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A recently developed time-domain multiscale waveform tomography (MWT) method is applied to synthetic and field marine data. Although the MWT method was already applied to synthetic data, the synthetic data application leads to a development of a hybrid method between waveform tomography and the salt flooding technique commonly use in subsalt imaging. This hybrid method can overcome a convergence problem encountered by inversion with a traveltime velocity tomogram and successfully provides an accurate and highly resolved velocity tomogram for the 2D SEG/EAGE salt model. In the application of MWT to the field data, the inversion process is carried out using a multiscale method with a dynamic early-arrival muting window to mitigate the local minima problem of waveform tomography and elastic effects. With the modified MWT method, reasonably accurate results as verified by comparison of migration images and common image gathers were obtained. The hybrid method with the salt flooding technique is not used in this field data example because there is no salt in the subsurface according to our interpretation. However, we believe it is applicable to field data applications.

This efficient multiscale method for time-domain waveform tomography incorporates filters that are more efficient than Hamming-window filters. A strategy for choosing optimal frequency bands is proposed to achieve computational efficiency in the time domain. A staggered-grid, explicit finite-difference method with fourth-order accuracy in space and second-order accuracy in time is used for forward modeling and the adjoint calculation. The adjoint method is utilized in inverting for an efficient computation of the gradient directions. In the multiscale approach, multifrequency data and multiple grid sizes are used to overcome somewhat the severe local minima problem of waveform tomography. The method is applied successfully to 1D and 2D heterogeneous models; it can accurately recover low- and high-wavenumber components of the velocity models. The inversion result for the 2D model demonstrates that the multiscale method is computationally efficient and converges faster than a conventional, single-scale method.

Recent applications of 2D and 3D turning-ray tomography show that near-surface velocities are important for structural imaging and reservoir characterization. For structural imaging, we used turning-ray tomography to estimate the near-surface velocities for static corrections followed by prestack time migration and the near-surface velocities for prestack depth migration. Two-dimensional acoustic finite-difference modeling illustrates that wave-equation prestack depth migration is very sensitive to the near-surface velocities. Field data demonstrate that turning-ray tomography followed by prestack time migration helps to produce superior images in complex geologic settings. When the near-surface velocity model is integrated into a background velocity model for prestack depth migration, we find that wave propagation is very sensitive to the velocities immediately below the topography. For shallow-reservoir characterization, we developed and applied azimuthal turning-ray tomography to investigate observed apparent azimuthal-traveltime variations, using a wide-azimuth land seismic survey from a heavy-oil field at Surmont, Canada. We found that the apparent azimuthal velocity variations are not necessarily related to azimuthal anisotropy, or horizontal transverse isotropy (HTI), induced by the stress field or fractures. Near-surface heterogeneity and the acquisition footprint also could result in apparent azimuthal variations.

Seismic imaging in compressional belts such as the Canadian Foothills is very challenging due to complex geological structures, rugged surface topography, and highly variable near-surface conditions. Seismic sections across the Canadian Foothills are usually progressively more distorted when approaching the Canadian Foothills region. Figure 1 shows the degree of structural complexity and topographic variations which are in part responsible for the deteriorated imaging in the thrust belt. Accurate velocity models of subsurface structures are critical for improving seismic images of thrust belts in both the time domain (e.g., tomostatics) and the depth domain (e.g., prestack depth migration).

We present an application of time-domain waveform tomography to a marine dataset. The data are lowpass filtered using a Wiener filter, and the inversion is carried out using a multiscale method with a dynamic early-arrival muting window. The adjoint method is used in the inversion for an efficient computation of the gradient directions. A staggered-grid, explicit finitedifference method with 4-order accuracy in space and 2-order accuracy in time is utilized for forward modeling and the adjoint calculation. Our method is applied to a marine seismic dataset. The initial velocity model for waveform tomography is obtained by using traveltime tomography with dynamic smoothing filters. The velocity tomogram obtained from waveform tomography has a higher resolution and a better accuracy than the initial model. The tomogram accuracy is verified by comparing common image gathers. INTRODUCTION Waveform tomography can theoretically provide an accurate and highly resolved estimate of the subsurface velocity structure. However, in practice, the problem is highly nonlinear, and a waveform tomography method will tend to converge to a local minimum if the starting model is not in the vicinity of the global minimum (Gauthier et al., 1986). Therefore, a good initial velocity model is required by waveform tomography to partially overcome the local minima problem. To further mitigate the nonlinearity, a multiscale approach can be utilized in either the frequency domain (Sirgue and Pratt, 2004; Brenders and Pratt, 2007) or the time domain (Bunks et al., 1995; Boonyasiriwat et al., 2008). A multiscale approach can be effectively applied to solve the local minima problem, and is computationally efficient. The nonlinearity of waveform tomography depends on the frequency content of seismic data. The misfit function at low frequencies is more linear than at high frequencies. Therefore, the inversion process that sequentially proceeds from low to high frequencies has a better chance to reach the global minimum compared to using highfrequency, raw data (Sirgue and Pratt, 2004; Boonyasiriwat et al., 2008). At low frequencies, coarser grids can be used for computing numerical solutions of the wave equation than at high frequencies resulting to a computational efficiency. In this paper, we present a multiscale method for timedomain waveform tomography proposed by Boonyasiriwat et al. (2008) and apply it to a marine dataset. The data are low-pass filtered into 2 frequency bands to allow the inversion to proceed from low to high frequencies. The inversion is carried out using a multiscale method and a dynamic early-arrival muting window. The inverted tomogram is more accurate than the initial model, and it further enhances the migration image. ACOUSTIC WAVEFORM TOMOGRAPHY In this section, we briefly review the theory of time-domain waveform tomography. The constant-density acoustic wave equation is used as our forward model, given by 1 c(r) ∂p(r, t|rs) ∂t −∇p(r, t|rs) = s(r, t|rs), (1) where p(r, t|rs) is the pressure field at position r at time t from a source at rs, c(r) is the velocity model, and s(t) is the source function. In term of the Green’s function G(r, t|r, 0) associated with equation 1, the solution, p(r, t|rs), can be written as

We propose a time-domain multiscale waveform tomography method by combining earlyarrival waveform tomography and time-domain multiscale waveform tomography. A Wiener filter is used for data processing and a multiscale V-cycle with an adaptive early-arrival muting window for the inversion. The proposed method is very robust and can reconstruct an accurate velocity structure from marine seismic data.

Accurate subsurface velocity estimation is crucial in seismic exploration, especially for prestack depth migration, depth conversion, geopressure prediction and AVO attribute computation. 3D reflection tomography is the most accurate method available for velocity estimation. The challenge that we face is in designing an accurate tomographic system capable of efficiently handling large volumes of seismic data acquired over increasingly complex targets.

Summary When complex structures with large velocity contrasts are present, wavefield techniques can provide improved imaging (structure, amplitude, and phase) over the more traditional Kirchhoff integral methods. Wavefield techniques rely on two elements: firstly, an advanced acquisition design with complete azimuthal coverage; and, secondly, wave equation based prestack imaging methods. Together, these two elements offer improved seismic imaging in complex structural environments by better handling of multipathing, amplitudes and phase. A wavefield experiment was conducted last year in a complex subsalt area of the deepwater Gulf of Mexico using a fullazimuth vertical cable acquisition strategy. Here, we discuss some of the unique challenges associated with wavefield imaging such as velocity analysis and residuals correction. Finally, comparisons will be shown between conventional Kirchhoff imaging and wavefield imaging.

Summary Wavefield imaging techniques take advantage of both advanced acquisition designs and wave-equation based prestack depth migration. Advanced acquisition designs, such as vertical cable seismic and ocean bottom seismometer, offer complete azimuthal coverage. Waveequation based prestack depth migration offers advantages over Kirchhoff methods by better handling of multipathing, amplitudes, and phase in complex velocity structures. To implement wavefield imaging techniques, we choose reverse-time migration because of its ability to handle large lateral velocity variations without dip limits. We focus our discussions on migration cost, internal reflections, boundary reflections, and coarse data sampling. Finally, we present synthetic vertical cable data tests.

We parameterize the analytical migration velocity analysis (AMVA) problem by analysis of the re ectornormal mis t versus di erent migration parameters. AMVA is then treated as a parameter iden ti cation problem. We introduce the re e ctor-normal directional derivatives, whic hconnect the measured mis t data with the perturbations to the parameters. The velocity gradien testimation problem is typically insu ciently constrained by the measured mis t data alone. How ever, the problem may turn into a w ellbeha ved system if other velocity constraints can be incorporated into the system to constrain the uncertainties. Here, we deriv e a linear system for velocity gradient estimation in such a way that di erent constrain ts can be e ciently incorporated into the system. T o test the approach, the proposed algorithms are applied to both a 3-D syn thetic data set and a 3-D streamer data set acquired in the Gulf of Mexico. It is found that, although the measured mis t data alone are not su cient to constrain the uncertainties, there are \enough" velocity constrain tsin both cases such that the vertical velocity gradien tsare resolv ed within acceptable precision.

Summary Tetrahedral anisotropic ray tracing has been applied to Kirchhoff prestack depth migration for 3-D media. Utilizing a tetrahedron as the basic model element permits complex structures to be accurately and efficiently represented. The algorithm for anisotropic ray tracing is semi-analytic, and thus is computationally efficient. The Kirchhoff method for prestack depth migration is a well-established and robust technique for improving subsurface imaging in complex geologic areas. The extension to anisotropic Kirchhoff prestack depth migration enables more accurate positioning and improved focusing of reflectivity associated with anisotropic media.

SUMMARY There is an increasing amount of seismic exploration in areas of complex geological structure and strong seismic velocity contrasts. Conventional 3D seismic processing in the time domain has proven inadequate to image these areas. Depth imaging technology applied in the poststack and prestack domain can provide significantly improved images. Obtaining reliable depth seismic images in areas of complex geology requires proper application of techniques in acquisition, processing, velocity modeling and imaging. To properly image seismic data, both the structure and velocity of a layer are needed. A velocity estimation package based on horizon-based prestack depth migration (HPSDM) has been developed to derive 3D seismic velocity models. This method can also be used to examine the effects of acquisition geometry on velocity estimation and subsurface illumination. This paper will present a case study using these procedures.

Wide angle recordings at offsets between 20 and 40 km in the Ruby Mountains consistently show 5 strong reflections between 4 and 11 s with enough moveout to estimate velocities to the base of the crust. The uppermost “layer” with a temperature corrected velocity of 6.2 km/s and thickness of 9 km corresponds to quartzofeldspathic rocks such as metasedimentary rocks, migmatites and deformed granites and is underlain by a 7-km-thick “layer” with velocities of 6.4 km/s which corresponds to quartzofeldspathic material interlayered with amphibolites. The lower crust consists of a heterogeneous, 9 km-thick zone with velocities of 6.7 to 6.8 km/s corresponding to mafic rocks interlayered with smaller amounts of quartzofeldspathic rock. The lowermost crust is marked by the “X” reflection overlying a 3-km-thick “layer” with velocities between 7.4-7.8 km/s corresponding to anomolous material, possibly layered cumulates. The subhorizontal, layered structure of the crust is caused primarily by ductile extension, which may well be superposed on material added to the crust by underplating. At most, approximately one third of the present crust could have been added by underplating in the Cenozoic.