Estimation of elastic anisotropy from three-component ultrasonic measurements using laser Doppler interferometry
Andrej Bóna 1 Maxim Lebedev 1 Roman Pevzner 1 Boris Gurevich 1 2 Mahyar Madadi 1 31 Department of Exploration Geophysics, Curtin University, GPO Box U1987, Perth, WA 6845, Australia.
2 CSIRO, Australian Resources Research Centre, 26 Dick Perry Avenue, Kensington, WA 6151, Australia.
3 Corresponding author. Email: Mahyar.Madadi@curtin.edu.au
Exploration Geophysics 49(5) 744-750 https://doi.org/10.1071/EG16156
Submitted: 20 December 2016 Accepted: 20 August 2017 Published: 1 November 2017
Abstract
Ultrasonic measurements using laser Doppler interferometry (LDI) have been reported to provide robust estimates of elastic anisotropy of rock samples. In this approach, an ultrasonic wave is emitted by a piezo-electric source and detected by the LDI, which can be configured to measure three components of the particle velocity in a very small area (~1 mm2) of the sample. Repeating these measurements for a dense array of points on the sample’s surface gives a distribution of traveltimes and polarisation fields on the surface. Anisotropy is then obtained by inverting these fields using analytical expressions or numerical algorithms for computing phase and group velocities. The existing implementation of this approach involves the inversion of direct compressional (P) and shear (S) wave arrivals only. A previous study showed that this approach produces stable results if only a small range of source–receiver offsets is included in the inversion. This limitation resulted in a relatively large uncertainty of the result. This uncertainty can be reduced by inverting the entire traveltime field. To this end, we numerically simulate the wavefield in the sample. Analysis of the computed wavefield reveals the presence of P- and S-waves as well as a critically refracted converted PS-wave. Hence, the inversion of the entire traveltime field must include these three waves. We implement this inversion using global minimisation of the traveltime misfit function, coupled with numerical computation of ray velocities. Application of this algorithm to laboratory LDI measurements on a transversely isotropic phenolic sample provides stable anisotropy estimates consistent with previous studies.
Key words: 3-C, anisotropy, elastic, rock physics, ultrasonic.
References
Aki, K., and Richards, P., 2002, Quantitative seismology: University Science Books.Allan, A. M., Kanitpanyacharoen, W., and Vanorio, T., 2015, A multiscale methodology for the analysis of velocity anisotropy in organic-rich shale: Geophysics, 80, C73–C88
| A multiscale methodology for the analysis of velocity anisotropy in organic-rich shale:Crossref | GoogleScholarGoogle Scholar |
Asgharzadeh, M., Nadri, D., and Bóna, A., 2014, Inversion based accuracy comparison of non-hyperbolic moveout approximations for P-waves in VTI media: 76th Conference and Exhibition, EAGE, Extended Abstracts, 1–4.
Bóna, A., Bucataru, I., and Slawinski, M. A., 2008, Inversion of ray velocity and polarization for elasticity tensor: Journal of Applied Geophysics, 65, 1–5
| Inversion of ray velocity and polarization for elasticity tensor:Crossref | GoogleScholarGoogle Scholar |
Bóna, A., Nadri, D., and Brajanovski, M., 2012, Thomsen’s parameters from p-wave measurements in a spherical sample: Geophysical Prospecting, 60, 103–116
| Thomsen’s parameters from p-wave measurements in a spherical sample:Crossref | GoogleScholarGoogle Scholar |
Bóna, A., Gurevich, B., Pevzner, R., Lebedev, M., and Madadi, M., 2015, Joint inversion of P-, and S-wave travel times for characterisation of anisotropic materials using laser Doppler interferometry measurements: 24th ASEG International Geophysical Conference and Exhibition, Extended Abstracts, 1–4.
Buddensiek, M. L., Krawczyk, C. M., Kukowski, N., and Oncken, O., 2009, Performance of piezoelectric transducers in terms of amplitude and waveform: Geophysics, 74, T33–T45
| Performance of piezoelectric transducers in terms of amplitude and waveform:Crossref | GoogleScholarGoogle Scholar |
Červený, V., 2005, Seismic ray theory: Cambridge University Press.
Dellinger, J., and Vernik, L., 1994, Do traveltimes in pulse-transmission experiments yield anisotropic group or phase velocities? Geophysics, 59, 1774–1779
| Do traveltimes in pulse-transmission experiments yield anisotropic group or phase velocities?Crossref | GoogleScholarGoogle Scholar |
Goldin, S., 1979, Seismic traveltime inversion: Society of Exploration Geophysicists.
Golikov, P., and Stovas, A., 2012, Accuracy comparison of nonhyperbolic moveout approximations for qP-waves in VTI media: Journal of Geophysics and Engineering, 9, 428–432
| Accuracy comparison of nonhyperbolic moveout approximations for qP-waves in VTI media:Crossref | GoogleScholarGoogle Scholar |
Grechka, V., Theophanis, S., and Tsvankin, I., 1999, Joint inversion of P- and PS-waves in orthorhombic media: theory and a physical modeling study: Geophysics, 64, 146–161
| Joint inversion of P- and PS-waves in orthorhombic media: theory and a physical modeling study:Crossref | GoogleScholarGoogle Scholar |
Guilbaud, S., and Audoin, B., 1999, Measurement of the stiffness coefficients of a viscoelastic composite material with laser-generated and detected ultrasound: The Journal of the Acoustical Society of America, 105, 2226–2235
| Measurement of the stiffness coefficients of a viscoelastic composite material with laser-generated and detected ultrasound:Crossref | GoogleScholarGoogle Scholar |
Jech, J., 1991, Computation of elastic parameters of anisotropic medium from travel times of quasi-compressional waves: Physics of the Earth and Planetary Interiors, 66, 153–159
| Computation of elastic parameters of anisotropic medium from travel times of quasi-compressional waves:Crossref | GoogleScholarGoogle Scholar |
Lebedev, M., Bóna, A., Pevzner, R., and Gurevich, B., 2011, Elastic anisotropy estimation from laboratory measurements of velocity and polarization of quasi-P-waves using laser interferometry: Geophysics, 76, WA83–WA89
| Elastic anisotropy estimation from laboratory measurements of velocity and polarization of quasi-P-waves using laser interferometry:Crossref | GoogleScholarGoogle Scholar |
Lokajíček, T., and Svitek, T., 2015, Laboratory measurement of elastic anisotropy on spherical rock samples by longitudinal and transverse sounding under confining pressure: Ultrasonics, 56, 294–302
| Laboratory measurement of elastic anisotropy on spherical rock samples by longitudinal and transverse sounding under confining pressure:Crossref | GoogleScholarGoogle Scholar |
Martin, D., Ehinger, A., and Rasolofosaon, P. N. J., 1992, Some aspects of seismic modeling and imaging in anisotropic media using laser ultrasonics: SEG Technical Program, Expanded Abstracts, 1373–1376.
Martin, D., Rasolofosaon, P. N. J., Gascón, F., Bayón, A., and Varadé, A., 1994, Physical modeling of 3D seismic wave propagation, in K. Helbig, ed., Modeling the earth for oil exploration: Pergamon, 637–686.
Nadri, D., Sarout, J., Bóna, A., and Dewhurst, D., 2012, Estimation of the anisotropy parameters of transversely isotropic shales with a tilted symmetry axis: Geophysical Journal International, 190, 1197–1203
| Estimation of the anisotropy parameters of transversely isotropic shales with a tilted symmetry axis:Crossref | GoogleScholarGoogle Scholar |
Pros, Z., and Babuška, V., 1968, An apparatus for investigating the elastic anisotropy on spherical rock samples: Studia Geophysica et Geodaetica, 12, 192–198
| An apparatus for investigating the elastic anisotropy on spherical rock samples:Crossref | GoogleScholarGoogle Scholar |
Rasolofosaon, P. N. J., and Zinszner, B. E., 2002, Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks: Geophysics, 67, 230–240
| Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks:Crossref | GoogleScholarGoogle Scholar |
Sahay, S., Kline, R., and Mignogna, R., 1992, Phase and group velocity considerations for dynamic modulus measurement in anisotropic media: Ultrasonics, 30, 373–382
| Phase and group velocity considerations for dynamic modulus measurement in anisotropic media:Crossref | GoogleScholarGoogle Scholar |
Sayers, C. M., and Ebrom, D. A., 1997, Seismic traveltime analysis for azimuthally anisotropic media: theory and experiment: Geophysics, 62, 1570–1582
| Seismic traveltime analysis for azimuthally anisotropic media: theory and experiment:Crossref | GoogleScholarGoogle Scholar |
Schmidt, H., and Jensen, F. B., 1985, A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid–solid interfaces: The Journal of the Acoustical Society of America, 77, 813–825
| A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid–solid interfaces:Crossref | GoogleScholarGoogle Scholar |
Shragge, J., Blum, T. E., van Wijk, K., and Adam, L., 2015, Full-wavefield modeling and reverse time migration of laser ultrasound data: a feasibility study: Geophysics, 80, D553–D563
| Full-wavefield modeling and reverse time migration of laser ultrasound data: a feasibility study:Crossref | GoogleScholarGoogle Scholar |
Tsvankin, I., 2001, Seismic signatures and analysis of reflection data in anisotropic media: Elsevier Science.
Tsvankin, I., and Thomsen, L., 1994, Nonhyperbolic reflection moveout in anisotropic media: Geophysics, 59, 1290–1304
| Nonhyperbolic reflection moveout in anisotropic media:Crossref | GoogleScholarGoogle Scholar |
Vernik, L., and Nur, A., 1992, Ultrasonic velocity and anisotropy of hydrocarbon source rocks: Geophysics, 57, 727–735
| Ultrasonic velocity and anisotropy of hydrocarbon source rocks:Crossref | GoogleScholarGoogle Scholar |
Wang, Y., 2011, Seismic anisotropy estimated from P-wave arrival times in crosshole measurements: Geophysical Journal International, 184, 1311–1316
| Seismic anisotropy estimated from P-wave arrival times in crosshole measurements:Crossref | GoogleScholarGoogle Scholar |