TY - JOUR
AU - Daglish, G. R.
PY - 2021/03/09
Y2 - 2022/12/03
TI - A Very Rapid Scan for Hypocentre Foci Driven by a Conformal Transformation
JF - Newest Updates in Physical Science Research Vol. 3
JA - NUPSR-V3
VL -
IS -
SE - Chapters
DO - 10.9734/bpi/nupsr/v3/1636F
UR - https://stm.bookpi.org/NUPSR-V3/article/view/571
SP - 17-36
AB - <p>This paper aims to suggest and demonstrate a method whereby very rapid scans for the Hypocentre foci can take place in real-time or near real-time. These scans are executed by point-to-point (P2P) ray-tracers, which, for each depth-point in the scan construct rays from the depth-point in question to each of the active seismographs which are in possession of a P-wave or S-wave onset timing. The P2P tracers may employ any of a set of 1-D (radial) Earth velocity models. Two methods are available to construct the set of segments that are to form the rays: Varying the radius, or varying the subtended angle, in the construction. The crux of the method is to use a conformal complex mapping from a disc on the z-plane to a rectangular area on the w-plane. The required ray-traces can take place in the w-plane. The geometry developed for any ray can be transformed back into discoid form in the z-plane and ray-path timings and path-lengths can be extracted. The indicators chosen here to define the possible depth coordinates of the Hypocentre foci, during and after scanning are the Fisher F-statistic and Fisher z-transform It can be suggested that a conformal mapping from the w-plane rectangular strip can proceed to an ellipse, (and hence encompass spheroidal Earth geometry), on a u-plane via the discoid on the z-plane. Otherwise, this suggested scanning system encompasses a spherical Earth model only.</p>
ER -