A tomographic technique (traveltime inversion) has been developed to obtain a two‐ or three‐dimensional velocity structure of the subsurface from well logs, vertical seismic profiles (VSP), and surface seismic measurements. The earth was modeled by continuous curved interfaces (polynomial or sinusoidal series), separating regions of constant velocity or transversely isotropic velocity. Ray tracing for each seismic source‐receiver pair was performed by solving a system of nonlinear equations which satisfy the generalized Snell’s law. Surface‐to‐borehole and surface‐to‐surface rays were included. A damped least‐squares formulation provided the updating of the earth model by minimizing the difference between the traveltimes picked from the real data and calculated traveltimes. Synthetic results indicated the following conclusions. For noise‐free cases, the inversion converged closely from the initial guess to the true model for either surface or VSP data. Adding random noise to the observations and performing the inversion indicated that (1) using surface data alone allows reconstruction of the broad velocity structure but with some inaccuracy; (2) using VSP data alone gives a very accurate but laterally limited velocity structure; and (3) the integration of both data sets produces a more laterally extensive, accurate image of the subsurface. Finally, a field example illustrates the viability of the method to construct a velocity structure from real data.

A computerized seismic tomographic method was developed to obtain body‐wave velocities and three‐dimensional (3-D) structure of interfaces from reflection data simultaneously. The medium consists of layers with continuous arbitrary 3-D curved interfaces separating homogeneous material with different acoustic properties. The interface is defined by a polynomial surface. The elastic waves are assumed to be transmitted or reflected at curved interfaces in which the raypaths satisfy Snell's law. The ray tracing for each source‐receiver pair is determined by solving a system of nonlinear equations. This method of 3-D ray tracing is effective in computing many seismic rays, including converted phases and multiples. A damped least‐squares inversion scheme is formulated to reconstruct the interval velocity and 3-D structure of the interface by minimizing the difference between observed traveltimes and computed traveltimes. The results from a synthetic model indicate that the solutions converge quickly to the true model. The seismic tomographic method was applied to a Vibroseis seismic section obtained in 1984 on Vancouver Island as part of PROJECT LITHOPROBE. The method was found to be useful for imaging the 3-D subsurface of subducting plates by taking advantage of crooked lines in the nominally two‐dimensional seismic reflection survey.

The attenuation of coherent and random noise still poses technical challenges in seismic data processing, especially in onshore environments. Multichannel Singular Spectrum Analysis (MSSA) is an existing and effective technique for random‐noise reduction. By incorporating a randomizing operator into MSSA, this modification creates a new and powerful filtering method that can attenuate both coherent and random noise simultaneously. The key of the randomizing operator exploits the fact that primary events after NMO are relatively horizontal. The randomizing operator randomly rearranges the order of input data and reorganizes coherent noise into incoherent noise but has a minimal effect on nearly horizontal primary reflections. The randomizing process enables MSSA to suppress both coherent and random noise simultaneously. This new filter, MSSARD (MSSA in the randomized domain) also resembles a combination of eigenimage and Cadzow filters. I start with a synthetic data set to illustrate the basic concept and apply MSSARD filtering on a 3D cross‐spread data set that was severely contaminated with ground roll and scattered noise. MSSARD filtering gives superior results when compared with a conventional 3D f‐k filter. For a random‐noise example, the application of MSSARD filtering on time‐migrated offset‐vector‐tile (OVT) gathers also produces images with higher signal‐to‐noise ratios than a conventional f‐xy deconvolution filter.

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Fourier-based minimum weighted norm interpolation (MWNI) has been widely used to regularize land seismic data. However, it has difficulty interpolating regular missing data that are spatially aliased. Minimizing the aliasing artifacts is still a technical challenge in MWNI. I have developed a novel method to address the aliasing problem in MWNI using a prior model as constraints. The prior model was constructed by a linear interpolation along dominant dips to produce a fully regular initial model. The spectral weights derived from this initial model are typically not aliased and can be used to constrain the least-squares inversion in MWNI, frequency by frequency, to overcome the aliasing artifacts. This new interpolation scheme expands the capability of conventional MWNI to handle spatially aliased data that are often associated with steeply dipping structures, and it reconstructs more reliable interpolation results. Decimation tests of a simple 2D synthetic data set and a complex 3D synthetic salt model revealed that model-constrained MWNI outperforms the conventional MWNI method in handling spatially aliased data. I applied this method to a land field data set and carried out a comprehensive evaluation of interpolated data through the processes of prestack analyses, prestack time migration, and prestack depth migration. The 5D interpolation successfully filled in missing data, increased spatial sampling of prestack gathers, and considerably improved migrated stacked images from the prestacked time and depth imaging.