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  • 1
    Electronic Resource
    Electronic Resource
    Fréchet Derivatives For Curved Interfaces In the Ray Approximation (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 97 (1989), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The sensitivity of ray and beam theoretical seismograms to changes in velocity models and curved interfaces is discussed in this paper. Previous results from Nowack & Lutter (1988) give the derivatives of travel-time and ray amplitude with respect to changes of smoothly varying velocities. These derivatives are required to perform linearized maximum likelihood inversions for structure. In the ray approximation, smooth interfaces are incorporated by applying Snell's law locally, correcting wavefront curvature, and using local plane-wave reflection and transmission coefficients. the partial derivatives for travel-time are directly calculated along the original ray trajectory using Fermat's principle. For perturbations of the ray amplitude of a reflected/transmitted ray, the ray shift of the perturbed two-point ray trajectory must be accounted for. the approach followed here is to calculate the approximately perturbed two-point ray using perturbation theory without additional ray tracing. the perturbed ray amplitudes are then computed directly, including modified reflection/transmission coefficients and geometric spreading, along this approximate two-point ray. Several numerical experiments are conducted which invert for velocity and interface shape using both travel-time and amplitude in order to test the derived partial derivative operators. Travel-time and amplitude inversion results are also contrasted with amplitude being less sensitive to larger scale features and more sensitive to heterogeneity curvature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1989.tb00519.x
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Wavefronts and solutions of the eikonal equation (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 110 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: In this paper, several methods for the solution of the eikonal equation are investigated. Using the method of characteristics, traveltimes are computed along rays. Approximate solutions of the eikonal equation can also be obtained. From Fermat's principle, first-order changes in the traveltime can be found by integrating along initial ray trajectories. Alternatively, linearized ray equations can be used to obtain perturbed rays for which traveltimes can be found. A comparison of the ray solution with approximate solutions for the traveltime is presented. The eikonal equation can also be solved directly without rays. This includes recent finite-difference methods for traveltimes. These methods avoid the ambiguity of multivalued time-fields by tracking only minimum traveltimes. The direct, numerical solution of the eikonal equation is illustrated by several examples using forward and reverse propagation of curved wavefronts. From these examples, it is shown that first-arrival wavefronts are generally non-reversible. This is relevant for tomographic applications which often use only first-arrival information. In order to obtain unique reverse propagation, multi-valued traveltimes must be accounted for. This is similar to difficulties encountered in traveltime inversion for 1-D structure when only first-arrivals are used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb00712.x
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Perturbation from isotropic to anisotropic heterogeneous media in the ray approximation (1991)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 106 (1991), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: In this paper, perturbation methods are used to obtain ray results in slightly anisotropic, heterogeneous media from a nearby isotropic medium. The advantage of this approach is that rays computed by available 2-D isotropic ray-tracing algorithms can be used to approximately compute, by perturbation, ray theoretical results in more general 3-D slightly anisotropic, heterogeneous media. The perturbation approach also makes possible an efficient computation of ray sensitivity operators necessary in seismic tomography studies. In order to compute approximate ray results for quasi-shear waves, degenerate perturbation theory must be used in order to split a single shear wave in an isotropic medium into two quasi-shear waves in a nearby anisotropic medium. The perturbation approach is tested on an effectively anisotropic model of aligned cracks within a linear, vertical velocity gradient. Perturbed traveltimes, ray paths and particle motions of quasi-compressional and quasi-shear waves for such an anisotropic medium are compared with exact ray results. Good agreement between the exact and perturbed results is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1991.tb04597.x
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Seismic attenuation values obtained from instantaneous-frequency matching and spectral ratios (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 123 (1995), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: In this paper, attenuation values are obtained from seismic data using instantaneous-frequency matching and spectral ratios. to obtain differential t* values using instantaneous-frequency matching, a near offset reference pulse is attenuated until the resulting instantaneous frequency matches the observed value at the receiver. Prior to matching, filtering can be applied to each trace in order to reduce the effects of noise on the calculated instantaneous frequencies. In the second method, the spectral ratio between a receiver pulse and a reference pulse is used to obtain differential t* values. to obtain an unbiased estimate, a variable spectral bandwidth is used depending on the noise level of the data. the two methods are tested using synthetic traces and then applied to crustal refraction data from the 1986 PASSCAL Ouachita experiment. Results show that the differential t* values obtained using filtered, instantaneous-frequency matching are consistent with and have less scatter than those obtained from spectral ratios with a variable bandwidth.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1995.tb06658.x
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Linearized rays, amplitude and inversion (1988)
    Springer
    Pure and applied geophysics 128 (1988), S. 401-421 
    Details
    ISSN: 1420-9136
    Keywords: Linearized inversion ; ray theory ; amplitude variations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract In this paper, ray theoretical amplitudes and travel times are calculated in slightly perturbed velocity models using perturbation analysis. Also, test inversions using travel time and amplitude are computed. The pertubation method is tested using a 3-D velocity model for NORSAR having velocity variations up to 8.0 percent. The perturbed amplitudes are found to be in excellent agreement with the calculated ray amplitudes. Velocity inversions based on travel time and amplitude are next investigated. Perturbation analysis using linearized ray equations is efficiently used to compute amplitude derivatives with respect to model parameters. The trial linearized inversions use smaller velocity variations of 1.7 percent to avoid possible effects due to ray shift, even though the perturbation analysis is valid for larger variations. The trial 2-D inversion results show that linearized amplitude inversions are complementary and not redundant to travel time inversions, even in smoothly varying models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01772606
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Tomography and the Herglotz-Wiechert inverse formulation (1990)
    Springer
    Pure and applied geophysics 133 (1990), S. 305-315 
    Details
    ISSN: 1420-9136
    Keywords: Tomography ; seismic inversion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract In this paper, linearized tomography and the Herglotz-Wiechert inverse formulation are compared. Tomographic inversions for 2-D or 3-D velocity structure use line integrals along rays and can be written in terms of Radon transforms. For radially concentric structures, Radon transforms are shown to reduce to Abel transforms. Therefore, for straight ray paths, the Abel transform of travel-time is a tomographic algorithm specialized to a one-dimensional radially concentric medium. The Herglotz-Wiechert formulation uses seismic travel-time data to invert for one-dimensional earth structure and is derived using exact ray trajectories by applying an Abel transform. This is of historical interest since it would imply that a specialized tomographic-like algorithm has been used in seismology since the early part of the century (seeHerglotz, 1907;Wiechert, 1910). Numerical examples are performed comparing the Herglotz-Wiechert algorithm and linearized tomography along straight rays. Since the Herglotz-Wiechert algorithm is applicable under specific conditions, (the absence of low velocity zones) to non-straight ray paths, the association with tomography may prove to be useful in assessing the uniqueness of tomographic results generalized to curved ray geometries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00877165
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  • 7
    Electronic Resource
    Electronic Resource
    Slant-stack velocity analysis for one-dimensional upper mantle structure using short-period data from MAJO (1993)
    Springer
    Pure and applied geophysics 141 (1993), S. 1-24 
    Details
    ISSN: 1420-9136
    Keywords: Slant-stack velocity analysis ; upper mantle structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract In this paper, regionalP-wave upper mantle structure is investigated using slant-stack velocity analysis of short-period earthquake data recorded at station MAJO (Matsushiro, Japan). Shallow earthquakes from 1980–1986 within 35° of MAJO are used to construct a common receiver gather. Processing of the wavefield data includes focal depth and static time corrections, as well as deterministic deconvolution, in order to equalize pulse shapes and align wavelets on the first arrivals. The processed wavefield data are slant stacked and interatively downward continued to obtain a regional upper mantle velocity model. The model includes a low velocity zone between 107 and 220 km. Beneath the LVZ, the velocity increases smoothly down to the discontinuity at 401 km. In the transition zone, the velocity model again increases linearly, although there is some suggestion of further complexity in the downward continued wavefield data. At the base of the transition zone, a second velocity discontinuity occurs at 660 km, with a linear velocity gradient below. In addition to slant-stack analysis, travel times and synthetic seismograms are computed and compared with the processed and unprocessed wavefield data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00876231
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Book review (1990)
    Springer
    Pure and applied geophysics 134 (1990), S. 135-161 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00878085
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    Paper (German National Licenses)
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