Nonhyperbolic Reflection Moveout For Azimuthally Anisotropic Media

Reflection moveout in azimuthally anisotropic media is not only azimuthally dependent but it is also nonhyperbolic. As a result, the conventional hyperbolic normal moveout (NMO) equation parameterized by the exact NMO (stacking) velocity loses accuracy with increasing offset (i.e., spreadlength). This is true even for a single-homogeneous azimuthally anisotropic layer. The most common azimuthally anisotropic models used to describe fractured media are the horizontal transverse isotropy (HTI) and the orthorhombic(ORT) symmetry. Here, we introduce an analytic representation for the quartic coefficient of the Taylor's series expansion of the two-way traveltime for pure mode reflection (I.e., no conversion) in arbitrary anisotropic media with arbitrary strength of anisotropy. In addition, we present an analytic description of the long-spread (large-offset) nonhyperbolic reflection moveout (NHMO). In multilayered azimuthally anisotropic media, the NMO (stacking) velocity and the quartic moveout coefficient can be calculated with good accuracy using the known averaging equations for VTI media. The interval NMO velocities and the interval quartic coefficients, however, are azimuthally dependent. This allows us to extend the nonhyperbolic moveout (NHMO) equation, originally designed for VTI media, to more general horizontally stratified azimuthally anisotropic media. As a result, our formalism allows rather simple transition from VTI to azimuthally anisotropic media. Numerical examples from reflection moveout in orthorhombic media, the focus of this paper, show that this NHMO equation accurately describes the azimuthally-dependent P-wave reflection traveltimes, even on spreadlengths twice as large as the reflector depth. This work provides analytic insight into the behavior of nonhyperbolic moveout, and it has important applications in modeling and inversion of reflection moveout in azimuthally anisotropic media.Saudi Aramc

Reflection Moveout Inversion In Azimuthally Anisotropic Media: Accuracy, Limitation, And Acquisition

Parameter estimation from elliptical variations in the normal-moveout (NMO) velocity in azimuthally anisotropic media is sensitive to the angular separation between the survey lines in 2D, or equivalently source-to-receiver azimuth in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the orientation of the NMO ellipse, the parameter cr, in particular, is also sensitive to the strength of anisotropy. To invert for the parameters the NMO ellipse, at least three NMO-velocity measurements along distinct azimuth directions are needed. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to-receiver directions 60° apart. Having more than three distinct source-to-receiver azimuths (e.g., full azimuthal coverage) provides a useful data redundancy that enhances the quality of the estimates. In orthorhombic media, inverting for the semi-axes of the NMO-ellipse allows the computation of the difference in the anisotropic parameters δ[superscript (1)] and δ[superscript (2)]. Additional information such as well data, is necessary in order to determine δ[superscript (1)] and δ[superscript (2)]. Furthermore, the accuracy in estimating the semi-axes of the NMO-velocity ellipse is about the same for any strength of anisotropy. To maximize quality in the inversion process, it is recommended that at the design stage of seismic data acquisition to have small sector sizes (≤ 10°) with adequate fold and offset distribution. For three azimuth directions, 60° apart, to perform the inversion, an azimuthally anisotropic layer overlain by an azimuthally isotropic overburden (as might happen for fractured reservoirs) should have a time thickness, relative to the total time, of at least the ratio of the error in the NMO (stacking) velocity to the interval anisotropy strength of the fractured layer. Coverage along more than three azimuths, however, improves this limitation, which is imposed by Dix differentiation, by at most 50% depending on the number of observations (NMO Velocities) that enter the inversion procedure.Saudi Aramc

Wingless Signalling Alters the Levels, Subcellular Distribution and Dynamics of Armadillo and E-Cadherin in Third Instar Larval Wing Imaginal Discs

Background: Armadillo, the Drosophila orthologue of vertebrate beta-catenin, plays a dual role as the key effector of Wingless/Wnt1 signalling, and as a bridge between E-Cadherin and the actin cytoskeleton. In the absence of ligand, Armadillo is phosphorylated and targeted to the proteasome. Upon binding of Wg to its receptors, the "degradation complex'' is inhibited; Armadillo is stabilised and enters the nucleus to transcribe targets. Methodology/Principal Findings: Although the relationship between signalling and adhesion has been extensively studied, few in vivo data exist concerning how the "transcriptional'' and "adhesive'' pools of Armadillo are regulated to orchestrate development. We have therefore addressed how the subcellular distribution of Armadillo and its association with E-Cadherin change in larval wing imaginal discs, under wild type conditions and upon signalling. Using confocal microscopy, we show that Armadillo and E-Cadherin are spatio-temporally regulated during development, and that a punctate species becomes concentrated in a subapical compartment in response to Wingless. In order to further dissect this phenomenon, we overexpressed Armadillo mutants exhibiting different levels of activity and stability, but retaining E-Cadherin binding. Arm(S10) displaces endogenous Armadillo from the AJ and the basolateral membrane, while leaving E-Cadherin relatively undisturbed. Surprisingly, Delta NArm(1-155) caused displacement of both Armadillo and E-Cadherin, results supported by our novel method of quantification. However, only membrane-targeted Myr-Delta NArm(1-155) produced comparable nuclear accumulation of Armadillo and signalling to Arm(S10). These experiments also highlighted a row of cells at the A/P boundary depleted of E-Cadherin at the AJ, but containing actin. Conclusions/Significance: Taken together, our results provide in vivo evidence for a complex non-linear relationship between Armadillo levels, subcellular distribution and Wingless signalling. Moreover, this study highlights the importance of Armadillo in regulating the subcellular distribution of E-CadherinPublisher PDFPeer reviewe

Advancing gendered analyses of entrepreneurship:A critical exploration of entrepreneurial activity among gay men and lesbian women

This paper advances contemporary gendered analyses of entrepreneurial activity by exploring self-employment amongst gay men and lesbian women. Within current entrepreneurial debate, heterosexual women have become the visible embodiment of the gendered subject. Our contribution is to queer this assumption when focusing upon the entrepreneurial activity of gays and lesbians. Our core question investigates if ‘there is evidence of differences between homosexuals and heterosexuals in their likelihood of being entrepreneurially active?’ To address this question, we contrast competing notions of gender stereotypes and discrimination whilst drawing on findings from a large-scale population-based study of 163,000 UK adults. We find few differences between homosexuals and heterosexuals; this persists after examining intersectional patterns and considering if gay and lesbian entrepreneurs choose particular sectors, geographies or forms of self-employment. As our discussion highlights, the value of this study lies within its critique of contemporary analyses of gender which assume it is an end point rather than a foundation for analysing gender as a multiplicity