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Contrary to popular belief, a linearized approximation of the Zoeppritz equations may be used to estimate the reflection coefficient for angles of incidence up to and beyond the critical angle. These supercritical reflection coefficients are complex, implying a phase variation with offset in addition to amplitude variation with offset (AVO). This linearized approximation is then used as the basis for an AVO waveform inversion. By incorporating this new approximation, wider offset and angle data may be incorporated in the AVO inversion, helping to stabilize the problem and leading to more accurate estimates of reflectivity, including density reflectivity.

A method is presented for efficiently and accurately calculating the spherical-wave generalization of the Zoeppritz P-wave reflection coefficients. The main assumptions are that the wavelet is an exponential form that allows for analytic integration over frequency, and the direction of propagation and arrival time are as dictated by ray theory. These assumptions result in calculations sufficiently rapid to be carried out interactively on the computer. Results for an AVO Class I model show that this method quantitatively reproduces exact spherical-wave reflection coefficients obtained using a Ricker wavelet.

We investigated the accuracy of surface seismic attributes in predicting fracture density variations within the Nordegg Formation in west central Alberta. We know from core, drill samples, well-log, and drilling data that the Nordegg zone is fractured to some degree. These fractures are of interest because the reservoir has very low permeability, and therefore natural fractures may materially affect well performance. 3D surface seismic techniques such as amplitude variation with azimuth or azimuthal AVO (AVAz), variation of velocity with azimuth (VVAz), curvature, and coherence techniques are all tools that have been used to predict fractures in a qualitative fashion. In this study, we wanted to understand how well these attributes predicted the reservoir quality in a quantitative fashion. Previous quantitative studies have used image log orientation data or estimated ultimate recoveries (EUR) in vertical wells as validation data. The conclusiveness of these studies has been subject to several problems: firstly, the limited sample statistics provided by vertical wells applied to the validation of lateral variations, and secondly by the potential nonuniqueness of the EUR to fracture density relationship.

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While their importance is increasingly recognized, there remain many challenges in the development of uncertainty visualizations. We introduce two uncertainty visualizations for 2D bidirectional vector fields: one based on a static glyph and the other based on animated flow. These visualizations were designed for the task of understanding and interpreting anisotropic rock property models in the domain of seismic data processing. Aspects of the implementations are discussed relating to design, interaction, and tasks.

Amplitude variation with offset and azimuth (AVOAz) analysis can be separated into two separate parts: amplitude variation with offset (AVO) analysis and amplitude variation with azimuth (AVAz) analysis. Useful information about fractures and anisotropy can be obtained just by examining the AVAz. The AVAz can be described as a sum of sinusoids of different periodicities, each characterized by its magnitude and phase. This sum is mathematically equivalent to a Fourier series, and hence the coefficients describing the AVAz response are azimuthal Fourier coefficients (FCs). This FC parameterization is purely descriptive. The aim of this paper is to help the interpreter understand what these coefficients mean in terms of anisotropic and fracture parameters for the case of P-wave reflectivity using a linearized approximation. The FC representation is valid for general anisotropy. However, to gain insight into the significance of FCs, more restrictive assumptions about the anisotropy or facture system must be assumed. In the case of transverse isotropic media with a horizontal axis of symmetry, the P-wave reflectivity linearized approximation may be rewritten in terms of azimuthal FCs with the magnitude and phase of the different FCs corresponding to traditional AVAz attributes. Linear slip theory is used to show that the FCs can be interpreted similarly for the cases of a single set of parallel vertical fractures in isotropic media and in transverse isotropic media with a vertical axis of symmetry (VTI). The magnitude of the FCs depends on the fracture weakness parameters and the background media. For the case of vertical fractures in a VTI background, the AVOAz inverse problem is underdetermined, so extra information must be incorporated to determine how the weights are modified due to this background anisotropy. We evaluated this on a 3D data set from northwest Louisiana for which the main target was the Haynesville shale.

A New Approach Traditional noise attenuation methods attempt to separate signal from noise by transforming data into a domain where the signal or noise is modeled mathematically, and signal and noise can be separated. Many methods simply stop at separating noise and signal. That is, the signal model itself is the output of the noise attenuation program. Some compensate for the 'too clean' synthetic look of the output by adding back a percentage of the original input data. LIFT (Choo and Sudhakar, 2003), a new amplitude-friendly technique to attenuate noise and multiples, takes a new approach by adding back an estimate of the signal lost during the modeling, rather than simply outputting the signal model or the signal model with a percentage of the original data added back. This is a fundamental shift in noise attenuation strategy. This approach greatly improves signal preservation. It is very flexible in that it can incorporate a variety of application domains, filtering tools, and ways of modeling data, as appropriate to address particular noise problems. As well, it is a practical and robust amplitude-preserving way to precondition data for pre-stack migration, to prevent migration artifacts and costly reruns. Noise Attenuation Current Practices Many and varied strategies have been used to model the signal or noise, all making various assumptions. For instance, the K-L transform assumes that the signal is flat in time with only amplitude variations. The Radon transform is more flexible in that it allows signal to follow varied trajectories, but a few fixed types of trajectories (hyperbolic, parabolic, and straight lines for example) cannot fully cover all signal behavior. The F-X prediction filter is a popular tool to attenuate random noise. It makes a general signal model assumption: that signal is similar from one trace to the next and spatially predictable by convolution filters-a less restrictive signal model than that of some other noise attenuation algorithms.