Seismic ray method: Recent developments

Červený, Vlastislav; Klimeš, Luděk; Pšenčı́k, Ivan

doi:10.1016/s0065-2687(06)48001-8

Cited by 58 publications

(24 citation statements)

References 124 publications

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“…Starting with a tomographic model parameterized by spherical harmonics, Bréger and Romanowicz (1998) and To et al (2005) achieved a good match to S waves interacting with the core-mantle boundary by preserving the boundaries between the largestscale positive and negative velocity anomalies but increasing the maximum and minimum values of velocity perturbation. Useful tools in assessing multipath behavior include the computation of the Lyapunov exponent along a ray, for example, Cerveny et al (2007). Steps in the analysis include an inversion for waveform multipaths represented by summing a predicted signal S(t) in a reference model with one or more delayed echoes of that signal.…”

Section: General 3d Modelsmentioning

confidence: 99%

Theory and Observations: Forward Modeling: Synthetic Body Wave Seismograms

Cormier

2015

Treatise on Geophysics

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Section: General 3d Modelsmentioning

confidence: 99%

Theory and Observations: Forward Modeling: Synthetic Body Wave Seismograms

Cormier

2015

Treatise on Geophysics

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“…Ray tracing and dynamic ray tracing are well described in seismological literature, and are not discussed here. For anisotropic inhomogeneous media, see, for example, Babich (1961), Červený (1972), Gajewski & Pšenčík (1987, 1990), Farra & Madariaga (1987), Klimeš (1994), Farra & Le Bégat (1995), Chapman (2004), Iversen (2004), Klimeš (2006b) and Červený et al (2007). Particularly detailed treatment, including additional literature, can be found in Červený (2001).…”

Section: Ray Tracing and Dynamic Ray Tracingmentioning

confidence: 99%

Two-point paraxial traveltimes in an inhomogeneous anisotropic medium

Červený

Iversen

Pšenčı́k

2012

Geophysical Journal International

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SUMMARY We derive formulae for the approximate computation of two‐point paraxial traveltimes (traveltimes between two points) for points arbitrarily chosen in a paraxial vicinity of a reference ray computed in a smoothly varying inhomogeneous anisotropic medium containing structural interfaces. The formulae have a form of the Taylor expansion in Cartesian coordinates of the two‐point paraxial traveltime or its square to the quadratic terms. The coefficients of the expansion depend on quantities obtained by ray tracing in Cartesian coordinates and by dynamic ray tracing in ray‐centred coordinates. Alternatively, the dynamic ray tracing can be performed in Cartesian coordinates. The advantages of the approach based on dynamic ray tracing in ray‐centred coordinates are its efficiency and elimination of possible complications that may arise from the redundant fundamental solutions of dynamic ray tracing in Cartesian coordinates (the ray‐tangent and non‐eikonal solutions). As a by‐product, we also obtain simple formulae for the slowness vectors at the two points in the paraxial vicinity of the reference ray. They belong to a paraxial ray passing through these points. Potential applications of the proposed formulae consist in the fast and flexible two‐point traveltime calculations from sources to receivers specified in Cartesian coordinates and situated close to a reference ray, along which dynamic ray tracing has been performed. The formulae for the paraxial slowness vectors can be used in two‐point ray tracing.

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“…where ω is the frequency and v is the medium velocity (see Cerveny et al, 1982;Popov, 1982;Nowack and Aki, 1984). For more recent overviews of Gaussian beam summations, see Cerveny (2001), Popov (2002), Nowack (2003) and Cerveny et al (2007). The correlation integral with complex beam parameters can then be written as…”

Section: Correlation Integral Evaluated With Gaussian Beamsmentioning

confidence: 99%

Seismic interferometry and estimation of the Green’s function using Gaussian beams

Nowack

2010

Earthq Sci

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This study investigates seismic interferometry in which the Green's function is estimated between two receivers by cross-correlation and integration over sources. For smoothly varying source strengths, the dominant contributions of the correlation integral come from the stationary phase directions in the forward and backward directions from the alignment of the two receivers. Gaussian beams can be used to evaluate the correlation integral and concentrate the amplitudes in a vicinity of the stationary phase regions instead of completely relying on phase interference. Several numerical examples are shown to illustrate how this process works. The use of Gaussian beams for the evaluation of the correlation integral results in stable estimates, and also provides physical insight into the estimation of the Green's function based on seismic interferometry.

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Seismic ray method: Recent developments

Cited by 58 publications

References 124 publications

Theory and Observations: Forward Modeling: Synthetic Body Wave Seismograms

Theory and Observations: Forward Modeling: Synthetic Body Wave Seismograms

Two-point paraxial traveltimes in an inhomogeneous anisotropic medium

Seismic interferometry and estimation of the Green’s function using Gaussian beams

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