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Prestack depth migration of shot profiles by downward continuation is a practical imaging algorithm that is especially cost-effective for sparse-shot wide-azimuth geometries. The interpretation of offset as the displacement between the downward-propagating (shot) wavefield and upward-propagating (receiver) wavefield enables us to extract offset-domainâ€¦ (More)

The acoustic time history of the sunâ€™s surface is a stochastic t x y -cube of information. Helioseismologists cross-correlate these noise traces to produce impulse response seismograms, providing the proof of concept for a long-standing geophysical conjecture. We pack the x y -mesh of time series into a single super-long one-dimensional time series. Weâ€¦ (More)

In order to estimate elastic parameters of the subsurface, geophysicists need reliable information about angle-dependent reflectivity. In this paper, we describe how to image nonzero offsets during shot-profile migration so that they can be mapped to the angle domain with Sava and Fomelâ€™s (2000) transformation. CIGs also contain information about how wellâ€¦ (More)

Previous authors have tried to image seismic reflectivity by crosscorrelating passive seismic data, and treating the resultant correlograms as active source seismograms. We provide a mathematical framework for working with passive seismic correlograms that is both appropriate for V (x , y, z) media, and arbitrary source location. Under this framework,â€¦ (More)

Wavefield extrapolation in the (Ï‰âˆ’x) domain provides a tool for depth migration with strong lateral variations in velocity. Implicit formulations of depth extrapolation have several advantages over explicit methods. However, the simple 3-D extension of conventional 2-D wavefield extrapolation by implicit finite-differencing requires the inversion of a 2-Dâ€¦ (More)

The change in the reflection polarity at normal incidence is a fundamental feature of converted-wave seismology due to the vector nature of the displacement field. The conventional way of dealing with this feature is to reverse the polarity of data recorded at negative offsets. However, this approach fails in presence of complex geology. To solve thisâ€¦ (More)

- James E. Rickett
- 2001

Illumination problems caused by finite-recording aperture and lateral velocity lensing can lead to amplitude fluctuations in migrated images. I calculate both model and data-space weighting functions that compensate for these illumination problems in recursive depth migration results based on downward-contination. These weighting functions can either beâ€¦ (More)

- James E. Rickett
- 2000

Fourier finite-difference (FFD) migration combines the complementary advantages of the phase-shift and finite-difference migration methods. However, as with other implicit finite-difference algorithms, direct application to 3-D problems is prohibitively expensive. Rather than making the simple x y splitting approximation that leads to extensive azimuthalâ€¦ (More)

For every two-dimensional system with helical boundary conditions, there is an isomorphic one-dimensional system. Therefore, the one-dimensional FFT of a 2-D function wrapped on a helix is equivalent to a 2-D FFT. We show that the Fourier dual of helical boundary conditions is helical boundary conditions but with axes transposed, and we explicitly link theâ€¦ (More)

Calculation of time-distance curves in helioseismology can be formulated as a blind-deconvolution (or system identification) problem. A classical solution in one-dimensional space is Kolmogorovâ€™s Fourier domain spectral-factorization method. The helical coordinate system maps two-dimensions to one. Likewise a three-dimensional volume is representable as aâ€¦ (More)