Seismic interferometry for seismic source location and interpolation of three-dimensional ocean bottom seismic data

This dissertation develops new seismic interferometry algorithms for estimation of seismic source locations and for the interpolation of sparse three-dimensional (3D) ocean bottom seismic (OBS) data. Unlike the conventional source location and interpolation methods, which heavily rely on the accuracy of the velocity models, the interferometric techniques extract the multiple scattering information in the data, and provide reliable results without knowledge of the velocity models. There are three main chapters in this dissertation. In Chapter 2 an interferometric imaging scheme, which is formulated as time-reversal mirrors (TRMs) in acoustics, is developed to backpropagate and refocus incident wavefields to their actual source location, with the subsequent benefits of imaging with superresolution and super-stacking properties. These benefits of TRMs have been previously verified with computer simulations and tank experiments, but not with exploration-scale seismic data. We now demonstrate, for the first time, the super-resolution and the super-stacking properties of TRMs with field seismic data. Tests on both synthetic data and field data show that TRM has the potential to exceed the Rayleigh resolution limit by factors of 7 or more. Results also show that TRM has a significant resilience to strong Gaussian noise, and that accurate imaging of source locations from passive seismic data can be accomplished with traces having signal-to-noise ratios as low as 0.001. Synthetic tests also demonstrate that TRMs enhance the signal by a factor proportional to the square root of the product of the number of traces and the number of events in the traces. This enhancement property is denoted as super-stacking and greatly exceeds the well-known square-root number-of-traces factor. Super-resolution and super-stacking are properties also enjoyed by seismic interferometry and reverse-time migration (RTM) with the exact velocity model. In Chapter 3 the equation for the vertical resolution limit ∆z is derived for the images obtained by cross-correlation migration (CCM). The analytical formula shows that ∆z = 4zo 2λ Lg 2 compared to the vertical resolution limit ∆z post. = λ2 for conventional migration; here λ is the dominant wavelength; zo is the depth of the scatterer, and Lg is the half length of the recording aperture. This result explains the degraded vertical resolution in CCM images compared to those obtained from poststack migration, and suggests that a good resolution at depth requires a large recording aperture. I extend the interferometric interpolation of ocean bottom seismic (OBS) traces from 2D data to 3D data in Chapter 4. The sparse OBS data are interferometrically correlated with the model-based Green’s functions for the sea-floor model to generate the densely recorded OBS traces, and a local matching filter is applied to reduce the artifacts in the interpolated data. Information about the source wavelet and the multilayered velocity model below the sea floor is not needed. Results with 3D synthetic data show that the OBS traces can be faithfully interpolated from a sparse sampling interval of 50 m, about one half of the minimum horizontal wavelength, in both the x and y directions. Interpolation results are also computed using sparse OBS data of different recording intervals, and the error analysis shows degrading interpolation accuracy when the recording interval increases. To mitigate the artifacts in the interferometry correlation results, an anti-aliasing condition is derived and demonstrated with a simple numerical example. The anti-aliasing theory developed here is a new development that establishes a fundamental criterion for numerically applying seismic interferometry to seismic data of any type.