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Anisotropic variations in attenuation are of interest since they can give information on the fracture system and may be more amenable to measurement than absolute attenuation values. We examine methods for detecting changes in relative attenuation with azimuth from VSP data, and validate the techniques on synthetic data. Analysis of a multi-azimuth walkaway VSP data set from a fractured hydrocarbon reservoir indicates that such azimuthal variations in P-wave attenuation are observable. The effects are localized in the reservoir, and analysis allows the prediction of a fracture strike direction, which agrees with geological information. The observed effects can be modelled under reasonable assumptions, which suggests the validity of the link between the anisotropic attenuation and the fracturing. [ABSTRACT FROM AUTHOR]

Consider a wireless sensor network consisting of n wireless sensors randomly distributed in a two-dimensional plane. In this paper, we show that with high probability we can locally find a path for any pair of sensors such that the length of the path is no more than a constant factor of the minimum. By assuming each sensor knows its position, our new routing method decides where to forward the message purely based on the position of current node, its neighbours, and the positions of the source and the target. Our method is based on a novel structure called localized Delaunay triangulation and a geometric routing method that guarantees that the distance travelled by the packets is no more than a small constant factor of the minimum when the Delaunay triangulation of sensor nodes are known. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies, and our localized routing protocol based on Delaunay triangulation works well in practice. We also conducted extensive simulations of another localized routing protocol, face routing. The path found by this protocol is also reasonably good compared with previous one although it cannot guarantee a constant approximation on the length of the path travelled theoretically. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We have developed a practical approach for updating the velocity of PS converted waves based on the inverse normal-moveout common-image-point gather obtained from prestack Kirchhoff time migration. We have integrated all the steps involved in updating the migration velocity model into an interactive tool and have applied this approach to a real seismic data set from the Alba Field in the North Sea. Based on experience in handling the real data, we discuss various practical aspects of updating the velocity model, including: what kind of initial velocity model should be used; which parameters in the velocity model should be updated; and how to update them. Application of prestack Kirchhoff time migration to the data set using the updated velocity model produces an improved image of the Alba Field. [ABSTRACT FROM AUTHOR]

A velocity model updating approach is developed based on moveout analysis of the diffraction curve of PS converted waves in prestack Kirchhoff time migration. The diffraction curve can be expressed as a product of two factors: one factor depending on the PS converted-wave velocity only, and the other factor depending on all parameters. The velocity-dependent factor represents the hyperbolic behaviour of the moveout and the other is a scale factor that represents the non-hyperbolic behaviour of the moveout. This non-hyperbolic behaviour of the moveout can be corrected in prestack Kirchhoff time migration to form an inverse normal-moveout common-image-point gather in which only the hyperbolic moveout is retained. This hyperbolic moveout is the moveout that would be obtained in an isotropic equivalent medium. A hyperbolic velocity is then estimated from this gather by applying hyperbolic moveout analysis. Theoretical analysis shows that for any given initial velocity, the estimated hyperbolic velocity converges by an iterative procedure to the optimal velocity if the velocity ratio is optimal or to a value closer to the optimal velocity if the velocity ratio is not optimal. The velocity ratio ( VP/ VS) has little effect on the estimation of the velocity. Applying this technique to a synthetic seismic data set confirms the theoretical findings. This work provides a practical method to obtain the velocity model for prestack Kirchhoff time migration. [ABSTRACT FROM AUTHOR]

Common-conversion-point binning associated with converted-wave (C-wave) processing complicates the task of parameter estimation, especially in anisotropic media. To overcome this problem, we derive new expressions for converted-wave prestack time migration (PSTM) in anisotropic media and illustrate their applications using both 2D and 3D data examples. The converted-wave kinematic response in inhomogeneous media with vertical transverse isotropy is separated into two parts: the response in horizontally layered vertical transverse isotrophy media and the response from a point-scatterer. The former controls the stacking process and the latter controls the process of PSTM. The C-wave traveltime in horizontally layered vertical transverse isotrophy media is determined by four parameters: the C-wave stacking velocity VC2, the vertical and effective velocity ratios γ0 and γeff, and the C-wave anisotropic parameter χeff. These four parameters are referred to as the C-wave stacking velocity model. In contrast, the C-wave diffraction time from a point-scatterer is determined by five parameters: γ0, VP2, VS2, ηeff and ζeff, where ηeff and ζeff are, respectively, the P- and S-wave anisotropic parameters, and VP2 and VS2 are the corresponding stacking velocities. VP2, VS2, ηeff and ζeff are referred to as the C-wave PSTM velocity model. There is a one-to-one analytical link between the stacking velocity model and the PSTM velocity model. There is also a simple analytical link between the C-wave stacking velocities VC2 and the migration velocity VCmig, which is in turn linked to VP2 and VS2. Based on the above, we have developed an interactive processing scheme to build the stacking and PSTM velocity models and to perform 2D and 3D C-wave anisotropic PSTM. Real data applications show that the PSTM scheme substantially improves the quality of C-wave imaging compared with the dip-moveout scheme, and these improvements have been confirmed by drilling. [ABSTRACT FROM AUTHOR]

We present a study of anisotropic parameter estimation in the near-surface layers for P-wave and converted-wave (C-wave) data. Near-surface data is affected by apparent anisotropy due to a vertical velocity compaction gradient. We have carried out a modelling study, which showed that a velocity gradient introduces apparent anisotropy into an isotropic medium. Thus, parameter estimation will give anomalous values that affect the imaging of the target area. The parameter estimation technique is also influenced by phase reversals with diminishing amplitude, leading to erroneous parameters. In a modelling study using a near-surface model, we have observed phase reversals in near-surface PP reflections. The values of the P-wave anisotropy parameter η estimated from these events are about an order of magnitude larger than the model values. Next, we use C-wave data to estimate the effect of anisotropy (χ) and compute η from these values. These calculated η-values are closer to the model values, and NMO correction with both η-values shows a better correction for the calculated value. Hence, we believe that calculating η from χ gives a better representation of the anisotropy than picked η from the P-wave. Finally, we extract the anisotropy parameters η and χ from real data from the Alba Field in the North Sea. Comparing the results with reference values from a model built according to well-log, VSP and surface data, we find that the parameters show differences of up to an order of magnitude. The η-values calculated from the C-wave anisotropy parameter χ fit the reference values much better and show values of the same order of magnitude. [ABSTRACT FROM AUTHOR]

ABSTRACT Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data. [ABSTRACT FROM AUTHOR]