Local Determination of Weak Anisotropy Parameters from Walkaway VSP qP-Wave Data in the Java Sea Region

Gomes, Ellen N. S.; Zheng, Xingqun; Pšenčı́k, Ivan; Horne, Steve; Leaney, Scott

doi:10.1023/b:sgeg.0000015593.29477.88

Cited by 23 publications

(12 citation statements)

References 10 publications

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“…& Plomerová 1996; Růžek et al 2003). Other authors have used polarities to determine the elastic parameters at the receiver (Gomes et al 2004). Therefore, they sample properties along the ray path but do not directly infer on the near‐source region.…”

Section: Discussionmentioning

confidence: 99%

Retrieval of moment tensors due to dislocation point sources in anisotropic media using standard techniques

Rössler¹,

Rümpker

2007

Geophysical Journal International

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SUMMARY Anisotropic material properties are commonly neglected during moment tensor inversion. On the other hand, anisotropy is a widely observed rock property. We show that anisotropy may greatly influence characteristics of moment tensors. For the inversion we apply a method based on amplitude spectra of waveforms in isotropic media. We investigate effects of anisotropy on seismic moment, moment‐tensor components, and apparent slip inclination of dislocation point sources. The direct calculation of moment tensors for shear sources in anisotropic regions shows spurious non‐double‐couple components that may be mistaken as an indication of (apparent) opening or closing of the fracture plane. On the other hand real volumetric components may be increased but also hidden in the presence of anisotropy. These effects as well as the seismic moment depend on the orientation of the elastic tensor relative to the fault plane and the slip direction. If anisotropy is present near the source but isotropy is assumed during inversion, the properties of the moment tensor can still be obtained in a good approximation. In the case where anisotropy extends to the medium along the ray path, only the fault orientation can be successfully retrieved by inverting qP waves to derive the deviatoric moment tensor. The inversions show that retrieved moment tensors can deviate systematically from moment tensors of shear and tensile sources expected in isotropic media. Further complications may arise when qS waves are included in the inversion process. We account for near‐source anisotropy to re‐interpret moment tensors derived for two events at the KTB super deep drill hole, SE‐Germany. The obtained source mechanisms are close to shear faulting although the moment tensors comprise non‐double‐couple components. We interpret the volumetric moment‐tensor components partly as a result of anisotropy. This indicates that for detailed studies of volumetric source components anisotropy should be considered during inversion. In addition, we show that for shear sources in anisotropic media the elastic properties near the source can also be derived from inverted moment tensors in media where anisotropy is restricted to the source region.

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Section: Discussionmentioning

confidence: 99%

Retrieval of moment tensors due to dislocation point sources in anisotropic media using standard techniques

Rössler¹,

Rümpker

2007

Geophysical Journal International

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“…Gomes et al ͑2004͒ show how anisotropy, and its uncertainty, can be estimated ͑and thereby separated from effects of heterogeneity͒ using the same slowness and polarization information that we use here, from a series of independent sources recorded in a borehole; polarization angles and slownesses are coupled in anisotropic media. Thus, in the present context, we assume that anisotropy can be dealt with when it is present, and we focus on the migration.…”

Section: Angle Calculation By Polarization Analysismentioning

confidence: 99%

Parsimonious migration of 3-C 3D VSP data

Agnihotri

McMechan

2007

GEOPHYSICS

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Conventional Kirchhoff migration can be made much faster by a priori calculation of wave arrival directions, and tracing rays back only along the measured directions; this is known as parsimonious migration. For surface seismic data, where acquisition with 2D arrays is common, the wave arrival directions can be measured by using local slant stacking to calculate the two horizontal slowness components. The vertical slowness is then deduced by using the dispersion relation. For vertical seismic profile ͑VSP͒ data, where multiline acquisition is not possible, only the vertical component of the slowness vector can be measured, which is insufficient to constrain the wave arrival direction. We overcome this limitation for three-component VSP data by polarization analysis of the incident waves. Polar and azimuth angles are calculated at the receivers by estimating the data covariance matrix and the vertical slowness, assuming isotropic media and linear polarization of both P-and S-waves. For P-waves, the data covariance matrix defines the polarization ellipsoid, which is then used to calculate the wave arrival direction. For S-waves, an additional step is required because the polarization is orthogonal to the propagation direction. Ray tracing along only the measured propagation directions eliminates the traditional traveltime table calculation, and enhances the efficiency of Kirchhoff migration of three-component VSP data. Distortions of the polarization caused by factors such as anisotropy are assumed to be corrected independently of the migration process described here. Synthetic examples for a flat reflector and for a salt flank model demonstrate the procedure and the image quality.

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“…The inversion formulae for the qP wave have been tested by a synthetic multi‐azimuthal multiple‐source walkaway VSP experiment and by real data (Zheng & Pšenčík 2002; Zheng 2003; Gomes et al 2004). In this section we shall use a similar configuration (Fig.…”

Section: Synthetic Experimentsmentioning

confidence: 99%

Inversion for elastic parameters in weakly anisotropic media

Zheng¹

2004

Geophysical Journal International

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S U M M A R YLinearized inversion equations of quasi P waves (qP) and quasi S waves (qS) in arbitrary weakly anisotropic media are presented. The equations can be used for local determination of weak anisotropy (WA) parameters in inhomogeneous media. The equations for qS waves hold not only in regular directions but also in singularities. In the case of qS-wave coupling, the first arrival of qS waves can be used alone for inversion. We obtain three equations for each wave expressed in terms of WA parameters. One of the equations relates the WA parameters to slowness and the other two relate the WA parameters to polarization vectors. By eliminating one or two components of the slowness vector from the three equations, we get a new equation system which enables us to perform inversion when two (or one) components of the slowness vector are known. Since a coordinate system is selected to be identical to the polarization vectors, the inversion formulae for qS waves become linear ones. A synthetic multi-azimuthal multiple-source walkaway vertical seismic profile experiment for an orthorhombic inhomogeneous medium with tilted symmetry axes is carried out to illustrate the applicability and efficiency of the method.Elastic waves propagating in an anisotropic medium satisfy the Christoffel equation. The phase velocities and polarization vectors corresponding to the eigenvalues and eigenvectors of the Christoffel matrix depend on the propagation direction. In general, the polarization vectors are neither parallel nor perpendicular to the wave normal. For a few simple symmetries, such as a transversely isotropic medium, we have analytic expressions for the eigenvalues and eigenvectors and thus for phase velocities and polarization vectors. Based on the observation that most anisotropic media are only weakly anisotropic, Backus (1965) first derived an approximate equation for the phase velocity of a qP wave in arbitrary weakly anisotropic media. Thomsen (1986) presented angle-dependent formulae for wave velocities appropriate for weak anisotropy by using anisotropy parameters. Sayers (1994), Mensch & Rasolofosaon (1997) and Pšenčík & Gajewski (1998) obtained approximate equations for the phase velocity of a qP wave in an arbitrary weakly anisotropic medium. The advantage of these approximations for a qP wave is that they are linear in terms of elastic parameters. But for qS waves, the approximate equations have a non-linear form (Jech & Pšenčík 1989) and it is difficult to apply them to inverse problems. In the cases of qS-wave singularities and coupling, the standard zeroth-order ray theory fails. Modifications of the ray theory such as the coupling theory (Chapman & Shearer 1989;Coates & Chapman 1990) or the quasi-isotropic approximation of the ray theory (Pšenčík 1998;Zillmer et al. 1998) have been used to reproduce qS waves correctly. Vavryčuk (1999) showed that the failure of the zeroth-order ray theory does not necessarily implicate a failure of the high-order ray theory or the ray theory at all. He showed that qS-wa...

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Local Determination of Weak Anisotropy Parameters from Walkaway VSP qP-Wave Data in the Java Sea Region

Cited by 23 publications

References 10 publications

Retrieval of moment tensors due to dislocation point sources in anisotropic media using standard techniques

Retrieval of moment tensors due to dislocation point sources in anisotropic media using standard techniques

Parsimonious migration of 3-C 3D VSP data

Inversion for elastic parameters in weakly anisotropic media

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