Scattering from a set of anisotropic layers to second order in frequency

Folstad, P.G.; Schoenberg, Michael

doi:10.3997/2214-4609.201411672

Cited by 3 publications

(3 citation statements)

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“…Intrinsically anisotropic materials are not thought to be the most common cause of observed anisotropy in the earth. One alternative explanation for seismic anisotropy is presented by the effective averaging that occurs when finely-layered isotropic materials are sampled by seismic energy with wavelengths greater than the thickness of the layers (Backus 1952;Folstad and Schoenberg 1993). In most cases where the layering is sub-horizontal, the resultant syrnmetry is transversely isotropic with a vertical (TIV) axis of symmetry (azimuthally isotropic).…”

Section: Introductionmentioning

confidence: 99%

Inversion for seismic anisotropy using genetic algorithms

Horne¹,

MacBeth²

1993

55th EAEG Meeting

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A general inversion scheme based on a genetic algorithm is developed to invert seismic observations for anisotropic parameters. The technique is applied to the inversion of shear-wave observations from two azimuthal VSP data sets from the Conoco test site in Oklahoma. Horizontal polarizations and time-delays are inverted for hexagonal and orthoghombic symmetries. The model solutions are consistent with previous studies using trial and error matching of full waveform synthetics. The shear-wave splitting observations suggest the presence of a shearwave line singularity and are consistent with a dipping fracture system which is known to exist at the test site. Application of the inversion scheme prior to full waveform modelling demonstrates that a considerable saving in time is possible whilst retaining the same degree of accuracy.

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Section: Introductionmentioning

confidence: 99%

Inversion for seismic anisotropy using genetic algorithms

Horne¹,

MacBeth²

1993

55th EAEG Meeting

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“…It appears necessary to calculate full synthetic seismograms in order to obtain estimates for comparison with observations of drift. Recent work by Folstad and Schoenberg (1993) indicates that these can be calculated accurately by careful blocking of the log, using the detailed structure to define optimal positions of block boundaries. Even then it must be remembered that the presence of layers finer than the resolution of sonic tools yet too thick to undergo effective Backus (1962) averaging at sonic frequencies may cause the total dispersion, from sonic to seismic frequencies, induced by layering, to be underestimated.…”

Section: Resultsmentioning

confidence: 99%

Backus averaging, scattering and drift¹

Sams¹,

Williamson²

1994

Geophysical Prospecting

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Differences between traveltimes from sonic to seismic frequencies, commonly known as drift, can be attributed to a combination of multiple scattering and absorption. The portion due to scattering can be estimated directly by calculating synthetic seismograms from sonic logs. A simple alternative approach is suggested by the long-wave equivalent averaging formulae for the effective elastic properties of a stack of thin layers, which gives the same traveltime delays as the lowfrequency limit of the scattering dispersion. We consider the application of these averaging formulae over a frequency-dependent window with the hope of extending their use to frequencies higher than those allowed by the original validity conditions. However, comparison of the time delay due to window-averaging with the scattering dispersion predicted by the O'Doherty-Anstey formula reveals that it is not possible to specify a form of window that will fit the dispersion across the spectrum for arbitrary log statistics. A window with a width proportional to the wavelength squared matches the behaviour at the low-frequency end of the dispersive range for most logs, and allows an almost exact match of the drift across the entire spectrum for exponential correlation functions.We examine a real log, taken from a hole in nearly plane-layered geology, which displays strong quasi-cyclical variations on one scale as well as more random, smaller-scale fluctuations. The details of its drift behaviour are studied using simple models of the gross features. The form of window which gave a good theoretical fit to the dispersion for an exponential log correlation function can only fit the computed drift at high or low frequencies, confirming that there are at least two significant scale-lengths of fluctuation. A better overall fit is obtained for a window whose width is proportional to the wavelength. The calculated scattering drift is significantly less than that observed from a vertical seismic profile, but the difference cannot be wholly ascribed to absorption. This is because the source frequency of the sonic tool is not appropriate for its resolution (receiver spacing) so that the scattering drift from sonic to seismic frequencies cannot be fully estimated from the layer model derived from the log.

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“…One alternative explanation for seismic anisotropy is presented by the effective averaging that occurs when finely-layered isotropic materials are sampled by seismic energy with wavelengths greater than the thickness of the layers (Backus 1952;Folstad and Schoenberg 1993). In most cases where the layering is sub-horizontal, the resultant syrnmetry is transversely isotropic with a vertical (TIV) axis of symmetry (azimuthally isotropic).…”

Section: Introductionmentioning

confidence: 98%