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Frequency-domain shot-record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computing cost of shotrecord migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade-off between accuracy and speed.Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency-domain shot-record migration algorithms. The difficulty with this approach is the production of so-called crossterms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the singleshot-per-migration result, we have introduced a process called phase encoding, which shifts or disperses these crossterms. The process of phase encoding thus allows one to trade S/N ratio for the speed of migrating the entire survey.Several encoding functions and two application strategies have been tested. The first strategy, combining multiple shots per migration and using each shot only once, reduces computation in direct relation to the number of shots combined. The second strategy, performing multiple migrations of all the shots in the survey, provides a means to reduce the crossterm noise by stacking the resulting images. The additional noise in both strategies may be tolerated if it is no stronger than the inherent seismic noise in the migrated image and if the final image is achieved with less cost.

A laboratory experiment was performed to study the dynamically rich interaction of a turbulent open channel flow with a bed-mounted axial-flow hydrokinetic turbine. An acoustic Doppler velocimeter and a torque transducer were used to simultaneously measure at high temporal resolution the three velocity components of the flow at various locations upstream of the turbine and in the wake region and turbine power, respectively. Results show that for sufficiently low frequencies the instantaneous power generated by the turbine is modulated by the turbulent structure of the approach flow. The critical frequency above which the response of the turbine is decoupled from the turbulent flow structure is shown to vary linearly with the angular frequency of the rotor. The measurements elucidate the structure of the turbulent turbine wake, which is shown to persist for at least fifteen rotor diameters downstream of the rotor, and a new approach is proposed to quantify the wake recovery, based on the growth of the largest scale motions in the flow. Spectral analysis is employed to demonstrate the dominant effect of the tip vortices in the energy distribution in the near-wake region and uncover meandering motions.

Reverse-time migration (RTM) exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models. However, low-frequency, high-amplitude noises commonly seen in a typical RTM image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly. We propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image. The method works by first decomposing the source and receiver wavefields to their one-way propagation components, followed by applying a correlation-based imaging condition to the appropriate combinations of the decomposed wavefields. We first give the physical explanation of the principle of such noises in the conventional RTM image. Then we provide the detailed mathematical theory for the new imaging condition. Finally, we propose an efficient scheme for its numerical implementation. It replaces the computationally intensive decomposition with the cost-effective Hilbert transform, which significantly improves the efficiency of the imaging condition. Applications to various synthetic and real data sets demonstrate that this new imaging condition can effectively remove the undesired low-frequency noises in the image.

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We present a comprehensive study of magnetohydrodynamic (MHD) waves and instabilities in a weakly-ionized system, such as an interstellar molecular cloud. We determine all the critical wavelengths of perturbations across which the sustainable wave modes can change radically (and so can their decay rates), and various instabilities are present or absent. Hence, these critical wavelengths are essential for understanding the effects of MHD waves (or turbulence) on the structure and evolution of molecular clouds. Depending on the angle of propagation relative to the zeroth-order magnetic field and the physical parameters of a model cloud, there are wavelength ranges in which no wave can be sustained as such. Yet, for other directions of propagation or different properties of a model cloud, there may always exist some wave mode(s) at all wavelengths (smaller than the size of the model cloud). For a typical model cloud, magnetically-driven ambipolar diffusion leads to removal of any support against gravity that most short-wavelength waves (or turbulence) may have had, and gravitationally-driven ambipolar diffusion sets in and leads to cloud fragmentation into stellar-size masses, as first suggested by Mouschovias more than three decades ago -a single-stage fragmentation theory of star formation, distinct from the then prevailing hierarchical fragmentation picture. The phase velocities, decay times and eigenvectors (e.g. the densities and velocities of neutral particles and the plasma, and the three components of the magnetic field) are determined as functions of the wavelength of the disturbances in a mathematically transparent way and are explained physically. Comparison of the results with those of nonlinear analytical or numerical calculations is also presented where appropriate, excellent agreement is found, and confidence in the analytical, linear approach is gained to explore phenomena difficult to study through numerical simulations. Mode splitting (or bifurcation) and mode merging, which are impossible in single-fluid systems for linear perturbations (hence, the term 'normal mode' and the principle of superposition), occur naturally in multifluid systems (as do transitions between wave modes without bifurcation) and have profound consequences in the evolution of such systems.

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