New Green's Theorem- Dr. Arthur Weglein

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The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow and levels of neurotransmitters and endorphins which elevate and stabilize mood.

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A new and general wave theoretical wavelet estimation method is derived. Knowing the seismic wavelet is important both for processing seismic data and for modeling the seismic response. To obtain the wavelet, both statistical (e.g., Wiener-Levinson) and deterministic (matching surface seismic to well-log data) methods are generally used. In the marine case, a far-field signature is often obtained with a deep-towed hydrophone. The statistical methods do not allow obtaining the phase of the wavelet, whereas the deterministic method obviously requires data from a well. The deep-towed hydrophone requires that the water be deep enough for the hydrophone to be in the far field and in addition that the reflections from the water bottom and structure do not corrupt the measured wavelet. None of the methods address the source array pattern, which is important for amplitude-versus- offset (AVO) studies.

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The inverse scattering series for tasks associated with primaries: direct non-linear inversion of 1D elastic media. In this paper, research on direct inversion for two parameter acoustic media (Zhang and Weglein, 2005) is extended to the three parameter elastic case. We present the first set of direct non-linear inversion equations for 1D elastic media (i.e., depth varying P-velocity, shear velocity and density). The terms for moving mislocated reflectors are shown to be separable from amplitude correction terms. Although in principle this direct inversion approach requires all four components of elastic data, synthetic tests indicate that consistent value-added results may be achieved given only ˆDPP measurements. We can reasonably infer that further value would derive from actually measuring ˆDPP , ˆD PS, ˆDSP and ˆDSS as the method requires. The method is direct with neither a model matching nor cost function minimization.

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Internal multiple attenuation using inverse scattering: Results from prestack 1 & 2D acoustic and elastic synthetics R. T. Coates*, Schlumberger Cambridge Research, A. B. Weglein, Arco Exploration and Production Technology Summary The attenuation of internal multiples in a multidimensional earth is an important and longstanding problem in exploration seismics. In this paper we report the results of applying an attenuation algorithm based on the inverse scattering series to synthetic prestack data sets generated in on and two dimensional earth models. The attenuation algorithm requires no information about the subsurface structure or the velocity field. However, detailed information about the source wavelet is a prerequisite. An attractive feature of: the attenuation algorithm is the preservation of the amplitude (and phase) of primary events in the data; thus allowing for subsequent AVO and other true amplitude processing.

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The Inverse Scattering Series (ISS) is a direct inversion method for a multidimensional acoustic, elastic and anelastic earth. It communicates that all inversion processing goals are able to be achieved directly and without any subsurface information. This task is reached through a task-specific subseries of the ISS. Using primaries in the data as subevents of the first-order internal multiples, the leading-order attenuator can predict the time of all the first-order internal multiples and is able to attenuate them. However, the ISS internal multiple attenuation algorithm can be a computationally demanding method specially in a complex earth. By using an approach that is based on two angular quantities and that was proposed in Terenghi et al. (2012), the cost of the algorithm can be controlled. The idea is to use the two angles as key-control parameters, by limiting their variation, to disregard some calculated contributions of the algorithm that are negligible. Moreover, the range of integration can be chosen as a compromise of the required degree of accuracy and the computational time saving. This time-saving approach is presented

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A multiple attenuation method derived from an inverse scattering series is described. The inversion series approach allows a separation of multiple attenuation subseries from the full series. The surface multiple attenuation subseries was described and illustrated in Carvalho et al. (1991, 1992). The internal multiple attenuation method consists of selecting the parts of the odd terms that are associated with removing only multiply reflected energy. The method, for both types of multiples, is multidimensional and does not rely on periodicity or differential moveout, nor does it require a model of the reflectors generating the multiples. An example with internal and surface multiples will be presented.

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Summary Methods for removal of free-surface and internal multiples have been developed from bath a feedback model approach and inverse scatterin g theory. White these two formulations derive from different mathematica) viewpoints, the resulting algorithm s for free-surface multiple are very similar. By contrast , the feedback and inverse scattering method for internal multiple are totally different and have different requirements for sub surface information or interpretive intervention . The former removes all multiple related to a certain boundary with the a of a surface integral along this boundary ; the alter wilt predict and attenuate a ll internal multiple a t the same time . In this paper, we continue our comparison study of these internal multiple attenuation method ; specifically , we examine two different realizations of the feedback method and the inverse scattering technique .

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