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Many methods exist for interpolation of seismic data in one and two spatial dimensions, but few can interpolate properly in three or four spatial dimensions. Marine multi-streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled. We approach the problem of interpolation of marine-streamer data in four spatial dimensions by splitting the problem into a 1D interpolation along the densely sampled streamers and a 3D Fourier reconstruction for the remaining spatial coordinates. In Fourier reconstruction, the Fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least-squares inversion. The method is computationally efficient, requires no subsurface information, and can handle uniform grids with missing data as well as nonuniform grids or random sampling.The output grid of the 1D interpolation in the first step is arbitrary. When the output grid has uniform inline midpoints spacing, the 3D Fourier reconstruction in the second step is performed in the crossline midpoint, absolute offset, and azimuth coordinates. When the first step outputs to uniform absolute offset, the 3D Fourier reconstruction handles the crossline/inline midpoint and the azimuth coordinates. In both cases, the main innovation is the inclusion of the azimuthal coordinate in the Fourier reconstruction. The azimuth multiplicity must be increased for the method to be successful, which means that overlap shooting is required. We have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored. Potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3D multiple prediction and regularization to reduce sampling-related differences in processing of time-lapse data.

Lack of facilities in supporting design reuse is a serious problem in product shape modeling, especially in computer-aided design systems. This becomes a bottleneck of fast shape conceptualization and creation in consumer product design, which consequently prohibits creativity and innovation. In the past, several efforts have been made in order to improve this situation, with confined methodologies in the spatial domain, following conventional ways of geometrical operations. These domain dependent researches did not yield satisfactory solutions. Looking at the state of the art technologies, to find a better solution, an investigation applying interdisciplinary knowledge has to be conducted. The present study aimed at finding a systematic approach to support design reuse in shape modeling, especially Freeform Feature (FFF) reuse, by hypothesizing that a better solution could be achieved by applying signal processing techniques. This global goal was further decomposed into a number of concrete objectives, each correlated to a broad spectrum of domain specific knowledge. Investigations on relevant subjects enrich the aggregation of knowledge, especially that concerning computer-assisted technologies in industrial design field. Solutions of this study functionally extend the capability of shape modeling, and enhance the interchange ability of shape depiction between the spatial and the frequency domain. A number of examples were employed to test the methods and mathematical formulations proposed. The results affirm that the hypothesis works, and the methodology developed in this research are both effective and beneficial.

We modeled time-domain EM measurements of induction currents for marine and land applications with a frequency-domain code. An analysis of the computational complexity of a number of numerical methods shows that frequency-domain modeling followed by a Fourier transform is an attractive choice if a sufficiently powerful solver is available. A recently developed, robust multigrid solver meets this requirement. An interpolation criterion determined the automatic selection of frequencies. The skin depth controlled the construction of the computational grid at each frequency. Tests of the method against exact solutions for some simple problems and a realistic marine example demonstrate that a limited number of frequencies suffice to provide time-domain solutions after piecewise-cubic Hermite interpolation and a fast Fourier transform.

In the virtual source (VS) method we crosscorrelate seismic recordings at two receivers to create a new data set as if one of these receivers were a virtual source and the other a receiver. We focus on the amplitudes and kinematics of VS data, generated by an array of active sources at the surface and recorded by an array of receivers in a borehole. The quality of the VS data depends on the radiation pattern of the virtual source, which in turn is controlled by the spatial aperture of the surface source distribution. Theory suggests that when the receivers are surrounded by multi-component sources completely filling a closed surface, then the virtual source has an isotropic radiation pattern and VS data possess true amplitudes. In practical applications, limited sourceaperture and deployment of a single source type create an anisotropic radiation pattern of the virtual source, leading to distorted amplitudes. This pattern can be estimated by autocorrelating the spatial Fourier transform of the downgoing wavefield in the special case of a laterally invariant medium. The VS data can be improved by deconvolving the VS data with the estimated amplitude radiation pattern in the frequency-wavenumber domain. This operation alters the amplitude spectrum but not the phase of the data. We can also steer the virtual source by assigning it a new desired amplitude radiation pattern, given sufficient illumination exists in the desired directions. Alternatively, time-gating the downgoing wavefield before crosscorrelation, already common practice in implementing the VS method, can improve the radiation characteristics of a virtual source.

The full-wave computation of transient acoustic fields with sizes in the order of 100x100x100 wavelengths by 100 periods requires a numerical method that is extremely efficient in terms of storage and computation. Iterative integral equation methods offer a good performance on these points, provided that the recurring spatiotemporal convolutions are computed with a coarse sampling and relatively few computational operations. This paper describes a method for the numerical evaluation of very large-scale, four-dimensional convolutions that employs a fast Fourier transformation and that uses a sampling rate close to or at the limit of two points per wavelength and per period. To achieve this, the functions involved are systematically filtered, windowed, and zero-padded with respect to all relevant coordinates prior to sampling. The method is developed in the context of the Neumann iterative solution of the acoustic contrast source problem for an inhomogeneous medium. The implementation of the method on a parallel computer is discussed. The obtained numerical results have a relative root mean square error of a few percent when sampling at two points per wavelength and per period. Further, the results prove that the method enables the computation of transient fields in the order of the indicated size.

An intermediate frequency (IF) band digitizing radiometer system in the 100–200 GHz frequency range has been developed for Tokamak diagnostics and control, and other fields of research which require a high flexibility in frequency resolution combined with a large bandwidth and the retrieval of the full wave information of the mm-wave signals under investigation. The system is based on directly digitizing the IF band after down conversion. The enabling technology consists of a fast multi-giga sample analog to digital converter that has recently become available. Field programmable gate arrays (FPGA) are implemented to accomplish versatile real-time data analysis. A prototype system has been developed and tested and its performance has been compared with conventional electron cyclotron emission (ECE) spectrometer systems. On the TEXTOR Tokamak a proof of principle shows that ECE, together with high power injected and scattered radiation, becomes amenable to measurement by this device. In particular, its capability to measure the phase of coherent signals in the spectrum offers important advantages in diagnostics and control. One case developed in detail employs the FPGA in real-time fast Fourier transform (FFT) and additional signal processing. The major benefit of such a FFT-based system is the real-time trade-off that can be made between frequency and time resolution. For ECE diagnostics this corresponds to a flexible spatial resolution in the plasma, with potential application in smart sensing of plasma instabilities such as the neoclassical tearing mode (NTM) and sawtooth instabilities. The flexible resolution would allow for the measurement of the full mode content of plasma instabilities contained within the system bandwidth.

Acoustic experiments on the propagation of guided waves along water-filled boreholes in water-saturated porous materials are reported. The experiments were conducted using a shock tube technique. An acoustic funnel structure was placed inside the tube just above the sample in order to enhance the excitation of the surface modes. A fast Fourier transform-Prony-spectral ratio method is implemented to transform the data from the time-space domain to the frequency-wave-number domain. Frequency-dependent phase velocities and attenuation coefficients were measured using this technique. The results for a Berea sandstone material show a clear excitation of the fundamental surface mode, the pseudo-Stoneley wave. The comparison of the experimental results with numerical predictions based on Biot’s theory of poromechanics [ J. Acoust. Soc. Am. 28, 168 (1956) ], shows that the oscillating fluid flow at the borehole wall is the dominant loss mechanism governing the pseudo-Stoneley wave and it is properly described by the Biot’s model at frequencies below 40 kHz. At higher frequencies, a systematic underestimation of the theoretical predictions is found, which can be attributed to the existence of other losses mechanisms neglected in the Biot formulation. Higher-order guided modes associated with the compressional wave in the porous formation and the cylindrical geometry of the shock tube were excited, and detailed information was obtained on the frequency-dependent phase velocity and attenuation in highly porous and permeable materials. The measured attenuation of the guided wave associated with the compressional wave reveals the presence of regular oscillatory patterns that can be attributed to radial resonances. This oscillatory behavior is also numerically predicted, although the measured attenuation values are one order of magnitude higher than the corresponding theoretical values. The phase velocities of the higher-order modes are generally well predicted by theory.