An inverse scattering series algorithm for depth imaging of reflection data from a layered acoustic medium with an unknown velocity model

Depth imaging of seismic reflection data plays an important role in discovering and characterizing oil and gas reservoirs. The quality of the image produced by current depth imaging algorithms is inextricably linked to the adequacy of the velocity model, which can be difficult to estimate in geologically complex areas.; The inverse scattering series, a multidimensional direct inversion procedure, can be applied to the seismic inverse problem to directly achieve seismic processing objectives without a priori knowledge of the Earth's material properties. Therefore, it has the potential to image reflectors in depth without requiring the velocity model. The inverse series is non-linear in the scattered field, which includes the source wavelet and a chosen reference medium's properties.; An imaging subseries of the inverse series for a 1-D constant density variable velocity acoustic medium is isolated and analyzed. This imaging series is a Taylor series expanded about each mislocated reflector whose approximate coefficients are leading order in the scattered field. This leading order imaging series is shown analytically (through the derivation of a closed form) to converge for arbitrarily large finite contrasts between the actual and reference velocities and for bandlimited data whose maximum frequency is finite. A condition is derived which, when satisfied, shows that the leading order imaging series improves the depths of reflectors over a linear imaging algorithm using the reference velocity. Whereas the computational expense of the series algorithm is proportional to the contrast between the actual velocity model and the chosen reference velocity, the closed form efficiently encapsulates an infinite number of terms in a single operation.; The impact of missing low frequencies on the leading order imaging series is examined. It is found that, while the predicted depths are more accurate when low frequency information is present, the algorithm can improve upon current linear imaging even when zero and some low frequencies are absent. Some improvement in the effectiveness of the algorithm when low frequency information is missing can be achieved by fixing the limits of the algorithm's integral to be over the known extent of the perturbation. The acquisition of lower frequency data, and the development of low frequency spectral extrapolation techniques will support the progression of this work to eventual field data tests.