"Viscoelastic finite difference modeling" J. O. Blanch and J. O. A. Robertsson and W. W. Symes in "Mathematical and numerical aspects of wave propagation" eds. R. Kleinman and T. Angell and D. Colton and F. Santosa and I. Stakold SIAM, 1993 pp. 69-81 Abstract: Real earth media disperse and attenuate propagating mechanical waves. This anelastic behavior can be described by a viscoelastic model. We have developed a finite difference simulator to model wave propagation in viscoelastic media. The finite difference method was chosen in favor of other methods for several reasons. Finite difference codes are more portable than pseudo spectral codes for instance. Moreover, finite difference schemes provide a convenient environment in which to define complicated boundaries. Several finite difference schemes for viscoelastic wave propagation are thoroughly investigated with convergence tests, dispersion and stability analyses. "Linear Inversion for 2D Viscoacoustic Media" J. O. Blanch and W. W. Symes TRIP annual report 1994, article 6 Abstract: Seismic waves attenuate and disperse while propagating through the earth. These anelastic effects can be large, and can adversely affect the results of imaging and inversion if neglected. Two dimensional viscoacoustics provides a reasonably realistic model for multidimensional simulation and inversion in the presence of attenuation and dispersion. The adjoint state method leads to an effective algorithm for linear least squares inversion of short wavelength model components. However the nonreversibility of the viscoacoustic system complicates its efficient implementation, as fields must be accessed in both forward and backward order in time during the adjoint state calculation. For 2D examples of dimensions typical of exploration seismology these fields are far to large too store in fast memory. A minor modification of an algorithm due to Griewank optimally balances the storage and computation resources needed to complete the adjoint state calculation. A synthetic 2D linearized viscoacoustic inversion example illustrates the method and its efficiency. "Linearized inversion in viscoelastic media" J. O. Blanch and W. W. Symes in "Full field inversion methods in ocean and seismo-acoustics" eds. O. Diachok and A. Caiti and P. Gerstoft and H. Schmidt Kluwer Academic Publishers, 1995 Abstract: Real earth media disperse and attenuate propagating waves. This anelastic behavior can be well described by a viscoelastic model. Here we introduce a viscoelastic linearized inversion routine developed through the adjoint state technique. It is based on a viscoelastic model of standard linear solids in parallel and built upon a recently developed finite difference simulator. The routine enables linearized inversion in viscoelastic media. We will show that the reproduction of reflectors can be very poor if anelastic effects are neglected. "Linear Inversion in Layered Viscoacoustic Media Using a Time Domain Method" J. O. Blanch and W. W. Symes in TRIP annual report 1994 Abstract: Real Earth media attenuate and disperse propagating waves. If these effects are neglected, inversion can produce erroneous results. Viscoelasticity provides an appropriate and powerful tool to model these anelastic effects, so forms a plausible basis for inversion algorithms. The tau-p (intercept time-slowness) domain permits economical modeling and inversion of 3-D wave propagation in layered media. The adjoint state method leads to an efficient algorithm for linear least squares inversion of short wavelength model components. Numerical experiments show that accurate inversion requires conditioning of thedata by a time varying gain, hence also of the simulator output, to ``equalize'' the influence of earlier strong events and later attenuated events. "Galerkin-wavelet modeling of wave propagation: Optimal finite-difference stencil design" J. O. A. Robertsson and J. O. Blanch and W. W. Symes and C. S. Burrus Mathl. Comput. Modelling, vol 19, 1994 pp. 31-38 Also in TRIP annual report 1994 Abstract: In this paper, we descibe a method for design of optimal finite-difference stencils for wave propagation problems using an intrinsically explicit Galerkin-wavelet formulation. The method enables an efficient choice of stencils optimal for a certain problem. We compare group velocity curves corresponding to stencils obtained by our choice of wavelet basis and traditional finite-difference schemes. Generally there exist choices of stencils with superior characteristics compared to conventional finite-difference stancils of the same size. Beside gain in accuracy, this leads to large computational savings. "Viscoelastic finite-difference modeling" J. O. A. Robertsson and J. O. Blanch and W. W. Symes Geophysics, vol. 59, 1994, pp. 1444-1456 Also in TRIP annual report 1993. Abstract: Real earth media disperse and attenuate propagating mechanical waves. This anelastic behavior can be described well by a viscoelastic model. We have developed a finite-difference simulator to model wave propagation in viscoelastic media. The finite-difference method was chosen in favor of other methods for several reasons. Finite-difference codes are more portable than, for example, pseudospectral codes. Moreover, finite-difference schemes provide a convenient environment in which to define complicated boundaries. A staggered scheme of second order accuracy in time and fourth order accuracy in space appears to be optimally efficient. Because of intrinsic dispersion, no fixed grid points per wavelength rule can be given; instead, we present tables, which enable a choice of gridparameters for a given level of accuracy. Since the scheme models energy absorption, natural and efficient absorbing boundaries may be implemented, merely by changing the parameters near the grid boundary. The viscoelastic scheme is only marginally more expensive than analogous elastic schemes. The efficient implementation of absorbing boundaries may therefore be a good reason for using the viscoelastic scheme also in purely elastic simulations. We illustrate our method and the importance of accurately modeling anelastic media through 2-D and 3-D examples from shallow marine environments. "Modeling, Inversion and Imaging of Seismic Data in Viscous Media" Joakim O. Blanch Rice MA thesis 1995. Abstract: Real Earth media is anelastic, which affects both kinematics and dynamics of prpagating waves. Waves are attenuated and dispersed. If anelastic effects are neglected, inversion and migration can yield erroneousresults. The anelastic effects, on propagating waves, in real rocks can be well describe by a viscoelastic model. Hence, viscoelastic wave propagation simulation is a well suited base for a realistic inversion algorithm derived through the adjoint state technique. We have developed a finite-difference simulator to model wave propagatin in viscoelastic media. The viscoelastic scheme is only slightly more expensive than analogous elastic schemes. This thesis also presents a method for modeling of constant Q as a function o frequency based on an explicit closed formula for calculation of the parameter fields. The tau-p (intercept time-slowness) domain permits economical modeling an inversion of 3-D wave propagation in layered media.
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