CitationLi V, Wang H, Tsvankin I, Díaz E, Alkhalifah T (2017) Inversion gradients for acoustic VTI wavefield tomography and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield 9 extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a gener-10 alized pseudospectral operator based on a separable approximation for the P-wave dispersion rela-11 tion. This operator is employed to derive the gradients of the differential semblance optimization 12(DSO) and modified image-power objective functions. We also obtain the gradient expressions for
Processing algorithms for transversely isotropic (TI) media are widely used in depth imaging and typically bring substantial improvements in reflector focusing and positioning. Here, we develop acoustic image-domain tomography (IDT) for reconstructing VTI (TI with a vertical symmetry axis) models from P-wave reflection data. The modeling operator yields an integral wave-equation solution, which is based on a separable dispersion relation and contains only P-waves. The zero-dip NMO velocity ([Formula: see text]) and anellipticity parameter [Formula: see text] are updated by focusing energy in space-lag images obtained by least-squares reverse-time migration (LSRTM). Application of LSRTM helps mitigate aperture- and illumination-induced artifacts in space-lag gathers and improve the robustness of [Formula: see text]-estimation. The impact of the trade-off between [Formula: see text] and [Formula: see text] is reduced by a three-stage inversion algorithm that gradually relaxes the constraints on the spatial variation of [Formula: see text]. Assuming that the depth profile of the Thomsen parameter [Formula: see text] is known at two or more borehole locations, we employ image-guided interpolation to constrain the depth scale of the parameter fields and of the migrated image. Image-guided smoothing is also applied to the IDT gradients to facilitate convergence towards geologically plausible models. The algorithm is tested on synthetic reflection and borehole data from the structurally complicated elastic VTI Marmousi-II model. Although the initial velocity field is purely isotropic and substantially distorted, all three relevant parameters ([Formula: see text], [Formula: see text], and [Formula: see text]) are estimated with sufficient accuracy. The algorithm is also applied to a line from a 3D ocean-bottom-node data set acquired in the Gulf of Mexico.
CitationLi V, Tsvankin I, Guitton A, Alkhalifah T (2017) Acoustic VTI wavefield tomography of P-wave surface and VSP data. SUMMARYTransversely isotropic (TI) models have become standard in depth imaging and are often used in waveform inversion. Here, we develop a robust wave-equation-based tomographic algorithm for building acoustic VTI (transversely isotropic with a vertical symmetry axis) velocity models from P-wave surface reflection and vertical seismic profiling (VSP) data. Wavefield extrapolation is performed with an integral operator to avoid generating shear-wave artifacts. Focusing energy in extended images produced by reverse-time migration (RTM) makes it possible to update the zero-dip NMO velocity V nmo and the anellipiticity parameter η. To constrain the anisotropy coefficient δ and improve the accuracy in V nmo and η, we employ borehole information by introducing an additional objectivefunction term designed to fit VSP data. Image-guided smoothing is applied to both data-and image-domain gradients to steer the inversion towards geologically plausible solutions.Testing on the VTI Marmousi model shows that the joint inversion of surface and VSP data helps estimate all three relevant medium parameters.
SUMMARYExtended images obtained from reverse-time migration (RTM) contain information about the accuracy of the velocity field and subsurface illumination at different incidence angles. Here, we evaluate the influence of errors in the anisotropy parameters on the shape of the residual moveout (RMO) in P-wave RTM extended images for VTI (transversely isotropic with a vertical symmetry axis) media. Considering the actual spatial distribution of the zero-dip NMO velocity (V nmo ), which could be approximately estimated by conventional techniques, we analyze the extended images obtained with distorted fields of the parameters η and δ . Differential semblance optimization (DSO) and stack-power estimates are employed to study the sensitivity of focusing to the anisotropy parameters. The results show that the signature of η is dip-dependent, whereas errors in δ cause defocusing only if that parameter is laterally varying. Hence, earlier results regarding the influence of η and δ on reflection moveout and migration velocity analysis remain generally valid in the extended image space for complex media. The dependence of RMO on errors in the anisotropy parameters provides essential insights for anisotropic wavefield tomography using extended images.
The paper considers the negative consequences of thermal softening of the contact wire material under the action of an electric arc, which is thermal wear. In order to determine the degree of softening of the contact wire in real time, the methodology for assessing the condition of the contact wire of electrified railways by the value of thermal wear is presented. The presented method is based on the criterial approach. The criteria for softening the material of the wire and the transition of the material to the liquid state are introduced. By comparing the amount of heat entering the wire in the event of an electric arc (with these criteria), the contact wire is diagnosed in terms of thermal wear. Calculations have been made using the proposed method; graphical dependences of the amount of heat entering the wire element on the current intensity of the electric arc for various times of its influence on the contact wire are constructed. A device for diagnosing the condition of the contact wire in terms of the amount of thermal wear is proposed, designed to record the place of occurrence of the electric arc, to collect and transmit the necessary initial data. The operating principle of the device is described and its structural diagram is given. The use of the method for assessing the condition of the contact wire in terms of the amount of thermal wear and the diagnostic device will make it possible to quantify the degree of thermal softening of the contact wire material in order to further determine its residual life.
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