ORIGINAL PAPER
Ranking of the utility of selected geostatistical interpolation methods in conditions of highly skewed seismic data distributions: a case study of the Baltic Basin (Poland)
1
AGH University of Science and Technology, Faculty of Geology, Geophysics and Environmental Protection, Kraków, Poland
Submission date: 2023-03-18
Final revision date: 2023-07-09
Acceptance date: 2023-08-23
Publication date: 2023-09-22
Corresponding author
Justyna Sowińska-Botor
AGH University of Science and Technology, Faculty of Geology, Geophysics and Environmental Protection, Kraków, Poland
AGH University of Science and Technology, Faculty of Geology, Geophysics and Environmental Protection, Kraków, Poland
Gospodarka Surowcami Mineralnymi – Mineral Resources Management 2023;39(3):149-172
KEYWORDS
TOPICS
ABSTRACT
The suitability of several low-labor geostatistical procedures in the interpolation of highly positively skewed seismic data distributions was tested in the Baltic Basin. These procedures were a combination of various estimators of the model of spatial variation (theoretical variogram) and kriging techniques, together with the initial data transformation to normal distribution or lack thereof. This transformation consisted of logarithmization or normalization using the anamorphosis technique. Two variations of the theoretical variogram estimator were used: the commonly used classical Matheron estimator and the inverse covariance estimator (InvCov), which is robust with regard to non-ergodic data. It was expected that the latter would also be resistant to strongly skewed data distributions. The kriging techniques used included the commonly used ordinary kriging, simple kriging useful for standardized data and the non-linear median indicator kriging technique. It was confirmed that normalization (anamorphosis) is the most useful and less laborious geostatistical procedure of those suitable for such data, which results in a standardized normal distribution. The second, not obvious statement for highly skewed data distributions suggests that the non-ergodic inverted covariance (InvCov) estimator of variogram has an advantage over the Matheron’s estimator. It gives a better assessment of the C0 (nugget effect) and C (sill) parameters of the spatial variability model. Such a conclusion can be drawn from the fact that the higher the estimation of the relative nugget effect L = C0/(C0 + C) using the InvCov estimator, the weaker the correlation between the kriging estimates and the observed values. The values of the coefficient L estimates obtained by using the Matheron’s estimator do not meet this expectation.
ACKNOWLEDGEMENTS
This research has been funded by the Polish National Centre for Research and Development (NCRD) grant under the “Blue Gas Programme” – “Badania sejsmiczne i ich zastosowanie dla detekcji stref występowania gazu z łupków. Dobór optymalnych parametrów akwizycji i przetwarzania w celu odwzorowania budowy strukturalnej oraz rozkładu parametrów petrofizycznych i geomechanicznych skał perspektywicznych” („Seismic surveys and their application for the detection of shale gas zones. Selection of optimal acquisition and processing parameters for the imaging of structural architecture and distribution of petrophysical and geomechanical parameters in prospective rock formations”). The Polish Oil and Gas Company in Warsaw (PGNiG) is acknowledged for access to seismic data.
METADATA IN OTHER LANGUAGES:
Polish
Ranking przydatności wybranych metod interpolacji geostatystycznej w warunkach silnie skośnych rozkładów danych sejsmicznych: studium przypadku Basenu Bałtyckiego (Polska)
sejsmika, przetwarzanie danych, strefa przypowierzchniowa, niepewność, zmienność
W ramach studium przypadku w rejonie basenu bałtyckiego przetestowano przydatność kilku mało pracochłonnych procedur geostatystycznych do interpolacji silnie skośnych rozkładów danych sejsmicznych. Były one kombinacją różnych estymatorów modelu zmienności przestrzennej (wariogramu teoretycznego) i technik krigingu, wraz ze wstępną transformacją danych do rozkładu normalnego lub jej brakiem. Transformacja ta polegała na logarytmowaniu bądź na normalizacji z użyciem techniki anamorfozy. Zastosowano dwie odmiany estymatora wariogramu teoretycznego: powszechnie stosowany klasyczny estymator Matherona oraz estymator odwróconej kowariancji (InvCov) odporny na dane nieergodyczne. Spodziewano się, że ten drugi okaże się również odporny na silnie skośne rozkłady dane. Wśród zastosowanych technik krigingu znalazł się powszechnie stosowany kriging zwyczajny, kriging prosty użyteczny dla danych zestandaryzowanych i nieliniowa technika krigingu wskaźnikowego. Najbardziej użyteczną i mało pracochłonną procedurą geostatystyczną, nadającą się do zastosowania w przypadku takich danych, okazała się normalizacja (anamorfoza), w efekcie której uzyskuje się rozkład normalny standaryzowany. Drugim, nieoczywistym wnioskiem dla silnie skośnych rozkładów danych, jest sugestia, iż estymator InvCov ma przewagę nad estymatorem Matherona, ponieważ pozwala na bardziej realistyczną ocenę parametrów C0 (efektu samorodka) i C (wariancji progowej) modelu zmienności przestrzennej. Taki wniosek można wyciągnąć z faktu, że im wyższa wartość relatywnego efektu samorodków L = C0/(C0 + C) obliczona za pomocą estymatora InvCov, tym słabsza korelacja między wartościami obliczonymi a danymi. Wartości współczynnika L obliczone za pomocą estymatora Matherona nie posiadają tej właściwości.
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