Quantitative thickness estimation below tuning thickness is a great challenge in seismic exploration. Most studies focus on the thin-beds whose top and bottom reflection coefficients are of equal magnitude and opposit...Quantitative thickness estimation below tuning thickness is a great challenge in seismic exploration. Most studies focus on the thin-beds whose top and bottom reflection coefficients are of equal magnitude and opposite polarity. There is no systematic research on the other thin-bed types. In this article, all of the thin-beds are classified into four types： thin-beds with equal magnitude and opposite polarity, thin-beds with unequal magnitude and opposite polarity, thin-beds with equal magnitude and identical polarity, and thin-beds with unequal magnitude and identical polarity. By analytical study, an equation describing the general relationship between seismic peak frequency and thin-bed thickness was derived which shows there is a Complex implicit non-linear relationship between them and which is difficult to use in practice. In order to solve this problem, we simplify the relationship by Taylor expansion and discuss the precision of the approximation formulae with different orders for the four types of thin-beds. Compared with the traditional amplitude method for thin-bed thickness calculation, the method we present has a higher precision and isn＇t influenced by the absolute value of top or bottom reflection coefficient, so it is convenient for use in practice.展开更多
In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to so...In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.展开更多
基金supported by National Key S&T Special Projects of Marine Carbonate 2008ZX05000-004CNPC Projects 2008E-0610-10
文摘Quantitative thickness estimation below tuning thickness is a great challenge in seismic exploration. Most studies focus on the thin-beds whose top and bottom reflection coefficients are of equal magnitude and opposite polarity. There is no systematic research on the other thin-bed types. In this article, all of the thin-beds are classified into four types： thin-beds with equal magnitude and opposite polarity, thin-beds with unequal magnitude and opposite polarity, thin-beds with equal magnitude and identical polarity, and thin-beds with unequal magnitude and identical polarity. By analytical study, an equation describing the general relationship between seismic peak frequency and thin-bed thickness was derived which shows there is a Complex implicit non-linear relationship between them and which is difficult to use in practice. In order to solve this problem, we simplify the relationship by Taylor expansion and discuss the precision of the approximation formulae with different orders for the four types of thin-beds. Compared with the traditional amplitude method for thin-bed thickness calculation, the method we present has a higher precision and isn＇t influenced by the absolute value of top or bottom reflection coefficient, so it is convenient for use in practice.
基金the European Union’s NextGenerationUE-Project:Centro Nazionale HPC,Big Data e Quantum Computing,“Spoke 1”(No.CUP E63C22001000006)E.Macca was partially supported by GNCS No.CUP E53C22001930001 Research Project“Metodi numericiper problemi differenziali multiscala:schemi di alto ordine,ottimizzazione,controllo”+1 种基金E.Macca and S.Boscarino would like to thank the Italian Ministry of Instruction,University and Research(MIUR)to supportthis research with funds coming from PRIN Project 2022(2022KA3JBA,entitled“Advanced numericalmethods for time dependent parametric partial differential equations and applications”)Sebastiano Boscarinohas been supported for this work from Italian Ministerial grant PRIN 2022 PNRR“FIN4GEO:forward andinverse numerical modeling of hydrothermalsystemsin volcanic regions with application to geothermal energyexploitation”(No.P2022BNB97).E.Macca and S.Boscarino are members of the INdAM Research groupGNCS.
文摘In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.
