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 Volume 50, Issue 4, 2002
Geophysical Prospecting  Volume 50, Issue 4, 2002
Volume 50, Issue 4, 2002


Seismic buffer recognition using wavelet‐based features and neural classification
Authors Alwyn Hoffman, Riaan Hoogenboezem, Theo Van Der Merwe and Tonie TolligOne of the first operations in a seismic signal processing system applied to earthquake data is to distinguish between valid and invalid records. Since valid signals are characterized by a combination of their time and frequency properties, wavelets are natural candidates for describing seismic features in a compact way. This paper develops a seismic buffer pattern recognition technique, comprising wavelet‐based feature extraction, feature selection based on the mutual information criterion, and neural classification based on feedforward networks. The ability of the wavelet transform to capture discriminating information from seismic data in a small number of features is compared with alternative feature reduction techniques, including statistical moments. Three different variations of the wavelet transform are used to extract features: the discrete wavelet transform, the single wavelet transform and the continuous wavelet transform. The mutual information criterion is employed to select a relatively small set of wavelets from the time–frequency grid. Firstly, it is determined whether wavelets can capture more informative data in an equal number of features compared with other features derived from raw data. Secondly, wavelet‐based features are compared with features selected based on prior knowledge of class differences. Thirdly, a technique is developed to optimize wavelet features as part of the neural network training process, by using the wavelet neural network architecture. The automated classification techniques developed in this paper are shown to perform similarly to human operators trained for this function. Wavelet‐based techniques are found to be useful, both for preprocessing of the raw data and for extracting features from the data. It is demonstrated that the definition of wavelet features can be optimized using the classification wavelet network architecture.



Traveltime computation with the linearized eikonal equation for anisotropic media
More LessA linearized eikonal equation is developed for transversely isotropic (TI) media with a vertical symmetry axis (VTI). It is linear with respect to perturbations in the horizontal velocity or the anisotropy parameter η. An iterative linearization of the eikonal equation is used as the basis for an algorithm of finite‐difference traveltime computations. A practical implementation of this iterative technique is to start with a background model that consists of an elliptically anisotropic, inhomogeneous medium, since traveltimes for this type of medium can be calculated efficiently using eikonal solvers, such as the fast marching method. This constrains the perturbation to changes in the anisotropy parameter η (the parameter most responsible for imaging improvements in anisotropic media). The iterative implementation includes repetitive calculation of η from traveltimes, which is then used to evaluate the perturbation needed for the next round of traveltime calculations using the linearized eikonal equation. Unlike isotropic media, interpolation is needed to estimate η in areas where the traveltime field is independent of η, such as areas where the wave propagates vertically.
Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach.



Out‐of‐plane geometrical spreading in anisotropic media
Authors Norman Ettrich, Anders Sollid and Bjørn UrsinTwo‐dimensional seismic processing is successful in media with little structural and velocity variation in the direction perpendicular to the plane defined by the acquisition direction and the vertical axis. If the subsurface is anisotropic, an additional limitation is that this plane is a plane of symmetry. Kinematic ray propagation can be considered as a two‐dimensional process in this type of medium. However, two‐dimensional processing in a true‐amplitude sense requires out‐of‐plane amplitude corrections in addition to compensation for in‐plane amplitude variation. We provide formulae for the out‐of‐plane geometrical spreading for P‐ and S‐waves in transversely isotropic and orthorhombic media. These are extensions of well‐known isotropic formulae.
For isotropic and transversely isotropic media, the ray propagation is independent of the azimuthal angle. The azimuthal direction is defined with respect to a possibly tilted axis of symmetry. The out‐of‐plane spreading correction can then be calculated by integrating quantities which describe in‐plane kinematics along in‐plane rays. If, in addition, the medium varies only along the vertical direction and has a vertical axis of symmetry, no ray tracing need be carried out. All quantities affecting the out‐of‐plane geometrical spreading can be derived from traveltime information available at the observation surface.
Orthorhombic media possess no rotational symmetry and the out‐of‐plane geometrical spreading includes parameters which, even in principle, are not invertible from in‐plane experiments. The exact and approximate formulae derived for P‐ and S‐waves are nevertheless useful for modelling purposes.



Fluid‐dependent shear‐wave splitting in fractured media
More LessAzimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. A shear wave propagating in an azimuthally anisotropic medium splits into two components with different polarizations if the source polarization is not aligned with the principal axes of the medium. For vertical propagation of shear waves in a horizontally layered medium containing vertical fractures, the shear‐wave splitting depends on the shear compliance of the fractures, but is independent of their normal compliance. If the fractures are not perfectly vertical, the shear‐wave splitting also depends on the normal compliance of the fractures. The normal compliance of a fluid‐filled fracture decreases with increasing fluid bulk modulus. For dipping fractures, this results in a decrease in shear‐wave splitting and an increase in shear‐wave velocity with increasing fluid bulk modulus. The sensitivity of the shear‐wave splitting to fluid bulk modulus depends on the interconnectivity of the fracture network, the permeability of the background medium and on whether the fracture is fully or partially saturated.



The Buffon's needle problem and the design of a geophysical survey
Authors Luigi Sambuelli and Claudio StrobbiaA logical procedure for designing a geophysical survey when sampling an area with a regular grid can be summarized as follows: model the expected anomaly, estimate the expected noise level, estimate the area of the anomaly above the noise level, choose the spacing, in both the x‐ and y‐directions, of the measurement grid. This last step can be approached according to two main strategies: either when applying the sampling theorem to the shortest dimension of the anomaly or when using a coarser grid, leaving a more complete definition of the anomaly to a later fitting. When following this second option, it can be constructive to estimate the probability of intercepting a given anomaly with a specific segment of profile and a given profile spacing. This latter procedure is analysed by considering a rectangle approximating the plane projection of the anomaly shape and taking into account various ratios between the grid spacing and the rectangle sides. The formulae for estimating the probability of intersecting a given anomaly with a given segment of a given profile spacing are calculated. To demonstrate the accuracy of the results, a Monte‐Carlo simulation on a synthetic magnetic map was performed, obtaining, for different ratios between the sides, segment length and profile interval, an agreement better than 0.1% with the analytical formulae.



Acquisition and processing of high‐resolution reflection seismic data from a survey within the complex terrain of the Bavarian Folded Molasse
Authors R. Thomas, K. Bram, J. Fertig and K. SchwerdA high‐resolution reflection seismic survey was carried out in the southern part of the Bavarian Molasse Basin in 1998 and 1999. The survey aimed to investigate the near‐surface structure of the complicated transition from the unfolded Foreland Molasse to the Folded Molasse, and the Folded Molasse to the internally complicated thrust systems of the Helveticum, the Ultrahelveticum and the Rhenodanubian Flysch. The study is linked to the TRANSALP seismic project, and the results help to fill the gap between the surface and the upper 300–500 ms two‐way traveltime (TWT), typical of deep‐reflection seismic experiments. The environmental conditions encountered in the study area required that particular attention be paid to the acquisition parameters for the three seismic lines (each about 4 km long). The energy source was a small vibrator; the geophone spread, spacing and frequency range were adjusted to image reflectors, which were expected to dip steeply southwards.
In general, the unprocessed field records did not show signals that could be attributed to specific reflectors. Individual trace processing considerably improved the data quality, taking into account the influence of the Quaternary cover and also the strong lateral velocity variations of the shallow subsurface. The effects of the various processing steps, such as muting, refraction statics, residual statics and velocity analysis, are discussed. To assess the NMO velocities, the qualitative analysis of the seismic energy in a common‐shotpoint gather offered advantages over an analysis in a common‐midpoint gather or in a stacked section, and proved to be very effective. As demonstrated along the Miesbach 9801 line, low‐velocity zones extend locally down to about 400 ms, adjacent to zones of extremely high velocities close to the surface, reflecting steeply dipping strata.
Besides the Quaternary cover on top, the Miesbach 9801 and Miesbach 9802 lines exhibit many horizontal reflections, in places down as far as 1400 ms TWT, indicating the sedimentary sequences of the unfolded Foreland Molasse. The southern part of both lines is dominated by southward‐dipping reflection bands, indicating units of the Folded Molasse. The reflection pattern shown by the Miesbach 9901 line suggests that there is almost no Quaternary cover. Southward‐dipping elements reflect the internal structure of the Folded Molasse, whereas a rather diffuse reflection signature may be attributed to Rhenodanubian Flysch units.

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