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.

SUMMARY Formulas are derived that relate the strength of the crosstalk noise in supergather migration images to the variance of time, amplitude and polarity shifts in encoding functions. A supergather migration image is computed by migrating an encoded supergather, where the supergather is formed by stacking a large number of encoded shot gathers. Analysis reveals that for temporal source static shifts in each shot gather, the crosstalk noise is exponentially reduced with increasing variance of the static shift and the square of source frequency. This is not too surprising because larger time shifts lead to less correlation between traces in different shot gathers, and so should tend to reduce the crosstalk noise. Analysis also reveals that combining both polarity and time statics is a superior encoding strategy compared to using either polarity statics or time statics alone. Signal‐to‐noise (SNR) estimates show that for a standard migration image and for an image computed by migrating a phase‐encoded supergather; here, G is the number of traces in a shot gather, I is the number of stacking iterations in the supergather and S is the number of encoded/blended shot gathers that comprise the supergather. If the supergather can be uniformly divided up into Q unique sub‐supergathers, then the resulting SNR of the final image is , which means that we can enhance image quality but at the expense of Q times more cost. The importance of these formulas is that they provide a precise understanding between different phase encoding strategies and image quality. Finally, we show that iterative migration of phase‐encoded supergathers is a special case of passive seismic interferometry. We suggest that the crosstalk noise formulas can be helpful in designing optimal strategies for passive seismic interferometry and efficient extraction of Green's functions from simulated supergathers.

With the expansion of the Internet and World Wide Web (or the Web), research environments have changed dramatically. As a result, the need to be able to efficiently and securely access information and resources from remote computer systems is becoming even more critical. This paper describes the development of an extendable integrated Web-accessible simulation environment for computational science and engineering called Computational Science and Engineering Online (CSE-Online; http://cse-online.net). CSE-Online is based on a unique client-server software architecture that can distribute the workload between the client and server computers in such a way as to minimize the communication between the client and server, thus making the environment less-sensitive to network instability. Furthermore, the new software architecture allows the user to access data and resources on one or more remote servers as well as on the computing grid while having the full capability of the Web-services collaborative environment. It can be accessed anytime and anywhere from a Web browser connected to the network by either a wired or wireless connection. It has different modes of operations to support different working environments and styles. CSE-Online is evolving into middleware that can provide a framework for accessing and managing remote data and resources including the computing grid for any domain, not necessarily just within computational science and engineering.

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.

SummaryWe have developed a multisource full-waveform inversion algorithm using a dynamic phase encoding strategy with dualrandomization-both the position and polarity of simultaneous sources are randomized and changed every iteration. The dynamic dual-randomization is used to promote the destructive interference of crosstalk noise resulting from blending a large number of common shot gathers into a supergather. We compare our multisource algorithm with various algorithms in a numerical experiment using the 3D SEG/EAGE overthrust model and show that our algorithm provides a higher-quality velocity tomogram than the other methods that use only monorandomization. This suggests that increasing the degree of randomness in phase encoding should improve the quality of the inversion result.

SUMMARYWe present the theory and numerical results for least-squares reverse time migration (LSRTM) of phase-encoded supergathers, where each supergather is the superposition of phasedencoded shots. Three type of encoding functions are used in this study: random time shift, random source polarity and random source location selected from a pre-designed table. Numerical tests for the 3D SEG/EAGE Overthrust model show that multi-source LSRTM can suppress migration artifacts in the migration image and remove most of the crosstalk noise from multi-source data. Empirical results suggest that multisource LSRTM can provide a noticeable increase in computational efficiency compared to standard RTM, when the CSGs in a supergather are modeled and migrated together with a finite-difference simulator. If the phase-encoding functions are dynamically changed after each iteration of LSRTM, the best images are obtained. The potential drawback is that the final results are very sensitive to the accuracy of the starting model.

S U M M A R YFormulas are derived that relate the strength of the crosstalk noise in supergather migration images to the variance of time, amplitude and polarity shifts in encoding functions. A supergather migration image is computed by migrating an encoded supergather, where the supergather is formed by stacking a large number of encoded shot gathers. Analysis reveals that for temporal source static shifts in each shot gather, the crosstalk noise is exponentially reduced with increasing variance of the static shift and the square of source frequency. This is not too surprising because larger time shifts lead to less correlation between traces in different shot gathers, and so should tend to reduce the crosstalk noise. Analysis also reveals that combining both polarity and time statics is a superior encoding strategy compared to using either polarity statics or time statics alone.Signal-to-noise (SNR) estimates show that SNR stand. = √ G S for a standard migration image and SNR super = √ G I for an image computed by migrating a phase-encoded supergather; here, G is the number of traces in a shot gather, I is the number of stacking iterations in the supergather and S is the number of encoded/blended shot gathers that comprise the supergather. If the supergather can be uniformly divided up into Q unique sub-supergathers, then the resulting SNR of the final image is SNR sub-super = √ QG I , which means that we can enhance image quality but at the expense of Q times more cost. The importance of these formulas is that they provide a precise understanding between different phase encoding strategies and image quality.Finally, we show that iterative migration of phase-encoded supergathers is a special case of passive seismic interferometry. We suggest that the crosstalk noise formulas can be helpful in designing optimal strategies for passive seismic interferometry and efficient extraction of Green's functions from simulated supergathers.

ABSTRACT:This study provides an analysis of the convergence of the Haar wavelet-based method for solving twodimensional boundary value problems. The convergence analysis shows that the approximation method is of order 2. The analytical results are validated via two numerical examples.