AMPLITUDE-VERSUS-ANGLE ANALYSIS AND WIDE-ANGLE-INVERSION OF CROSSWELL SEISMIC DATA IN A CARBONATE RESERVOIR

Crosswell data set contains a range of angles limited only by the geometry of the source and receiver configuration, the separation of the boreholes and the depth to the target. However, the wide angles reflections present in crosswell imaging result in amplitude-versus-angle (AVA) features not usually observed in surface data. These features include reflections from angles that are near critical and beyond critical for many of the interfaces; some of these reflections are visible only for a small range of angles, presumably near their critical angle. High-resolution crosswell seismic surveys were conducted over a Silurian (Niagaran) reef at two fields in northern Michigan, Springdale and Coldspring. The Springdale wells extended to much greater depths than the reef, and imaging was conducted from above and from beneath the reef. Combining the results from images obtained from above with those from beneath provides additional information, by exhibiting ranges of angles that are different for the two images, especially for reflectors at shallow depths, and second, by providing additional constraints on the solutions for Zoeppritz equations. Inversion of seismic data for impedance has become a standard part of the workflow for quantitative reservoir characterization. Inversion of crosswell data using either deterministic or geostatistical methods can lead to poor results with phase change beyond the critical angle, however, the simultaneous pre-stack inversion of partial angle stacks may be best conducted with restrictions to angles less than critical. Deterministic inversion is designed to yield only a single model of elastic properties (best-fit), while the geostatistical inversion produces multiple models (realizations) of elastic properties, lithology and reservoir properties. Geostatistical inversion produces results with far more detail than deterministic inversion. The magnitude of difference in details between both types of inversion becomes increasingly pronounced for thinner reservoirs, particularly those beyond the vertical resolution of the seismic. For any interface imaged from above and from beneath, the results AVA characters must result from identical contrasts in elastic properties in the two sets of images, albeit in reverse order. An inversion approach to handle both datasets simultaneously, at pre-critical angles, is demonstrated in this work. The main exploration problem for carbonate reefs is determining the porosity distribution. Images of elastic properties, obtained from deterministic and geostatistical simultaneous inversion of a high-resolution crosswell seismic survey were used to obtain the internal structure and reservoir properties (porosity) of Niagaran Michigan reef. The images obtained are the best of any Niagaran pinnacle reef to date.

MIMO waveform design using continuous phase modulation

Hybrid MIMO Phased-Array Radar (HMPAR) is an emerging technology that combines MIMO (multiple-in, multiple-out) radar technology with phased-array radar technology. The new technology is in its infancy, but much of the theoretical work for this specific project has already been completed and is explored in great depth in [1]. A brief overview of phased-array radar systems, MIMO radar systems, and the HMPAR paradigm are explored in this paper. This report is the culmination of an effort to support research in MIMO and HMPAR utilizing a concept called intrapulse beamscan. Using intrapulse beamscan, arbitrary spatial coverage can be achieved within one MIMO beam pulse. Therefore, this report focuses on designing waveforms for MIMO radar systems with arbitrary spatial coverage using that phenomenon. With intrapulse beamscan, scanning is done through phase-modulated signal design within one pulse rather than phase-shifters in the phased array over multiple pulses. In addition to using this idea, continuous phase modulation (CPM) signals are considered for their desirable peak-to-average ratio property as well as their low spectral leakage. These MIMO waveforms are designed with three goals in mind. The first goal is to achieve flexible spatial coverage while utilizing intrapulse beamscan. As with almost any radar system, we wish to have flexibility in where we send our signal energy. The second goal is to maintain a peak-to-average ratio close to 1 on the envelope of these waveforms, ensuring a signal that is close to constant modulus. It is desired to have a radar system transmit at the highest available power; not doing so would further diminish the already very small return signals. The third goal is to ensure low spectral leakage using various techniques to limit the bandwidth of the designed signals. Spectral containment is important to avoid interference with systems that utilize nearby frequencies in the electromagnetic spectrum. These three goals are realized allowing for limitations of real radar systems. In addition to flexible spatial coverage, the report examines the spectral properties of utilizing various space-filling techniques for desired spatial areas. The space-filling techniques examined include Hilbert/Peano curves and standard raster scans.