Conservation of lateral stochastic structure of a medium in its simulated seismic response

Abstract

Mapping correlation lengths of continental lower crustal heterogeneity directly from deep reflection data can be a valuable additional interpretation tool for deep seismic imaging. In this feasibility study we investigate the conservation of lateral correlation length and power law structure in the seismic response of lower‐crustal stochastic lithology. The conservation of von Karman power law heterogeneity in backscattered wavefields is evaluated in a range of challenging seismic scenarios. We pay special attention to the limitations of this conservation due to the effect of spatial band limitation, caused by limited seismic recording aperture and to the effect of complex seismic scattering conditions. The comparison of average lateral correlations in von Karman media and their modeled reflection responses reveals two important facts: spatial band limitation by limited seismic illumination severely affects the estimated power law exponent (the Hurst number) of the von Karman heterogeneity distribution, but the estimated correlation length is unaffected and scales linearly with the original value. The original type of lateral power law distribution is conserved under nearly all seismic scattering conditions investigated, albeit with an underestimated correlation length and overestimated Hurst number. Our results can be quantitatively explained which allows for stable estimations of correlation length under various seismic scattering scenarios. This study confirms the potential of utilizing estimates of lateral von Karman structure to characterize the middle and lower crust from deep seismic reflection data.