Borehole‐guided AVO analysis of P‐P and P‐S reflections: Quantifying uncertainty on density estimates

Abstract

A B S T R A C TSeismic properties of isotropic elastic formations are characterized by the three parameters: acoustic impedance, Poisson's ratio and density. Whilst the first two are usually well estimated by analysing the amplitude variation with angle (AVA) of reflected P-P waves, density is known to be poorly resolved. However, density estimates would be useful in many situations encountered in oil and gas exploration, in particular, for minimizing risks in looking ahead while drilling. We design a borehole seismic experiment to investigate the reliability of AVA extracted density. Receivers are located downhole near the targeted reflectors and record reflected P-P and converted P-S waves. A non-linear, wide-angle-based Bayesian inversion is then used to access the a posteriori probability distributions associated with the estimation of the three isotropic elastic parameters. The analysis of these distributions suggests that the angular variation of reflected P-S amplitudes provides additional substantial information for estimating density, thus reducing the estimate uncertainty variance by more than one order of magnitude, compared to using only reflected P-waves.

Support Vector Machine (SVM) based prestack AVO inversion and its applications

“…The method of using linearized approximation is usually not accurate enough and easy to be affected by the background information, while the accurate method is more likely to be trapped in a local minimum and more computationally expensive. In addition, due to the paucity of large angle incident information and the different sensitivity for the reflection coefficients to the bulk density term, usually the estimation of density is difficult (Tarantola, 1986;Beydoun and Mendes, 1989;Crase et al, 1990;Nicolao et al, 1993;Swan, 1993;Chen et al, 2001;Cambois, 2001;Lebrun et al, 2001;Djikpesse et al, 2006;Choi et al, 2008;Virieux and Operto, 2009;Zong et al, 2013).…”

A practical sequential lexicographic approach for derivative-free black-box constrained optimization

“…This situation necessitates the use of derivative-free methods such as nonlinear downhill simplex (Nelder andMead 1965, Takahama andSakai 2005), pattern search (Swann 1972, Kolda et al 2003, Audet and Dennis 2004, or stochastic optimization algorithms (Dixit and Pindyck 1994, Spall 2003, Djikpéssé et al 2006. If inexpensive and expensive constraint functions are furthermore mixed, it is desirable for better computational performance to have the inexpensive constraints satisfied prior to computing the objective and expensive nonlinear constraint functions.…”

Guided Bayesian optimal experimental design

“…Assuming that the observation noise and the prior can be approximated by a multinormal distribution, the posterior is also multinormal [10,17,20,27]. The multinormal distribution is often used since it is the optimal choice when all that is known are the mean and covariance of the uncertainty [9].…”