Hudson Model Research Articles

Estimation of fracture density and orientation from azimuthal elastic impedance difference through singular value decomposition

Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs. Here, we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance (AEI) difference using singular value decomposition (SVD). Based on Hudson's model, we first derive the AEI equation containing fracture density in HTI media, and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD. Analysis shows that the basis function changing with azimuth is related to fracture orientation, fracture density is the linearly weighted sum of singular values, and the first singular value contributes the most to fracture density. Thus, we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters. Synthetic example shows that fracture density and orientation can be stably estimated, and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2. Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data, and the estimated fracture density reliably indicates fractured gas-bearing reservoir, which could help to guide the exploration and development of fractured reservoirs.

Collaborating for Mental Health Services in Wales: A Process Evaluation

The need for inter‐agency collaboration between managers of mental health services has long been recognized, as has the difficulty of achieving and maintaining such relationships. Hudson et al. (1999) have developed a model for collaboration in the public sector and the current research has tested the model against attempts to achieve and maintain inter‐agency collaboration between mental health managers in Wales. We find Hudson's model a useful analytical framework but our evidence suggests that it needs to be amended by giving greater emphasis to the importance of ‘uninterrupted . . . opportunities for interaction’ between key managers. Forthcoming changes to NHS structures in Wales (for example, the abolition of Health Authorities and the conversion of Local Health Groups into Local Health Boards) will not necessarily facilitate collaboration if the Local Health Boards are given the role of planning and commissioning mental health services without having the necessary ‘critical mass’ of knowledge, expertise and dedicated staff capacity for planning and commissioning mental health services.

Frequency-dependent seismic anisotropy and its implication for estimating fracture size in low porosity reservoirs

The use of seismic anisotropy for characterizing subsurface fracture orientations and intensity has become increasingly popular. However, the reluctance of reservoir engineers to accept seismic anisotropy as a routine technique for fracture characterization is partly because of its inability to provide information about sizes and volume of fractures. Although both grain-scale micro-cracks and formation-scale macro-fractures are considered causes of seismic anisotropy, reservoir engineers are more interested in the latter as permeability in many hydrocarbon reservoirs is believed to be dominated by formation-scale fluid units (on the order of meters). We intend to fill this gap by developing new practical applications of seismic anisotropy including new theoretical models and new analysis methods. Frequency-dependent anisotropy has been observed and can be explained by two mechanisms: seismic scattering by heterogeneities and fluid flow in fractured porous rock. In this article, we present a synthetic study demonstrating the dependence of seismic anisotropy on fracture sizes using a newly proposed multiscale fracture model. We then use this model to invert fracture sizes from field multicomponent shear-wave VSP data acquired in Bluebell-Altamonta, Utah. Our study has indicated a great potential of fracture size estimation in low porosity fractured reservoir, and thus we may potentially go beyond the conventional application of seismic anisotropy to predict fracture sizes and fracture volumes. The two most popular models for describing the elastic properties of fractured media are the so-called Thomsen's equant porosity model, and Hudson's thin-crack model. Thomsen's model assumes perfect fluid pressure equalization between the cracks and the surrounding rock, whereas Hudson's model assumes that the cracks are isolated with respect to fluid flow. Both models predict frequency independent behavior. In both models the magnitude of anisotropy is related to the fracture density, although the precise dependence is different in each case. This fracture density is defined as e= …

Effects of fractures on seismic-wave velocity and attenuation

The effects of fractures on the seismic velocity and attenuation of a rock are investigated using theoretical results and experimental data. Fractures in a rock mass influence the traveltimes and amplitudes of seismic waves that have propagated through them. The displacement discontinuity model, recently employed in fracture investigations, is modified to describe the effect of fractures on seismic-wave velocity and attenuation. This new model, the modified displacement discontinuity model (MDD), is formulated in a way analogous to transmission-line analysis. The fractures are treated as transmission lines for the passage of seismic waves. The MDD takes into consideration realistic fracture parameters which include the fracture length, the fractional area of a fracture surface in contact, and the nature of the infilling material. A single fracture of varying geometric and material properties is shown to affect dramatically the transmission properties of a propagating waveform, and hence the seismic velocity and attenuation. These effects have been shown to result in a frequency-dependent velocity and attenuation. The sensitivity of the fracture parameters to seismic-wave velocity and attenuation was investigated and interesting results were obtained. Fracture parameters used in designing experimental models consisting of synthetically manufactured cracks were fed into the MDD and a well-known crack model, Hudson's model, for comparison. Velocities as a function of the incident-wave angle were obtained from both numerical models and were compared with the results from the experimental modelling. For P waves, the MDD model results show better agreement with those of the experimental model for all crack densities investigated than those from Hudson's model.

P‐ and S‐wave anisotropy of a synthetic sandstone with controlled crack geometryl1

AbstractA method is reported for the production of synthetic porous sandstones containing cracks of known dimensions and geometry with respect to the matrix. A synthetic sandstone was manufactured from Sand cemented with an epoxy glue. The cracks of known geometry were introduced into the material in the manufacturing stage, by emplacing thin metallic discs in the Sand‐epoxy matrix. These discs were chemically leached out of the consolidated porous sandstone. Acoustic anisotropy. and shear‐wave splitting were observed in the synthetic sandstones. For the dry sample the observed angular dependence of the P‐ and S‐ wave velocities (at 100 kHz) compares well, qualitatively, with the theoretical models of Hudson and of Thomsen. Quantitatively, however, the experimental data fits Hudson's model better. For the case of a saturated sample the experimental results are in excellent agreement with Thomsen's model. Hudson's model, on the other hand, predicts a different angular dependence for P‐waves. This demonstrates that the concept of fluid transfer between cracks and the ambient porosity can be a significant process. The results reported here are from the first successful experiment in which the theoretical models were tested on a porous material containing a known crack geometry.

Crustal anisotropy from local observations of shear-wave splitting in West Bohemia, Czech Republic

Abstract The results of a systematic study of shear-wave splitting, observed in the three-component digital seismograms of about 400 local microearthquakes that occurred during the 1985/1986 West-Bohemian earthquake swarm are presented. Two shear phases, polarized nearly perpendicularly in horizontal projection, were observed at all five stations of the local seismic network for most of the events. The polarization of the faster shear wave is aligned in the WNW-ESE direction, regardless of the mechanism and hypocenter location of the individual events, and coincides with the direction of the maximum horizontal compressive tectonic stress in the region. These effects are interpreted in terms of effective anisotropy of the upper crust in the region. The maximum delay time between the split shear waves is 0.15 sec and corresponds to 6% anisotropy. Directional variation of the delay time was observed at the nearest station (epicentral distance ≈ 5 km). This variation was compared with functions predicted by theoretical models of cracked media to resolve which model is the most appropriate for crustal anisotropy. Surprisingly, no agreement could be found for Hudson's model of dry or water-filled parallel cracks that is widely used by many authors. A successful fit was obtained for Schoenberg — Douma's model of a medium with parallel fractures. The fracture normal pointed N31°E, and the optimum fracture parameters were EN = 0.4 and ET = 0.02. The theoretically calculated fractures are aligned parallel to the tectonic stress direction and do not correspond to any real tectonic lines in the region.

Settlement Succession on the Pajarito Plateau, New Mexico

ABSTRACTPrevious explanations of puebloan settlement pattern change in the northern Rio Grande have largely been atheoretical and unparticularistic. In contrast, this study uses Hudson's theory of rural settlement to explain settlement change on the Pajarito Plateau, New Mexico, from A.D. 1150 to 1550. Quadrat and nearest-neighbor analyses are used to describe settlement distribution, and basic descriptive statistics are used to characterize changes in site size over time. The results of the analyses suggest that despite certain theoretical limitations and methodological problems, Hudson's model provides an important starting point for the explanation of settlement succession in the study area.

The verbal system in Godié

From the introduction: "The goal of this paper is to describe the verbal system of Godié, a Kru language spoken in southwest Ivory Coast, within the framework of daughter dependency grammar. This model has been recently developed by the British linguist, R. A. Hudson. The model could be called "generative" since structures are built up through the application of various sets of rules. This type of grammar varies considerably, however, from other generative grammars in that it generates only one structure for each construction (rather than the traditional deep and surface structures, with several intermediate structures in between). Rather than concerning itself with sentence relatedness, DDG concentrates on showing dependencies within a single construction. An important innovation in Hudson's model is the use of features on higher nodes. The paper contains three sections besides the introduction and conclusion. In the first section, there will be a justification of the features used to describe Godié verbs. In section two, rules needed to generate basic and more complex structures will be discussed. Finally, section three contains a discussion of how certain generalizations can be captured by redundancy rules in the lexicon."

On the form of a systemic grammar

This paper concerns the theory of SYSTEMIC GRAMMAR, developed by Halliday (1961, 1967a, 1967b 1968, 1970), Hudson (1967, 1970, 1971, 1973, forthcoming, ms. a, ms. b) and others. In Hudson (1971) a detailed generative version of the theory has been presented, and specifically I want to suggest modifications of this model which I believe improve it. Although a fair amount of the paper consists of criticism of, and comparison with, Hudson's model, the description of what I propose is self-contained and that portion can be read independently.