Thanks to Lionel Jannaud, inspired by the great pioneering seismologist Keiti Aki in his work on wave propagation in random media, for allowing us to use some of his results for the writing of chapter 5 on Frequency/wavelength dependence.Finally we would like to give

Background/Aims: To investigate the clinical features and rates of progression of conditions that are not considered to be normal, but do not fulfill criteria for mild cognitive impairment (MCI).Methods: We longitudinally evaluated 269 elderly subjects who did not meet formal criteria for MCI at baseline but had: (1) a clinical history suggesting MCI without neuropsychological deficits (PreMCI-Clinical); or (2) neuropsychological deficits on one or more memory measures in conjunction with a negative clinical examination (amnestic PreMCI-NP) or were normal on both neuropsychological and clinical examination.Results: The rate of progression to MCI or dementia over an average of 2- to 3 years was 3.7% for no cognitive impairment subjects, whereas it was significantly greater for all PreMCI subtypes (22.0% for PreMCI-Clinical, 38.9% for amnestic PreMCI-NP subjects with two or more memory impairments). Among PreMCI subjects as a whole, lower baseline scores on object memory and category fluency tests were the best predictors of progression to MCI or dementia. Cardiovascular risk factors, Parkinsonian symptoms, and hippocampal atrophy were not associated with progression.Conclusion: Distinct PreMCI subtypes defined on the basis of clinical and neuropsychological evaluations were found to have distinct characteristics, but both subtypes demonstrated elevated risk for progression to MCI or dementia. Despite the lack of evidence of clinical impairment, subjects with neuropsychological deficits in two memory domains were particularly at increased risk for progression of their deficits. (C) 2012 The Alzheimer's Association. All rights reserved.

The exact problem of the interaction of an arbitrary plane wave in a homogeneous elastic medium with a fluid‐filled circularly cylindrical borehole is formulated to analyze three‐axis, full‐waveform borehole seismic data. The plane elastic wave (which may be incident upon the borehole from any direction) is partially scattered around the hole and an acoustic field is induced in the borehole fluid. Since seismic wavelengths tend to be much larger than diameters of boreholes, the exact solution may be expanded in powers of Ω (a small number), the incident wavenumber times the borehole radius. In the limit as Ω→0, the scattered field in the elastic medium is of O(Ω); in this limit the borehole crosssection is undistorted and moves with the velocity of the incident wave as if no borehole were present. Neglecting terms proportional to [Formula: see text] or higher leaves three kinds of θ‐dependent terms, where θ is the azimuthal angle about the borehole axis measured with respect to the wavenumber vector of the incident wave. Terms independent of θ (n = 0) give radial motion for incident P- or SV-waves, or rotational motion for incident SH-waves, and fall off as inverse distance from the borehole axis, i.e., 1/r. Terms proportional to cos θ for incident P- or SV-waves or sin θ for incident SH-waves (n = 1) give axial motion that falls off as 1/r. Terms proportional to sin 2θ or cos 2θ (n = 2) give motion in the plane perpendicular to the borehole axis, part of which falls off as 1/r and part as [Formula: see text]. At the borehole wall, the n = 2 terms express the deformation of the borehole cross‐section into an ellipse whose major and minor axes interchange as the wave passes. In the limit as Ω→0, the fluid velocity is constant over the borehole cross‐section. In the plane perpendicular to the borehole axis the fluid is constrained to move with the solid. However, in the axial direction the fluid velocity differs from that of the borehole wall for incident P- or SV-waves (for incident SH-waves the axial fluid and solid velocities both vanish as Ω→0). The ratio of axial fluid velocity to axial solid velocity at the borehole wall, for given elastic medium and acoustic fluid properties, is a function of both the wave type and the angle between the incident wavenumber vector and the borehole axis. Further, for incident P-waves, the axial fluid and solid velocities are in‐phase while for incident SV-waves, they are 180 degrees out‐of‐phase. Thus, as a plane wave passes a given level in a fluidfilled borehole, the plane‐wave type and (for P- or SV-waves) its angle of propagation relative to the borehole axis are theoretically obtainable by measuring fluid and solid axial velocities at that level.

OBJECTIVE:To compare clinical, imaging, and neuropsychological characteristics and longitudinal course of subjects with pre-mild cognitive impairment (pre-MCI), who exhibit features of MCI on clinical examination but lack impairment on neuropsychological examination, to subjects with no cognitive impairment (NCI), nonamnestic MCI (naMCI), amnestic MCI (aMCI), and mild dementia. METHODS:For 369 subjects, clinical dementia rating sum of boxes (CDR-SB), ApoE genotyping, cardiovascular risk factors, parkinsonism (UPDRS) scores, structural brain MRIs, and neuropsychological testing were obtained at baseline, whereas 275 of these subjects received an annual follow-up for 2-3 years. RESULTS:At baseline, pre-MCI subjects showed impairment on tests of executive function and language, higher apathy scores, and lower left hippocampal volumes (HPCV) in comparison to NCI subjects. Pre-MCI subjects showed less impairment on at least one memory measure, CDR-SB and UPDRS scores, in comparison to naMCI, aMCI and mild dementia subjects. Follow-up over 2-3 years showed 28.6% of pre-MCI subjects, but less than 5% of NCI subjects progressed to MCI or dementia. Progression rates to dementia were equivalent between naMCI (22.2%) and aMCI (34.5%) groups, but greater than for the pre-MCI group (2.4%). Progression to dementia was best predicted by the CDR-SB, a list learning and executive function test. CONCLUSION:This study demonstrates that clinically defined pre-MCI has cognitive, functional, motor, behavioral and imaging features that are intermediate between NCI and MCI states at baseline. Pre-MCI subjects showed accelerated rates of progression to MCI as compared to NCI subjects, but slower rates of progression to dementia than MCI subjects.

Identification of an early predementia stage of Alzheimer's disease as a basis for intervention at a stage when treatment is likely to be most successful, requires definition of a discrete cognitive syndrome that is earlier than MCI, which can be diagnosed reliably. At baseline, subjects were diagnosed with no cognitive impairment (NCI) (n=216), PreMCI (n=125), early MCI (eMCI) (n=90), non-amnestic MCI (naMCI) (n=26), or late MCI (LCMI) (n=30) using the following criteria: (1) PreMCI = CDR score of 0.5, logical memory-delayed (LM-D) test score within 0.5 SD of age and education adjusted means (AEAMs), and all non-amnestic tests within 1.5 SD of AEAMs; (2) eMCI = CDR score of 0.5, MMSE of > 24, LM-D score between 0.5 and 1.5 SD of EAMs; (3) naMCI = CDR score of 0.5, MMSE of > 24, LM-D score within 0.5 SD of AEAMs, and one or more non-amnestic measures at > 1.5 SD below AEAMs; (4) LMCI = CDR score of 0.5, MMSE of > 24, LM-D score > 1.5 SD below AEAMs. APOE allele frequencies, medial temporal atrophy (MTA) scores based on visual ratings of brain MRIs, and progression rates to dementia (on 2-3 year follow-up) were assessed for each subject group. ApoE4 frequencies were not different between groups, although differences in MTA scores were found, i.e., 31% of LMCI, 23% of eMCI, 23% of PreMCI, 4.5% of naMCI, and 9.4% of NCI subjects scored above the threshold (defined as 1.50) (range 0 to 4) [X2 (df=4)=16.88; p < .003]. Differences in rates of progression to dementia were also present, i.e., 23.1% for CDR 0.5 alone; 28% for PreMCI, 34.0% for eMCI, and 43.8% for LMCI [X2 (df = 4)=44.52; p < .001]. Subjects with naMCI or NCI subjects did not progress to dementia. PreMCI and eMCI (but not naMCI) subjects have greater MTA scores and progression rates to dementia than NCI subjects, and are therefore appropriate targets for very early intervention clinical trials. Although the diagnosis of PreMCI is more labour-intensive requiring additional non-amnestic tests, it is likely to be a better-defined and less heterogeneous entity. In the absence of any deficit in LM-D scores, naMCI appears to be a variant of normal cognition.

Negative outcomes in treating AD may be a consequence of targeting relatively advanced stages of the neurodegenerative disease. As clinical symptoms of AD generally lag well behind its neuropathology, a very early diagnosis of AD becomes crucial. To identify an early Pre-mild cognitive impairment (Pre-MCI) stage of Alzheimer's disease (AD), we assessed neuropsychological, clinical and imaging features among elderly subjects that were diagnosed with no cognitive impairment (NCI), non-amnestic MCI (naMCI), or amnestic MCI (aMCI). To generate a diagnosis for 425 elderly subjects, neuropsychological testing (NPDx) and a physician/neurologist's clinical diagnosis (PhyDx) were combined algorithmically. For an amnestic MCI diagnosis, both the PhyDx and NPDX were required to be “MCI”, while for the Pre-MCI diagnosis only the PhyDx was required to be “MCI.” For 145 subjects, CDR-Sum of Boxes (CDR-SB), geriatric depression scale (GDS), apathy scores, volumetric analysis of structural brain MRIs of the hippocampus (HPCVol), ApoE-4 allele blood work, and annual follow-ups for at least two years were collected and evaluated. Compared to NCI (n = 165), Pre-MCI (n = 76), naMCI (n = 30), and aMCI (n = 89) had higher CDR-SB and apathy scores, and lower left HPCVol. Over the follow-up period, less than 6% of NCI subjects, but significantly more (52%) of Pre-MCI subjects progressed to MCI (p < .002). Progression rates to probable AD were 3.2% for Pre-MCI subjects, 27% for naMCI and 33% for aMCI subjects. Thus, progression rates were equivalent among MCI groups, but greater than for the Pre-MCI (p < .05) group. In addition to a diagnosis of MCI, progression to probable AD was most reliably predicted by smaller HPCVol and higher CDR-SB scores. Utilizing an algorithm combining neuropsychological and clinical diagnoses, a Pre-MCI state can be distinguished from MCI and NCI states. The Pre-MCI state can be distinguished from MCI and NCI states by neuropsychological, clinical and neuroimaging characteristics, as well as rates of progression to aMCI and naMCI. Pre-MCI should meet clinical but not neuropsychological criteria for MCI, while Pre-MCI progresses to dementia at a significantly slower rate than MCI states.

Rotational motions in homogeneous anisotropic elastic media are studied under the assumption of plane wave propagation. The main goal is to investigate the influences of anisotropy in the behavior of the rotational wavefield. The focus is on P-waves that theoretically do not generate rotational motion in isotropic media. By using the Kelvin–Christoffel equation, expressions are obtained of the rotational motions of body waves as a function of the propagation direction and the coefficients of the elastic modulus matrix. As a result, the amplitudes of the rotation rates and their radiation patterns are quantified and it is concluded that (1) for strong local earthquakes and typical reservoir situations quasi P-rotation rates induced by anisotropy are significant, recordable, and can be used for inverse problems; and (2) for teleseismic wavefields, anisotropic effects are unlikely to be responsible for the observed rotational energy in the P coda.

ABSTRACTA vertically fractured transversely isotropic (VFTI) elastic medium is one in which any number of sets of vertical aligned fractures (each set has its normal lying in the horizontal x1, x2‐plane) pervade the medium and the sets of aligned fractures are the only features of the medium disturbing the axi‐symmetry about the x3‐axis implying that in the absence of fractures, the background medium is transversely isotropic (TI). Under the assumptions of long wavelength equivalent medium theory, the compliance matrix of a fractured medium is the sum of the background medium's compliance matrix and a fracture compliance matrix. For sets of parallel rotationally symmetric fractures (on average), the fracture compliance matrix is dependent on 3 parameters − its normal and tangential compliance and its strike direction. When one fracture set is present, the medium is orthorhombic and the analysis is straightforward. When two (non‐orthogonal) or more sets are present, the overall medium is in general elastically monoclinic; its compliance tensor components are subject to two equalities yielding an 11 parameter monoclinic medium. Constructing a monoclinic VFTI medium with n embedded vertical fracture sets, requires 5 TI parameters plus 3×n fracture set parameters. A deconstruction of such an 11 parameter monoclinic medium involves using its compliance tensor to find a background transversely isotropic medium and several sets of vertical fractures which, in the long wavelength limit, will behave exactly as the original 11 parameter monoclinic medium. A minimal deconstruction, would be to determine, from the 11 independent components, the transversely isotropic background (5 parameters) and two fracture sets (specified by 2 × 3 = 6 parameters). Two of the background TI medium's compliance matrix components are known immediately by inspection, leaving nine monoclinic components to be used in the minimal deconstruction of the VFTI medium. The use of the properties of a TI medium, which are linear relations on its compliance components, allows the deconstruction to be reduced to solving a pair of non‐linear equations on the orientations of two fracture sets. A single root yielding a physically meaningful minimum deconstruction yields a unique minimal representation of the monoclinic medium as a VFTI medium. When no such root exists, deconstruction requires an additional fracture set and uniqueness is lost. The boundary between those monoclinic media that have a unique minimal representation and those that do not is yet to be determined.

Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.

Fluid flow in the Earth's crust plays an important role in a number of geological processes. In relatively tight rock formations such flow is usually controlled by open macrofractures, with significant implications for ground water flow and hydrocarbon reservoir management. The movement of fluids in the fractured media will result in changes in the pore pressure and consequently will cause changes to the effective stress, traction and elastic properties. The main purpose of this study is to numerically examine the effect of pore pressure changes on seismic wave propagation (i.e. the effects of pore pressures on amplitude, arrival time, frequency content). This is achieved by using dual simulations of fluid flow and seismic propagation in a common 2-D fracture network. Note that the dual simulations are performed separately as the coupled simulations of fluid flow and seismic wave propagations in such fracture network is not possible because the timescales of fluid flow and wave propagation are considerably different (typically, fluid flows in hours, whereas wave propagation in seconds). The flow simulation updates the pore pressure at consecutive time steps, and thus the elastic properties of the rock, for the seismic modelling. In other words, during each time step of the flow simulations, we compute the elastic response corresponding to the pore pressure distribution. The relationship between pore pressure and fractures is linked via an empirical relationship given by Schoenberg and the elastic response of fractures is computed using the equivalent medium theory described by Hudson and Liu. Therefore, we can evaluate the possibility of inferring the changes of fluid properties directly from seismic data. Our results indicate that P waves are not as sensitive to pore pressure changes as S and coda (or scattered) waves. The increase in pore pressure causes a shift of the energy towards lower frequencies, as shown from the spectrum (as a result of scattering attenuation). Another important observation is that the fluid effects on the wavefield vary significantly with the source-receiver direction, that is, the azimuth relative to the fracture orientation. These results have significant implications for the characterization of naturally fractured reservoirs using seismic methods, and may impact on experimental design to infer such attributes in a real reservoir situation, particularly in acquiring time-lapse seismic data.

Fractures in a porous rock can be modelled as very thin and highly porous layers in a porous background. First, a dispersion equation for a P wave propagating in periodically layered poroelastic medium is obtained using propagator matrix approach applied to Biot equations of poroelasticity with periodic coefficients. Then in the limit of low stiffness and thickness this dispersion equation yields an expression for the effective P-wave modulus of the fractured porous material. When both pores and fractures are dry, this material is equivalent to a transversely isotropic elastic porous material with linear-slip interfaces. When saturated with a liquid this material exhibits significant attenuation and velocity dispersion due to wave-induced fluid flow between pores and fractures. In the low-frequency limit the material properties are equal to those obtained by anisotropic Gassmann (or Brown-Korringa) theory applied to a porous material with linear-slip interfaces. At low frequencies inverse quality factor scales with the first power of frequency omega. At high frequencies the effective elastic properties are equal to those for isolated fluid-filled fractures in a solid (non-porous) background, and inverse quality factor scales with omega(-1/2). The magnitude of both attenuation and dispersion strongly depends on both the degree of fracturing and background porosity of the medium. The characteristic frequency of the attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing.

In an elastic medium, fractures can be modeled as thin layers, the elastic stiffnesses of which approach zero as the volume fraction of the fractures hf→0. This yields linear slip theory [M. Schoenberg, J. Acoust. Soc. Am. 68, 1516–1521 (1980)], shown to be a robust way to account for the acoustic effect of fracturing. From Norris’ [J. Acoust. Soc. Am. 94, 359–370 (1993)] dispersion relation for alternating porous layers, fractures must be modeled similarly in porous media. However, another fracture parameter of great interest is permeability. If fracture permeability is taken to be O(hf−1) or taken to be independent of hf, one arrives at a dispersion relation for the fast P-wave dependent on porous background properties and a real excess compliance which takes the fractures into account. However, if fracture permeability is assumed to be small, and is taken to be O(hf), the P-wave dispersion dependence on background parameters remains the same, but the term accounting for the fractures is frequency dependent. Only in the zero frequency limit does this result agree with that of the other two cases.

P345 Summary 1 Fractures in a porous rock are modeled as thin soft layers of high permeability within a porous background. The starting point is the effective elastic modulus for waves propagating in periodically layered poroelastic medium obtained using Biot’s theory of poroelasticity (Biot 1962). The limit as one of the constituent layers become very thin yields the effective elastic modulus of such a fractured medium. When such a porous fractured system is dry it is equivalent to a transversely isotropic dry elastic porous material with linear-slip interfaces. When saturated with a liquid this system exhibits significant attenuation and velocity

Fluid flow in the earth's crust plays an important role in a number of geologic processes. In carbonate reservoirs, fluid flow is thought to be controlled by open macrofractures. The movement of fluids in the fractured media results in changes in the pore pressure and consequently causes changes in the effective stress, traction, and elastic properties. Many recent examples in time-lapse or 4D seismic surveys have demonstrated that seismic waves can be used to monitor changes in oil or gas reservoirs as a function of time (e.g., Landro, 2002; Angerer et al., 2002). During production from a reservoir, the movement of fluids is accompanied by substantial change in the pore pressure field. As fluids drain, pore pressure decreases, which increases the effective pressure on fractures, grain boundaries, and microcracks. Higher static load on these surfaces decreases their compliance nonlinearly and decreases fracture opening and/or pore throat size, thus increasing the stiffness of the rock (by increasing compressional and shear velocities) and decreasing permeability (Schoenberg, 2002). Conversely, pore pressure buildup due to injection leads to a decrease in effective pressure and an increase in rock compliance. Fractured rock is often modeled as a relatively rigid, defect-free, “background” medium with embedded sets of linear slip interfaces. A linear slip interface is a surface across which anomalously large strain occurs due to the passage of a wave. In linear slip deformation theory, the large strain is approximated by a displacement discontinuity across the surface that is linearly related to the dynamic traction acting on the interface (to the first order). The dynamic elastic properties of the rock are determined by adding the compliance tensor of the background to an excess fracture compliance tensor associated with the fractures (e.g., Liu et al., 2000). The linear parameters governing the infinitesimal slip on these planes have …

Quasi-shear (qSV) wavefront triplication, classically known as shear wave bi-refringence, occurs in TI media when anellipticity parameter E2≡BC−A2 differs significantly from 0 (equality is the elliptic case), where A≡c13+c55, B≡c11−c55, C≡c3−c55 [Helbig and Schoenberg, J. Acoust. Soc. Am. 81, 1235–1245 (1987)]. The region of the slowness curve corresponding to the triplicating region of the wavefront curve must be concave. Most common hexagonal crystals and all TI media long wavelength equivalent to isotropic layering exhibit positive anellipticity. In general, the exact condition for positive anellipticity triplication (the triplicating region then is between the 3-axis and its normal) requires the solution of a cubic equation [Peyton, Elastic Wave Propagation in Transversely Isotropic Media (Martinus Nijhoff, 1983)]; however, a good approximation for triplication is that E2>KBCc55/(c11+c33), where K is almost always within a few percent of 1.39. For negative anellipticity media, a simpler case, triplication centers about the 3-direction when A2>c11C and/or about the normal to the 3-axis when A2>c33B.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2003qSV wavefront triplication in a tranversely isotropic materialAuthors: Michael SchoenbergThomas M. DaleyMichael SchoenbergLawrence Berkeley Lab, Berkeley CA 94720 and Thomas M. DaleyLawrence Berkeley Lab, Berkeley CA 94720https://doi.org/10.1190/1.1817546 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Permalink: https://doi.org/10.1190/1.1817546FiguresReferencesRelatedDetailsCited byTriplications for the converted wave in transversely isotropic media with a tilted symmetry axis19 December 2019 | Geophysical Prospecting, Vol. 68, No. 4Traveltime approximation in vertical transversely isotropic layered media19 March 2017 | Geophysical Prospecting, Vol. 65, No. 6On shear-wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axis1 December 2009 | Geophysical Prospecting, Vol. 58, No. 4 SEG Technical Program Expanded Abstracts 2003ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2003 Pages: 2452 publication data© 2003 Copyright © 2003 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 03 Jan 2005 CITATION INFORMATION Michael Schoenberg and Thomas M. Daley, (2003), "qSV wavefront triplication in a tranversely isotropic material," SEG Technical Program Expanded Abstracts : 137-140. https://doi.org/10.1190/1.1817546 Plain-Language Summary PDF DownloadLoading ...