Shear data in the presence of azimuthal anisotropy: Dilley, Texas

Alford, R. M.

doi:10.1190/1.1893036

Cited by 417 publications

(310 citation statements)

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“…The derivatives of these expressions with respect to the variables (xĴ ,xJ , t) are linearly independent, so Φ M N is nondegenerate. From expression (3)(4) it follows that the canonical relation of this operator is given by (3)(4)(5)(6). By the hypothesis the canonical relation contains no elements withξ 0 +ξ 0 = 0, hence it is continuous as a map…”

Section: High-frequency Born Modeling and Imagingmentioning

confidence: 98%

“…The first equality in (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) represents the velocity ∂x/∂t of the bicharacteristic identified as the group velocity. Because B prin M is homogeneous in ξ and Euler's relation, ξ, ∂ ξ B prin M = B prin M = ∓τ it follows directly that the group velocity is orthogonal to the slowness surface.…”

Section: Propagation Of Elastic Waves In Smoothly Varying Mediamentioning

confidence: 99%

“…Because B prin M is homogeneous in ξ and Euler's relation, ξ, ∂ ξ B prin M = B prin M = ∓τ it follows directly that the group velocity is orthogonal to the slowness surface. Solving (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) reveals the formation of caustics. Caustics may form progressively in the presence of heterogeneities, or instantaneously in the presence of anisotropy even in the absence of heterogeneity.…”

Section: Propagation Of Elastic Waves In Smoothly Varying Mediamentioning

confidence: 99%

“…wherexĴ (xÎ , x 0 ,ξĴ , τ ),xJ (xĨ , x 0 ,ξJ , τ ) are as defined in (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), for the receiver side and the source side respectively. The derivatives of these expressions with respect to the variables (xĴ ,xJ , t) are linearly independent, so Φ M N is nondegenerate.…”

Section: High-frequency Born Modeling and Imagingmentioning

confidence: 99%

“…In the following theorem we parametrize (3)(4)(5)(6) by (x 0 ,ξ 0 ,ξ 0 ,t,t) using the parametrization of C φ M given by (2-15). Thus we let τ = ∓B M (x 0 ,ξ 0 ) and…”

Section: High-frequency Born Modeling and Imagingmentioning

confidence: 99%

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Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Stolk¹,

Hoop²

2001

Comm Pure Appl Math

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Abstract. We review applications of microlocal analysis (MA) to reflection seismology. In this inverse method one attempts to estimate the index of refraction of waves in the earth from seismic data measured at the Earth's surface. Seismic imaging creates images of the Earth's upper crust using seismic waves generated by artificial sources and recorded into extensive arrays of sensors (geophones or hydrophones). The technology is based on a complex, and rapidly evolving, mathematical theory that employs advanced solutions to a wave equation as tools to solve approximately the general seismic inverse problem, with complications introduced by the heterogeneity and anisotropy of the Earth's crust. We describe several important developments using MA to generate these wave-solutions by manipulating the wavefields directly on their phase space. We also consider some recent applications of MA to global seismology.

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Section: High-frequency Born Modeling and Imagingmentioning

confidence: 98%

Section: Propagation Of Elastic Waves In Smoothly Varying Mediamentioning

confidence: 99%

Section: Propagation Of Elastic Waves In Smoothly Varying Mediamentioning

confidence: 99%

Section: High-frequency Born Modeling and Imagingmentioning

confidence: 99%

“…In the following theorem we parametrize (3)(4)(5)(6) by (x 0 ,ξ 0 ,ξ 0 ,t,t) using the parametrization of C φ M given by (2-15). Thus we let τ = ∓B M (x 0 ,ξ 0 ) and…”

Section: High-frequency Born Modeling and Imagingmentioning

confidence: 99%

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Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Stolk¹,

Hoop²

2001

Comm Pure Appl Math

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Geophysical Prospecting Using Sonics and Ultrasonics

Sinha

Zeroug

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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The sections in this article are Sonic Measurements Elastic Wave Propagation in a Borehole Recent Developments I: Radial Alterations Recent Developments II: Formation Shear Anisotropy Recent Developments III: Sonic Measurements in the Presence of Formation Stresses Recent Developments IV: Formation Nonlinear Constants Ultrasonic Measurements Acknowledgments

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Spatial variations of shear wave anisotropy near the San Jacinto Fault Zone in Southern California

Peng

Ben‐Zion

et al. 2015

JGR Solid Earth

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We examine crustal anisotropy at several scales along and across the San Jacinto Fault Zone (SJFZ) by systematically measuring shear wave splitting (SWS) parameters. The analyzed data are recorded by 86 stations during 2012–2014, including five linear dense arrays crossing the SJFZ at different locations and other autonomous stations within 15 km from the main fault trace. Shear phase arrivals and SWS parameters (fast directions and delay times) are obtained with automated methods. The measurement quality is then assessed using multiple criteria, resulting in 23,000 high‐quality measurements. We find clear contrast of fast directions between the SW and NE sides of the SJFZ. Stations on the SW side have fast directions consistent overall with the maximum horizontal compression direction (SHmax), while stations on the NE side show mixed patterns likely reflecting lithological/topographic variations combined with fault zone damage. The fast directions in the Anza gap section with relatively simple fault geometry agree with the inferred SHmax, and the delay times at an array within that section are smaller than those observed at other across‐fault arrays. These indications of less pronounced damage zone in the Anza section compared to other segments of the SJFZ are correlated generally with geometrical properties of the surface traces. Significant variations of fast directions on several across‐fault arrays, with station spacing on the orders of a few tens of meters, suggest that shallow fault structures and near‐surface layers play an important role in controlling the SWS parameters.

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Shear data in the presence of azimuthal anisotropy: Dilley, Texas

Cited by 417 publications

References 1 publication

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Geophysical Prospecting Using Sonics and Ultrasonics

Spatial variations of shear wave anisotropy near the San Jacinto Fault Zone in Southern California

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