A scheme for estimating the location and tangential plane of a reflector

Magmatic reflectors have been detected beneath some volcanic regions by analysing some reflection phases of seismograms. In this letter we consider a problem to determine the location and tangential plane of such a reflector from the ray parameter, back-azimuth and travel time of a reflection phase, and present a scheme to solve it. It is then shown that the problem is essentially a one-dimensional root-finding problem whose independent variable is only the depth of the reflection point, and thus it can be solved by a line search method such as the one-dimensional grid search. While homogeneous velocity structure models have been used in the conventional analyses, the present scheme employs a vertically inhomogeneous one and can also easily treat converted phases at the reflector.