Technique for measuring the plane-wave reflection coefficient of the ocean bottom

Frisk, George V.; Oppenheim, Alan V.; Martinez, David R.

doi:10.1121/1.2016315

Cited by 15 publications

(14 citation statements)

References 2 publications

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“…The frequency-domain point-source τ -p transform, involving a sequence of Fourier and Hankel transforms, can be numerically evaluated in several ways, for instance, the AbelFourier method (e.g., Frisk et al, 1980;Wilson, 1986), the Fourier-Bessel summation method (e.g., Dietrich, 1990), and the frequency-domain singular integral method (Fokkema et al, 1992). The BFT method, based directly on equation (3) is, however, considered the classical algorithm for plane-wave decomposition.…”

Section: The Bessel-fourier Transform Methodsmentioning

confidence: 99%

Point‐source τ‐p transform: A review and comparison of computational methods

Wang

Houseman

1997

GEOPHYSICS

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The τ -p transformation of reflection seismic data excited by a point source requires a cylindrical slant stack, which includes compensation for the phase shift and geometrical spreading associated with cylindrical geometry. Using a simple test model, we review and compare the different computational methods used for the cylindrical slant stack. The two major method types are the BesselFourier transform (BFT) method and a set of methods (TD2D, TDX, TDTC and TDTS) based on timedomain convolution. The stack integral in each of these approaches can be separated into two parts, with the part corresponding to the contribution of incoming waves being negligible for large ray parameter p. Neglecting the latter term for large p generally avoids a major problem caused by aliasing between time and space domains.The TDTS method introduced here has the advantage of being expressed in terms of a conventional 2-D slant stack (weighted by offset x) plus a correction term. This formulation facilitates a quantitative comparison of the 3-D cylindrical slant stack with a 2-D slant stack. The TDTS method compares favorably with the TD2D method, in which the cylindrical slant stack is expressed as a weighted integral of the 2-D slant stacks. TDTS avoids the singular weighting function needed in the integral for the TD2D method, and therefore has less problems with numerical noise. For all of the methods considered, the accuracy of the map transformation is limited by the spatial and temporal resolution of the test data set. Some corrections to previously published methods are also provided.

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Section: The Bessel-fourier Transform Methodsmentioning

confidence: 99%

Point‐source τ‐p transform: A review and comparison of computational methods

Wang

Houseman

1997

GEOPHYSICS

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“…The technique described here was developed by Frisk and co-workers [22,46]. Given the pressure as a function of range at constant source and receiver depth, the Green's function can be computed as the inverse transform…”

Section: Measurement Of the Reflection Coefficient From Acoustic Presmentioning

confidence: 99%

“…In this chapter, we apply a technique developed by Frisk and co-workers [22,461 to the measurement of the reflection coefficient using monochromatic acoustic data from the deep water experiment at the Icelandic Basin described by Frisk, Doutt, and Hays [21].…”

Section: Thesis Overviewmentioning

confidence: 99%

Inversion for subbottom sound velocity profiles in the deep and shallow ocean

Souza¹

2005

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This thesis investigates the application of acoustic measurements in the deep and shallow ocean to infer the sound velocity profile (svp) in the seabed. For the deep water ocean, an exact method based on the Gelfand-Levitan integral equation is evaluated. The input data is the complex plane-wave reflection coefficient estimated from measurements of acoustic pressure in water. We apply the method to experimental data and estimate both the reflection coefficient and the seabed svp. A rigorous inversion scheme is hence applied in a realistic problem.For the shallow ocean, an inverse eigenvalue technique is developed. The input data are the eigenvalues associated with propagating modes, measured as a function of sourcereceiver range. We investigate the estimation of eigenvalues from acoustic fields measured in laterally varying environments. We also investigate the errors associated with estimating varying modal eigenvalues, analogous to the estimation of time-varying frequencies in multicomponent signals, using time-varying autoregressive (TVAR) methods. We propose and analyze two AR sequential estimators, one for model coefficients, another for the zeros of the AR characteristic polynomial. The decimation of the pressure field defined in a discrete range grid is analyzed as a tool t o improve AR estimation.The nonlinear eigenvalue inverse problem of estimating the svp from a sequence of eigenvalues is solved by iterating linearized approximations. The solution to the inverse problem is proposed in the form of a Kalman filter. The resolution and variance of the eigenvalue inverse problem are analyzed in terms of the Cramer-Rao lower bound and the Backus-Gilbert (BG) resolution theory. BG theory is applied to the design of shallow-water experiments. A method is developed to compensate for the Doppler deviation observed in experiments with moving sources.

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“…Special function transforms are a widely used and well-understood tool of applied mathematics; they are encountered, inter alia, in weather and climate modeling [19], [20], [21], tomography [14], [9], electromagnetics [13], and acoustics [6], [16]. Examples of such transforms include the Fourier transform, the Fourier-Bessel transform, orthogonal polynomial transforms, etc.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm for the Rapid Evaluation of Special Function Transforms

O’Neil¹,

Woolfe²,

Rokhlin³

2008

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. We introduce a fast algorithm for the numerical application to arbitrary vectors of several special function transforms. The algorithm requires O(n log(n)) operations to apply to an arbitrary vector any n×n matrix such that the rank of any p×q contiguous submatrix is bounded by a constant times pq/n. These rank bounds are proven here for the case of the Fourier-Bessel transform. Numerical experiments demonstrate a much wider applicability. The performance of the algorithm is illustrated via several numerical examples.

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Technique for measuring the plane-wave reflection coefficient of the ocean bottom

Cited by 15 publications

References 2 publications

Point‐source τ‐p transform: A review and comparison of computational methods

Point‐source τ‐p transform: A review and comparison of computational methods

Inversion for subbottom sound velocity profiles in the deep and shallow ocean

An Algorithm for the Rapid Evaluation of Special Function Transforms

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