PP-PS registration in the reflectivity domain: A waveform-preserving approach

Daniel O. Pérez; Danilo R. Velis

doi:10.24215/18527744e001

Autores/as

Daniel O. Pérez Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina https://orcid.org/0000-0003-2856-9306
Danilo R. Velis Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina https://orcid.org/0000-0002-2078-926X

DOI:

https://doi.org/10.24215/18527744e001

Palabras clave:

Registración PP-PS, inversión, velocidad, optimización

Resumen

La inversión simultánea y el análisis de atributos de ondas PP y ondas convertidas PS requieren la transformación de las ondas PS al dominio temporal de las ondas PP, de modo que reflectores similares compartan los tiempos de propagación. Este proceso, conocido como registración PP-PS, a menudo genera soluciones PS no estacionarias donde el contenido espectral de las ondículas varía con el tiempo y la ubicación, afectando procesos posteriores como la inversión simultánea. Para abordar esta limitación, proponemos un método de registración PP-PS en el dominio de la reflectividad. La estrategia consta de dos pasos. Primero, realizamos una deconvolución de tipo rala (sparse) de los datos PP y PS para transformarlos al dominio de la reflectividad. Dichas soluciones se obtienen resolviendo un problema inverso regularizado con una norma que promueva soluciones sparse de la reflectividad. En el segundo paso, ajustamos iterativamente la reflectividad sparse PS para que coincida con su contraparte PP mediante una función de deformación suave y monótona representada por un spline cúbico con un número fijo de nudos. En cada iteración, ambas reflectividades se convolucionan con una ondícula de reemplazo estacionaria y se evalúa su diferencia. La estimación óptima de la posición de los nudos genera un problema no lineal y multimodal, que resolvemos mediante el algoritmo Very Fast Simulated Annealing. A diferencia de los métodos convencionales que operan en el dominio de los datos, nuestro método produce datos sísmicos PP y PS estacionarios con reflectores alineados, eliminando las distorsiones de las ondículas y sin necesidad de procesamiento adicional. Las pruebas numéricas confirman que el método preserva la amplitud y es una alternativa superadora a técnicas como Dynamic Time Warping, generando un espectro más limpio y formas de onda sin distorsiones que contribuyen a una interpretación fiable del dato sísmico.

Descargas

Los datos de descarga aún no están disponibles.

Referencias

Anderson, K. R., & Gaby, J. E. (1983). Dynamic waveform matching. Information Sciences, 31(3), 221–242. https://doi.org/10.1016/0020-0255(83)90054-3

Backus, G. E. (1962). Long-wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research (1896-1977), 67(11), 4427–4440. https://doi.org/10.1029/JZ067i011p04427

Beck, A., & Teboulle, M. (2009). Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Transactions on Image Processing, 18(11), 2419–2434. https://doi.org/10.1109/TIP.2009.2028250

Castagna, J., Batzle, M., & Eastwood, R. (1985). Relationships between compressional and shear-wave velocities in clastic silicate rocks. Geophysics, 50, 551–570. https://doi.org/10.1190/1.1441933

Chai, X., Tang, G., Lin, K., Yan, Z., Gu, H., Peng, R., Sun, X., & Cao, W. (2021). Deep learning for multitrace sparse-spike deconvolution. Geophysics, 86(3), V207–V218. https://doi.org/10.1190/geo2020-0342.1

Chambolle, A. (2004). An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision, 20(1), 89–97. https://doi.org/10.1023/B:JMIV.0000011325.36760.1e

Chopra, S., & Sharma, R. K. (2020). Addressing artifacts in PP-PS registration prior to performing joint impedance inversion. The Leading Edge, 39(1), 47–52. https://doi.org/10.1190/tle39010047.1

Compton, S., & Hale, D. (2014). Estimating VP/VS ratios using smooth dynamic image warping. Geophysics, 79(6), V201–V215. https://doi.org/10.1190/geo2014-0022.1

Cooke, D., & Schneider, W. (1983). Generalized linear inversion of reflection seismic data. Geophysics, 46(6), 665–676. https://doi.org/10.1190/1.1441497

Debeye, H. W. J., & van Riel, P. (1990). L p -norm deconvolution. Geophysical Prospecting, 38(4), 381–403. https://doi.org/10.1111/j.1365-2478.1990.tb01852.x

Fomel, S. (2007). Local seismic attributes. Geophysics, 72(3), A29–A33. https://doi.org/10.1190/1.2437573

Fomel, S., & Backus, M. M. (2003). Multicomponent seismic data registration by least squares. SEG Technical Program Expanded Abstracts, 781–784. https://doi.org/10.1190/1.1818052

Fomel, S., Backus, M., Fouad, K., Hardage, B., & Winters, G. (2005). A multistep approach to multicomponent seismic image registration with application to a West Texas carbonate reservoir study. SEG Technical Program Expanded Abstracts,1018–1021. https://doi.org/10.1190/1.2147852

Fritsch, F. N., & Butland, J. (1984). A method for constructing local monotone piecewise cubic interpolants. SIAM Journal on Scientific and Statistical Computing, 5(2), 300–304. https://doi.org/10.1137/0905021

Gaiser, J. E. (1996). Multicomponent VP/VS correlation analysis. Geophysics, 61(4), 1137–1149. https://doi.org/10.1190/1.1822598

Gao, W., & Sacchi, M. D. (2018). Multicomponent seismic data registration by nonlinear optimization. Geophysics, 83(1), V1–V10. https://doi.org/10.1190/geo2017-0105.1

Gardner, G., Gardner, L., & Gregory, A. (1974). Formation velocity and density: The diagnostic basics for stratigraphic traps. Geophysics, 74, 770–780. https://doi.org/10.1190/1.1440465

Geis, W. T., Stewart, R. R., Jones, M. J., & Katapodis, P. E. (1990). Processing, correlating, and interpreting converted shear waves from borehole data in southern Alberta. Geophysics, 55(6), 660–669. https://doi.org/10.1190/1.1442878

Gelpi, G., Pérez, D. O., & Velis, D. R. (2020). Automatic well tying and wavelet phase estimation with no waveform stretching or squeezing. Geophysics, 85(3), D83–D91. https://doi.org/10.1190/geo2019-0284.1

Gelpi, G. R., Pérez, D. O., & Velis, D. R. (2019). Seismic wavelet phase estimation by l1-norm minimization. Journal of Seismic Exploration, 28(4), 393–411. https://geophysical-press.com/journal/JSE/articles/150

Geng, W., Chen, X., Li, J., Wang, J., Wu, F., Tang, W., & Zhang, J. (2023). Warped P-SV wavelet distortion correction using a time-frequency adaptive shaping filter. Geophyiscs, 88(2), V101–V112. https://doi.org/10.1190/geo2022-0368.1

Hale, D. (2013). Dynamic warping of seismic images. Geophysics, 78(2), S105–S115. https://doi.org/10.1190/geo2012-0327.1

Hennenfent, G., van den Berg, E., Friedlander, M. P., & Hermann, F. J. (2008). New insights into one-norm solvers from the Pareto curve. Geophysics, 73(4), 23–26. https://doi.org/10.1190/1.2944169

Herrera, H., Fomel, S., & van der Baan, M. (2014). Automatic approaches for seismic to well tying. Interpretation, 2(2), SD101–SD109. https://doi.org/10.1190/INT-2013-0130.1

Ingber, L. (1989). Very fast simulated re-annealing. Journal of Mathematical Computation and Modelling, 12, 967–973. https://doi.org/10.1016/0895-7177(89)90202-1

Kazemi, N. (2018). Automatic blind deconvolution with Toeplitz-structured sparse total least squares. Geophysics, 83(6), V345–V357. https://doi.org/10.1190/geo2018-0136.1

Lindsay, R., & Van Koughnet, R. (2001). Sequential Backus averaging: Upscaling well logs to seismic wavelengths. The Leading Edge, 20(2), 188–191. https://doi.org/10.1190/1.1438908

Liner, C. L., & Clapp, R. G. (2004). Nonlinear pairwise alignment of seismic traces. The Leading Edge, 23(11), 1146–1150. https://doi.org/10.1190/1.1825937

Lines, L., Zou, Y., Zhang, A., Hall, K., Embleton, J., Palmiere, B., Reine, C., Bessette, P., Cary, P., & Secord, D. (2005). VP/VS characterization of a heavy-oil reservoir. The Leading Edge, 24(11), 1134–1136. https://doi.org/10.1190/1.2135111

Lu, J., Yang, Z., Wang, Y., & Shi, Y. (2015). Joint PP and PS AVA seismic inversion using exact zoeppritz equations. Geophysics, 80(5), R239–R250. https://doi.org/10.1190/geo2014-0490.1

Needleman, S. B., & Wunsch, C. D. (1970). A general method applicable to the search for similarities in the amino acid sequence of two proteins. Journal of Molecular Biology, 48(3), 443–453. https://doi.org/10.1016/0022-2836(70)90057-4

Oldenburg, D. W., Scheuer, T., & Levy, S. (1983). Recovery of the acoustic impedance from reflection seismograms. Geophysics, 48(10), 1318–1337. https://doi.org/10.1190/1.1441413

Pereg, D., Cohen, I., & Vassiliou, A. A. (2020). Sparse seismic deconvolution via recurrent neural network. Journal of Applied Geophysics, 175, 103979. https://doi.org/10.1016/j.jappgeo.2020.103979

Pérez, D. O., Velis, D. R., & Sacchi, M. D. (2013). High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy. Geophysics, 78(5), R185–R195. https://doi.org/10.1190/geo2013-0077.1

Pérez, D. O., & Velis, D. R. (2011). Sparse-spike AVO/AVA attributes from prestack data. SEG Technical Program Expanded Abstracts, 30, 340–344. https://doi.org/10.1190/1.3627906

Pérez, D. O., & Velis, D. R. (2018). Simple and fast gradient-based impedance inversion using total variation regularization. Journal of Seismic Exploration, 27(5), 473–486. https://geophysical-press.com/journal/JSE/articles/174

Pérez, D. O., Velis, D. R., & Sacchi, M. D. (2017). Three-term inversion of prestack seismic data using a weighted l 2,1 mixed norm. Geophysical Prospecting, 65(6), 1477–1495. https://doi.org/10.1111/1365-2478.12500

Ricker, N. (1940). The form and nature of seismic waves and the structure of seismograms. Geophysics, 5, 348–366. https://doi.org/10.1190/1.1441816

Robinson, E. A., & Ebrom, D. A. (1996). Deconvolution 2. SEG.

Rudin, L. I., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 60(1), 259–268. https://doi.org/10.1016/0167-2789(92)90242-F

Sacchi, M. D. (1997). Reweighting strategies in seismic deconvolution. Geophysical Journal International, 129(3), 651–656. https://doi.org/10.1111/j.1365-246X.1997.tb04500.x

Sacchi, M. D., Velis, D. R., & Ulrych, T. J. (1996). Wavelet via polycepstra. SEG Technical Program Expanded Abstracts, 1583–1586.

Sakoe, H., & Chiba, S. (1978). Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech, and Signal Processing, 26(1), 43–49. https://doi.org/10.1109/TASSP.1978.1163055

Stewart, R. R., Gaiser, J. E., Brown, R. J., & Lawton, D. C. (2003). Converted-wave seismic exploration: Applications. Geophysics, 68(1), 40–57. https://doi.org/10.1190/1.1543193

Sui, Y., & Ma, J. (2020). Blind sparse-spike deconvolution with thin layers and structure. Geophysics, 85(6), V481–V496. https://doi.org/10.1190/geo2019-0423.1

Taner, M. T., Koehler, F., & Sheriff, R. E. (1979). Complex seismic trace analysis. Geophysics, 44(6), 1041–1063. https://doi.org/10.1190/1.1440994

Taylor, H. L., Banks, S. C., & McCoy, J. F. (1979). Deconvolution with the l 1 norm. Geophysics, 44(1), 39–52. https://doi.org/10.1190/1.1440921

van den Berg, E., & Friedlander, M. (2008). Probing the Pareto frontier for basis pursuit solutions. SIAM Journal of Scientific Computing, 31(2), 890–912. https://doi.org/10.1137/080714488

Walden, A., & Hosken, J. (1986). The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution. Geophysical Prospecting, 34, 1038–1066.

Wiggins, R. (1978). Minimum entropy deconvolution. Geoexploration, 16, 21–35. https://doi.org/10.1016/0016-7142(78)90005-4

Yilmaz, Ö. (2001). Seismic data analysis: Processing, inversion, and interpretation of seismic data. Society of Exploration Geophysicists. https://doi.org/10.1190/1.9781560801580

Yuan, J. J., Nathan, G., Calvert, A., & Bloor, R. (2008). Automated C-wave registration by simulated annealing. SEG Technical Program Expanded Abstracts, 1043–1047. https://doi.org/10.1190/1.3059105

Zhang, F., & Wang, Y. (2009). Amplitude-preserving calibration of PP- and PS-wave reflection events. SEG Global Meeting Abstracts, 82–82. https://doi.org/10.1190/1.3603607

Zoeppritz, K. (1919). Vii b. über reflexion und durchgang seismischer wellen durch unstetigkeitsflächen. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1919, 66–84. http://eudml.org/doc/59042

Zuleta, L. M., & Lawton, D. C. (2012). VP/VS characterization of a shale gas basin, northeast British Columbia, Canada. SEG Technical Program Expanded Abstracts, 1–5. https://doi.org/10.1190/segam2012-1172.1