Is barrier island geologic framework fractal? Evidence from Padre Island National Seashore, Texas, USA

The surface morphology of coastlines has been observed to be fractal over different length-scales. Whether this phenomena extends into the subsurface has not been previously examined. Recent assessments of shoreline change suggest that the statistical behavior of shoreline change is self-affine, where the nonstationary time-series exhibits long-range dependence (LRD) that can be approximated by a power law. The scaling exponent determines the fractal dimension where high spectral power at low frequencies dominates shoreline position over large spatial scales (~ 101 to 102 km). Here, we explore the fractality of subsurface barrier island framework geology through the lens of a portable electromagnetic induction (EMI) sensor. Responses of apparent conductivity σa measured by the EMI sensor at 3 kHz (~ 4 m depth) were collected along two alongshore surveys (100 and 10 km) in Padre Island National Seashore, Texas, USA. A 10 m step-size was used for the 100 km survey, whereas a 1 m step-size was used for the 10 km survey. Thus, each spatial data series consists of n ~ 10,000 data points enabling detailed tests for LRD using traditional wavelet analysis and unconventional forecasting FARIMA techniques. In general, high powers in the wavelets correspond to previously-identified Pleistocene paleo-channels suggesting that lower-frequencies dominate the signal and are geologically controlled. Higher frequencies are proposed to reflect small-scale variations in changing hydrology. Tests for LRD by the Hurst exponent and PSD plots suggest that autocorrelations are stronger in measurements that are closer together (i.e., 1 vs 10 m step-size) over the sensor footprint. Nonetheless, the scaling exponents for both surveys suggest that σa responses are fractal signals (over different spatial scales), reflecting a very rough distribution of varying barrier island framework geology.