A Very Rapid Scan for Hypocentre Foci Driven by a Conformal Transformation
The aim of this paper is to propose and demonstrate a method for performing real-time or near-real-time scans for Hypocentre foci. These scans are carried out by point-to-point (P2P) ray-tracers, which create rays from the depth-point in question to each of the active seismographs with a P-wave or S-wave onset timing for each depth-point in the survey. Any of a number of 1-D (radial) Earth velocity models can be used by the P2P tracers. The set of segments that will shape the rays can be constructed in one of two ways: by varying the radius or by varying the subtended angle. The method relies on a conformal complex mapping from a disc in the z-plane to a rectangular region in the w-plane as its core. In the w-plane, the necessary ray-traces can be performed. In the z-plane, any ray’s geometry can be converted back into discoid form, and ray-path timings and path lengths can be extracted. The Fisher F-statistic and Fisher z-transform were used to describe the potential depth coordinates of the Hypocentre foci during and after scanning. It’s possible that a conformal mapping from the w-plane rectangular strip to an ellipse on a u-plane through the discoid on the z-plane will encompass spheroidal Earth geometry. Aside from that, this proposed scanning device only includes a spherical Earth model.
Author (s) Details
G. R. Daglish
Independent Analysis and Computation Ltd., Camberley, UK.
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