventions Vector quantities appear in bold-face type (e.g. x). Two-dimensional projections of threedimensional vectors are given a ∼ overhead, as in x = (x, y), as a projection of x = (x, y, z). Matrices are represented as bold-face capitals.

Operator argument conventions

Some quantities can be viewed as operations which map a set of input coordinates onto a set of output coordinates. We represent such quantities with the form D (xg|xs;t). The xs is placed right of the vertical bar to indicate that it is an input coordinate, while the xg is placed left of the vertical bar to indicate that it is an output coordinate. The t is placed on the far right to separate it from the input and output coordinates. We could define a source time as an input coordinate and a measurement time as an output coordinate but, since we consider only the difference between these two times to be important, have chosen not to. Our notation is analogous to a generalized matrix notation in which the receiver locations xg indicate rows and the source locations xs indicate columns. Were we to employ Dirac notation (commonly used in physics), D (xg|xs; t) would become 〈xg|D(t)|xs). Though better in many respects, Dirac notation is not in common use within the geophysics community, so we refrain from using it in this volume.