A critical appraisal of asymptotic 3D-to-2D data transformation in full-waveform seismic crosshole tomography

Abstract

Seismic full-waveform inversion (FWI) is often based on forward modeling in the computationally attractive 2D domain. This implies the assumption of a line source extended in the out-of-plane medium invariant direction, with far-field amplitudes decaying inversely with the square root of distance. Realistic point sources, however, generate amplitudes that decay approximately with the inverse of distance. Conventionally, practitioners correct for this amplitude difference and the associated phase shift by transforming the recorded 3D field data to the approximate 2D equivalent by using simplistic asymptotic filter algorithms. Such filters assume straight raypaths, a constant velocity medium, and far-field recordings. We have assessed the validity of 3D-to-2D data transformation in the context of crosshole seismic full-waveform tomography by propagating 3D and 2D wavefields through 2D media and comparing 2D reference synthetics with their filtered 3D equivalent. The filter performs well in simple situations, which confirms the general applicability of the conventional asymptotic approach. However, we have observed substantial errors in more complex elastic models, associated with overlapping arrivals and strongly curved raypaths. To test if this error translates into deficient model reconstruction in FWI, we performed complementary inversion experiments using a frequency-domain algorithm. Purely acoustic waveform inversions of 3D-to-2D filtered data are only weakly affected, but in the case of elastic FWI, in which an S-wave influence is present, adverse effects increase substantially. Two-dimensional FWI in combination with filtering seems to be an acceptable strategy as long as the model is two-dimensional, the recording geometry is straight and perpendicular to strike, and only slight S-wave energy is contained in the data. The latter two conditions are generally met in exploration-type marine seismic surveys at short offsets and in some crosswell applications using explosive sources and nondirectional pressure receivers.