Compact Gradient Research Articles

A wave equation technique for designing compact gradient coils

A primary purpose of this research is to design a gradient coil that is planar in construction and can be inserted within existing infrastructure. The proposed wave equation method for the design of gradient coils is novel within the field. It is comprehensively shown how this method can be used to design the planar x-, y-, and z-gradient wire windings to produce the required magnetic fields within a certain domain. The solution for the cylindrical gradient coil set is also elucidated. The wave equation technique is compared with the well-known target field method to gauge the quality of resultant design. In the case of the planar gradient coil design, it is shown that using the new method, a set of compact gradient coils with large field of view can be produced. The final design is considerably smaller in dimension when compared with the design obtained using the target field method, and therefore the manufacturing costs and materials required are somewhat reduced. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 29B: 62–74, 2006

The effects of near‐surface conditions on anisotropy parameter estimations from 4C seismic data

ABSTRACTWe 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.

Dynamics of Hydrocarbon Expulsion from Shale Source Rocks

Expulsion of hydrocarbons from a shale source rock can be divided in four stages. In the first stage, only a small amount of hydrocarbons can be expelled in water solution and by diffusion. Compaction and hydrocarbon concentration gradient are the major driving forces, whereas their corresponding hydrocarbon expulsion amounts make up 30% and 70% to the total, respectively. In the second stage, in addition to transport by water solution and by diffusion, source rocks expel a large quantity of gas in free phase. In the third stage, the most important feature is that source rocks expel oil as a separate phase and gas in oil solution. Hydrocarbon expulsion by diffusion through the source rock organic network, dehydration of clay minerals, and thermal expansion of fluids and rocks are the three major driving forces in the second and the third stages, whereas the corresponding hydrocarbon expulsion accounts for 40–60%, 10–20%, and 5–10%, respectively, of the total amount expelled. In the fourth stage, source rocks mainly expel dry gas as a free phase. Volume expansion of kerogen products and capillary force are the two major driving forces for hydrocarbon expulsion. The expulsion accounts for 60% and 30% to the total gas expulsion of this stage, respectively, for each driving force. Hydrocarbon expulsion, including the hydrocarbon expulsion threshold (HET), the relative phases and the dynamics, are controlled by two factors: the hydrocarbon generation amount, and the ability of source rocks to retain hydrocarbons. Source rocks cross the HET and begin to expel a large quantity of hydrocarbons when the generated hydrocarbons have met all of the needs for hydrocarbon retention. HET is divides the processes of hydrocarbon expulsion into the various four stages.

Enhanced velocity estimation using gridded tomography in complex chalk

ABSTRACTThe theme of the 2003 EAGE/SEG imaging workshop concerned the contrast between different philosophies of ‘model building’: whether an explicit, user‐determined model should be imposed throughout the processing, with user updates at each step; or alternatively, whether user intervention should be kept to a minimum so as to avoid preconceived bias, and instead to allow the data itself to guide some heuristic process to converge to an optimal solution.Here we consider a North Sea study where our initial approach was to build the subsurface model using interpreted horizons as a guide to the velocity update. This is common practice in the North Sea, where the geology ‘lends itself’ to a layer‐based model representation. In other words, we encourage preconceived bias, as we consider it to be a meaningful geological constraint on the solution.However, in this instance we had a thick chalk sequence, wherein the vertical compaction gradient changed subtly, in a way not readily discernible from the seismic reflection data. As a consequence, imposing the explicit top and bottom chalk horizons, with an intervening vertical compaction gradient (of the form v(x, y, z) =v0(x, y) +k(x, y).z), led to a misrepresentation of the subsurface.To address this issue, a gridded model building approach was also tried. This relied on dense continuous automatic picking of residual moveout in common‐reflection point gathers at each iteration of the model update, followed by gridded tomography, resulting in a smoothly varying velocity field which was able to reveal the underlying local changes within the chalk.

Mussel Assemblages in a Developing Oxbow and a Newly-cut Channel of the Neosho River, Kansas

We compared freshwater mussel assemblages (Bivalvia: Unionidae) in a developing oxbow (old channel) and a newly-cut (new) channel of the Neosho River, Kansas, during 2001. We sampled mussels at approximately 1.5 km intervals, totaling 19 sites in the old channel and seven in the new, by groping substrate from bank to bank in a zigzag fashion along a 100 m reach. We found 1239 live individuals of 20 mussel species in the old channel and 20 live individuals of six species in the new channel. Mussel abundance, diversity and current species richness were greater in the old channel than in the new. Abundance, diversity and historic and current species richness all declined significantly from upstream to downstream in the old channel. Historic richness was greater than current richness in the old channel, but both decreased from upstream to downstream at the same rate. The loss of historic species from the old channel was no different from that in the rest of the Neosho River in Kansas; however, a further decrease in lotic species will likely occur as the channel continues to evolve into an oxbow lake. Canonical correspondence analysis illustrated a substrate compaction, substrate composition and depth gradient in the old channel, with three species in flowing waters with sand and gravel substrate and all other species in still waters with silt substrate. Information regarding habitat use by freshwater mussels is important in designing surveys and recovery plans for rare species (Strayer, 1993).

The development of a simulation model of the dense packing of large particulate assemblies

The dense packing of particulate assemblies is an enduring theoretical and practical problem. In spite of its apparent simplicity, this problem still remains challenging. Recent progress in the performance of computers boosted the development and realization of a number of effective packing algorithms. Yet, because of the complexity of the problem, many of existing methods have difficulties in handling large numbers of particles. A simulation model is proposed to overcome this. The model assumes that the centers of the spheres are randomly generated at the intersections of a cubic lattice. The largest possible spheres are packed first; subsequent spheres are limited by the set of minimum diameters, which is specified by the constraints imposed by two major parameters imitating the compaction gradient: a reduction coefficient and the number of packing trials. Importantly, the packing arrangements are not defined by the initially specified particle size distribution (as considered by many existing packing algorithms), but rather the most dense particle size distribution, along with the corresponding value of packing degree, is generated by the proposed model. Based on these criteria, a very fast algorithm was developed for simulating of the dense packing of large assemblies of particulate, spherical material (in the order of millions of particles). Using this approach, the influence of geometrical parameters and model variables on the degree of packing and the corresponding distribution of particles was studied.

On optimizing performance indices with pole assignment constraints

In this paper, a unified gradient-based treatment for optimizing certain performance indices under the constraint of pole assignment is provided. By introducing a free optimization parameter and solving a special Sylvester matrix equation, compact gradient formulae are derived for general-purpose gradient descent numerical implementation. Special problems including robust stability pole assignment and H2 sensitivity reduction are employed to illustrate the technique. In particular, comparisons of different performance indices to maximize the complex stability radius are made.

Mechanisms of signal loss in magnetic resonance imaging of stenoses.

Some of the factors affecting the signal losses that occur in magnetic resonance images at a stenosis or other region of complex flow have been evaluated. The important determinants of dephasing within a volume element are the net gradient moments, which can be kept small even at long echo times. For compact gradient wave forms, the echo time by itself is unimportant and does not affect signal losses. Reducing the fraction of echo sampled is an alternate method to velocity compensation for reducing gradient moment dephasing that keeps higher moments small. The effects of reducing the fraction of echo sampled on the signal losses in flow distal to a stenosis have been measured experimentally. Another source of signal loss at a stenosis is the variation of the mean phase within a volume element that occurs for flow that varies from one phase encoded view to another. Changes in flow behavior between acquisitions lead to signal displacement in the image. These view to view changes have also been quantified.

Magnetic resonance angiography by selective inversion recovery using a compact gradient echo sequence.

We have studied a pulse sequence using compact imaging gradients for MR angiography by selective inversion recovery. By acquiring signals approaching a half-echo, we achieve significant immunity to artifacts from flow-induced dephasing. Initial clinical results on carotid arteries accurately depict stenoses without the problems of signal dephasing.

On sparse and compact preconditioned conjugate gradient methods for partial differential equations

This paper generalises the preconditioning techniques, introduced by Evans [2], and defines sparse and compact preconditioned iterative methods for the numerical solution of the linear system Au = b.The difference between the methods is shown to depend on whether a conditioning matrix R consists of components derived from a splitting or factorization of A. Some theoretical results for the iterative schemes are given when A has particular properties such as consistent ordering, irreducibility, diagonal dominance, positive definiteness, etc., when derived from the finite difference discretisation of a 2nd order self-adjoint elliptic partial differential equation. Finally, the application of both forms of preconditioning to the Conjugate Gradient method is presented and computational results compared.

Significance of Reservoir Diagenetic Alteration for Petroleum Exploration, Gulf of Alaska Tertiary Basin: ABSTRACT

The Tertiary clastic section of the Gulf of Alaska sedimentary basin is considered an important potential future petroleum province. Considerable work in the onshore area has been carried out by industry preparatory to a projected sale of federal leases on the continental shelf. Examination of numerous samples collected from measured sections in Oligocene to Pleistocene strata has shown that the sandstones are mineralogically immature and unstable. Diagenetic alteration of these potential reservoir sands at shallow to intermediate depths of burial has resulted in the ubiquitous formation of authigenic clay rims and coats around detrital grains and of pore-filling zeolite cements. These diagenetic alterations adversely affect both porosity and permeability and will provide a major limitation on the thickness of the sedimentary section than can be considered prospective. A compaction versus depth gradient, which is related to the sandstone porosity gradient, can be determined in offshore areas by combination of seismically derived interval, velocity depth profiles, with a velocity-density calibration based on well data from the Hecate Strait (a geologically similar Pacific Margin basin lying off British Columbia). The resultant density configuration can be cross checked by gravity modeling along the same seismic line. Work on a line off Cape Yakataga shows that the prospective section is characterized by a high velocity and density gradient, indicating rapid loss of reservoir porosity with increasing depth of burial, as predicted by the onshore diagenetic m del. Semiquantitative evaluation of the compaction profile using the onshore reservoir data suggests that even in the youngest sections porosity decreases to less than 20% at depths of 5,000 to 8,000 ft. End_of_Article - Last_Page 1898------------