Slowness surface approximations for qSV‐waves in transversely isotropic media

Stovas, Alexey; Roganov, Y.

doi:10.1111/j.1365-2478.2008.00728.x

Cited by 9 publications

(7 citation statements)

References 26 publications

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“…Next we test the qSV-wave slowness-surface approximations from Stovas and Roganov (2009). The slownesssurface approximations for qSV-waves (similar to acoustic Figure 4 Slowness-surface approximations from Stovas and Roganov (2009) and triplications for model 1 (top) and 2 (bottom) from case 1 (see Table 1).…”

Section: N U M E R I C a L E X A M P L E Smentioning

confidence: 99%

“…We are listing the qSV-wave slowness-surface approximations from Stovas and Roganov (2009) in order to test these approximations for triplications. The approximation (1) is the acoustic approximation for qP-wave (Alkhalifah 1998) but redefined for qSV-wave…”

Section: Slowness-surface Approximationsmentioning

confidence: 99%

“…Next we test the qSV‐wave slowness‐surface approximations from Stovas and Roganov (2009). The slowness‐surface approximations for qSV‐waves (similar to acoustic approximation for qP‐waves) are used for processing (in particular, phase‐shift migration) and modelling purposes with a reduced number of medium parameters.…”

Section: Numerical Examplesmentioning

confidence: 99%

“… Slowness‐surface approximations from Stovas and Roganov (2009) and triplications for model 1 (top) and 2 (bottom) from case 1 (see Table 1). …”

Section: Numerical Examplesmentioning

confidence: 99%

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On shear‐wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axis

Roganov

Stovas

2010

Geophysical Prospecting

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A B S T R A C TThe presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The traveltime curve becomes multi-valued and the geometrical spreading correction factor tends to zero due to energy focusing.We analyse the conditions for the qSV-wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis. The proposed technique can easily be extended to the case of horizontally layered vertical symmetry axis medium. We show that the triplications of the qSV-wave in a multilayered medium imply certain algebra. We illustrate this algebra on a two-layer vertical symmetry axis model. I N T R O D U C T I O NThe qSV-wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis (VTI medium) have been discussed by many authors (Dellinger ). The condition for incipient triplication was given in Dellinger (1991) and Thomsen and Dellinger (2003). According to Musgrave (1970), we consider axial (on-axis vertical), basal (on-axis horizontal) and oblique (off-axis) triplications. He also provided the conditions for the generation of all the types of triplications. The approximate condition for off-axis triplication was derived in Schoenberg and Daley (2003) and Vavryčuk (2003). The condition for on-axis triplication in multilayered VTI medium was shown in Tygel et al. (2007).We use the parametrization of a VTI medium proposed by Schoenberg and Daley (2003). In our paper we define the conditions and the range of qSV-wave triplications in a multilayered VTI medium based on the ray theory and consider * two special cases: two-layer VTI medium and converted wave in a homogeneous VTI medium. q S V -W A V E I N A H O M O G E N E O U S V T I M E D I U MThe parametric offset-traveltime equations in a homogeneous VTI medium of thickness z are given bywhere p and q are respectively the horizontal and vertical components of the slowness vector, q = dq/dp is the derivative of vertical slowness. The condition for triplication (caustic in the group space or concavity region on the slowness curve) is given by setting the curvature of the vertical slowness to zero, q = 0 , or by setting the first derivative of offset to zero, x = 0. These points at slowness surface have the curvature equal to zero. If the triplication region is degenerated to a single point, it is called incipient triplication. At that point we have q = 0 and q = 0. For the incipient horizontal on-axis triplication, this is not the case, because at that point q is equal to infinity and we have to take the corresponding limit.

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Section: N U M E R I C a L E X A M P L E Smentioning

confidence: 99%

Section: Slowness-surface Approximationsmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

“… Slowness‐surface approximations from Stovas and Roganov (2009) and triplications for model 1 (top) and 2 (bottom) from case 1 (see Table 1). …”

Section: Numerical Examplesmentioning

confidence: 99%

See 2 more Smart Citations

On shear‐wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axis

Roganov

Stovas

2010

Geophysical Prospecting

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show abstract

“…Next we test the qSV-wave slowness-surface approximations from Stovas and Roganov (2009). The slowness-surface approximations for qSV waves (similar to acoustic approximation for qP waves) are used for processing (in particular, phase-shift migration) and modeling purpose with reduced number of medium parameters.…”

Section: Single-layer Caustics Versus Multi-layer Causticsmentioning

confidence: 99%