A new parameterization for generalized moveout approximation, based on three rays

Abstract

A B S T R A C TA simple and accurate traveltime approximation is important in many applications in seismic data processing, inversion and modelling stages. Generalized moveout approximation is an explicit equation that approximates reflection traveltimes in general two-dimensional models. Definition of its five parameters can be done from properties of finite offset rays, for general models, or by explicit calculation from model properties, for specific models. Two versions of classical finite-offset parameterization for this approximation use traveltime and traveltime derivatives of two rays to define five parameters, which makes them asymmetrical. Using a third ray, we propose a balance between the number of rays and the order of traveltime derivatives. Our tests using different models also show the higher accuracy of the proposed method. For acoustic transversely isotropic media with a vertical symmetry axis, we calculate a new moveout approximation in the generalized moveout approximation functional form, which is explicitly defined by three independent parameters of zero-offset twoway time, normal moveout velocity and anellipticity parameter. Our test shows that the maximum error of the proposed transversely isotropic moveout approximation is about 1/6 to 1/8 of that of the moveout approximation that had been reported as the most accurate approximation in these media. The higher accuracy is the result of a novel parameterization that do not add any computational complexity. We show a simple example of its application on synthetic seismic data.with a limited number of independent parameters has been the subject of a large amount of research. Shifted hyperbola approximation (Malovichko 1978;de Bazelaire 1988), rational approximation (Tsvankin and Thomsen 1994; Alkhalifah and Tsvankin 1995) and generalized moveout approximation (GMA; Fomel and Stovas 2010; Stovas 2010; Stovas and Fomel 2017) are more commonly employed, because of their simplicity, applicability or higher accuracy. Other known explicit moveout approximations include methods of Alkhalifah

Comparison of objective function topology and accuracy between different travel-time approaches for converted wave events

“…This method was used to compare the accuracy of several non-hyperbolic travel-time approximations and showed to be an efficient manner to determine the best approximation to be used in a type of model, such as q-P reflection events in VTI media (e.g., Aleixo and Schleicher, 2010;Golikov and Stovas, 2012), converted wave events in near-surface structures (e.g., Bokhonok, 2011;Lu et al, 2018), converted waves in VTI media (e.g., Hao and Stovas, 2015;Tseng et al, 2016), OBN data (e.g., Wang and Pham, 2001;Wang et al, 2014), converted waves andOBN data (e.g., Zuniga, 2017;Zuniga et al, 2017 and2019c), orthorhombic media (e.g., Stovas, 2018 and2019), and anisotropic media (e.g., Farra and Pšenčík, 2018;Abedi and Stovas, 2019b). Li and Yuan (2003) approximation presented a very good result with an error of less than 0.05% for the PP event and slightly above 0.08% for the PS reflection event (Fig.…”

Comparison between L2- and L1-norm and among optimization algorithms for a nonhyperbolic multiparametric approach for converted-wave and OBN data

“…Accomplishing the comparison of the optimization algorithms is an important step to find out which algorithm is the most accurate for nonhyperbolic multiparametric approximation and which is the most efficient manner to perform the inversion; therefore, the aimed parameters can be recovered for the analysed scenario in a more reliable way. This comparison can be applied for several types of reflection events, such as for q-P reflection events in VTI media (e.g., Aleixo and Schleicher, 2010;Golikov and Stovas, 2012), converted wave events in near-surface structures (e.g., Bokhonok, 2011;Lu et al, 2018), converted waves in VTI media (e.g., Hao and Stovas, 2015;Tseng et al, 2016), OBN data (e.g., Wang and Pham, 2001;Wang et al, 2014), converted waves and OBN data (e.g., Zuniga, 2017;Zuniga et al, 2017Zuniga et al, , 2019a, orthorhombic media (e.g., Stovas, 2018, 2019), and anisotropic media (e.g., Farra and Pšenčík, 2018;Abedi and Stovas, 2019b). In this work, it was computed the residual error between the observed curve and the calculated one, for each optimization algorithm used with L2-and L1-norm.…”