Predictive deconvolution from the point of view of kriging
Broadhead, M.K., 2009. Predictive deconvolution from the point of view of kriging. Journal of Seismic Exploration, 18: 239-247. We review the geostatistical method of simple kriging and consider its application to the predictive deconvolution problem in seismology. We find that when kriging is applied to the 1D time-series prediction problem, it can be used to obtain the usual Wiener-Levinson system of equations that are normally arrived at with the methods of stationary time-series analysis. The kriging weights can then be interpreted in terms of the prediction filter coefficients. This connection between predictive decon and geostatistics does not appear to be known. Perhaps a better understanding and exploitation of this type of connection can lead to productive synergies between signal processing and geostatistics.
- Dubrule, O., 2003. Geostatistics for Seismic Data Integration in Earth Models. SEG, Tulsa, OK.
- Goovaerts, P., 1997. Geostatistics for Natural Resources Evaluation. Oxford Univ. Press, Oxford.
- Hansen, T.M., Journel, A.G., Tarantola, A. and Mosegaard, K., 2006. Linear inverse Gaussian
- theory and geostatistics. Geophysics, 71: R101-R111.
- Krige, D.G., 1951. A statistical approach to some basic mine valuation problems on the
- Witwatersrand. J. of the Chem., Metal. and Mining Soc. of South Africa, 52: 119-139.
- Matheron, G., 1963. Principles of geostatistics. Economic Geol., 58: 1264-1266.
- Piazza, J.L., Sandjivy, L. and Legeron, S., 1997. Use of geostatistics to improve seismic velocities:
- Case studies. Expanded Abstr., 67th Ann. Internat. SEG Mtg. Dallas: 1293-1296.
- Robinson, E.A., 1976. Physical Applications of Stationary Time-Series: with special reference to
- digital data processing of seismic signals. Macmillan Inc., New York.
- Robinson, E.A. and Treitel, S., 2000. Geophysical Signal Analysis. SEG, Tulsa, OK.
- Ruiz-Alzola, J., Alberola-Lopez, C. and Westin, C.F., 2005. Kriging filters for multidimensional
- signal processing. Signal Proces., 85: 413-439.
