Estimation of the Hurst exponents of irregularly sampled subsurface fault geometries by the lifting scheme

Seismic fault surfaces have complex geometries over a broad-scale range. The Hurst exponent (H) is an important parameter characterizing the complexity of fault geometries. This exponent of seismic faults has only been estimated at outcrops and from surface traces of large earthquakes. This is because geometry data of subsurface faults usually have large uncertainties and many gaps. This study examined the applicability of the lifting scheme, which is one of the wavelet transform methods, to estimate H of irregularly sampled geometry of subsurface faults. We analysed the surface geometry of the subducting oceanic plate at the Nankai trough, Japan, which is part of the fault plane of interplate earthquakes. The geometries of the subducting plate were estimated along six survey lines by integrating seismic refraction and reflection surveys. Two-way traveltimes of reflected waves from the plate surface, which were measured from the reflection survey data, were converted to depth using the velocity structure estimated by refraction survey. The intervals between sampled points were irregular because the reflected waves were obscured or invisible in some places. The Hurst exponents were estimated from the scale dependence of the wavelet coefficients that were derived by the lifting scheme without interpolation. Analyses of the synthetic data simulating the irregularly sampled plate geometries indicated that the lifting scheme yields stable but largely biased estimates of H, especially for small H (<0.5). We introduced the empirical bias correction to achieve an unbiased estimation of the exponent. The analysis of plate geometry at the Nankai trough was conducted at narrow-scale ranges with consideration for the accuracy of velocity structures. We may conclude that H of five survey lines across the trough axis is > 0.8, and that of a line along trough is > 0.7. These estimated exponents had large uncertainties due to analyses at narrow-scale ranges, but were close to the estimates in studies of the surface traces of large earthquakes.