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This discrepancy may result from a trade-off between the depth of a reflector and velocity above the reflector.
Inamori et al. (1992) assume that coda waves after direct S waves are composed of S waves reflected at horizontal planes, and convert travel times of coda waves to depths of reflectors.
The location and depth of this reflector correspond to those of the S wave reflector in this analysis.
The average depth of the reflector is 55 km, which is about 25 km below the crust mantle transition, and amplitude modelling suggests that the reflecting interface represents a velocity increase.
By these attributes, the curvature, dip, and depth of the reflector in the considered element shown by red line in Fig. 2c are defined.
Although the depth of the reflector in this study is 5 10 km shallower than the slab depth proposed by passive-source seismic data (e.g., Nakajima et al. 2009), the geometry (gently dipping northwestward) is consistent.
Subsequently, the depth of a reflector d is calculated from the following equation (Balanis 1989) d = frac{{C_{air} T}}{{2sqrt {varepsilon_{r} } }} (2 where, T is the two-way travel time of an electromagnetic wave in a material.
Based on the misfit of travel times (within 0.1 s) and the uncertainty of the velocity model (0.5 km/s), we roughly estimated the error for the depth of the reflector to be less than 2.0 km.
Parameter b controls the variation of the offset rang versus time or depth of the reflectors.
This is to be expected as the depth of sub-reflectors are on the order of wavelengths, which are in millimeters.
They reported that the reflector existed at depth of 20 30 km and LFEs occurred beneath this reflector.
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