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Thin interbed AVA inversion based on a fast algorithm for refectivity

Yang Zhen, Lu Jun

Acta Geophysica

2020

Vol. 68, no. 4

1007--1020

Zoeppritz equations form the theoretical basis of most existing amplitude variation with incident angle (AVA) inversion methods. Assuming that only primary refections exist, that is, the multiples are fully suppressed and the transmission loss and geometric spreading are completely compensated for, Zoeppritz equations can be used to solve for the elastic parameters of strata efectively. However, for thin interbeds, conventional seismic data processing technologies cannot suppress the internal multiples efectively, nor can they compensate for the transmission loss accurately. Therefore, AVA inversion methods based on Zoeppritz equations or their approximations are not applicable to thin interbeds. In this study, we propose a prestack AVA inversion method based on a fast algorithm for refectivity. The fast refectivity method can compute the full-wave responses, including the refection, transmission, mode conversion, and internal multiples, which is benefcial to the seismic inversion of thin interbeds. A further advantage of the fast refectivity method is that the partial derivatives of the refection coefcient with respect to the elastic parameters can be expressed as analytical solutions. Based on the Gauss– Newton method, we construct the objective function and model-updating formula considering sparse constraint, where the Jacobian matrix takes the form of an analytical solution, which can signifcantly accelerate the inversion convergence. We validate our inversion method using numerical examples and feld seismic data. The inversion results demonstrate that the fast refectivity-based inversion method is more efective for thin interbed models in which the wave-propagation efects, such as interval multiples, are difcult to eliminate.

Results of laboratory measurements of index curves

Tabaka P.

Przegląd Elektrotechniczny

2008

R. 84, nr 8

147-150

Results of laboratory measurements of index curves of selected reflecting materials have been presented. Measurements have been applied for flat samples of materials utilized in luminaires design. All the reflecting samples have been shaped in square surfaces of the same dimensions (60x60 mm). The measurements have been carried out in different surfaces with the angular step depending on the nature of the reflection. The index curves have been measured for ten selected illumination directions: 20 o, 30 o, 40 o, 50 o, 60 o, 65 o, 70 o, 75 o, 80 o and 85 o.

Przedstawiono wyniki pomiarów laboratoryjnych krzywej wskaźnikowej wybranych materiałów odbłyśnikowych. Pomiarom poddano płaskie próbki wykonane z rzeczywistych materiałów wykorzystywanych w produkcji opraw oświetleniowych. Wszystkim powierzchniom odbłyśników nadano jednakowy wymiar (60x60 mm). Pomiary wykonano z krokiem kątowym zależnym od charakteru odbicia. Pomierzone krzywe wskaźnikowe wyznaczono dla dziesięciu wybranych kierunków oświetlania próbki, a mianowicie dla: 20 o, 30 o, 40 o, 50 o, 60 o, 65 o, 70 o, 75 o, 80 o i 85 o.