An Ensemble 4D Seismic History Matching Framework with Sparse Representation Based on Wavelet Multiresolution Analysis
Authors: Luo Xiaodong , Bhakta Tuhin , Jakobsen Morten , Nædal Geir 
Published: March 2016

Abstract
In this work we propose an ensemble 4D seismic history matching framework for reservoir characterization. Compared to similar existing frameworks in reservoir engineering community, the proposed one consists of some relatively new ingredients, in terms of the type of seismic data in choice, wavelet multiresolution analysis for the chosen seismic data and related data noise estimation, and the use of recently developed iterative ensemble history matching algorithms.
Typical seismic data used for history matching, such as acoustic impedance, are inverted quantities, whereas extra uncertainties may arise during the inversion processes. In the proposed framework we avoid such intermediate inversion processes. In addition, we also adopt wavelet-based sparse representation to reduce data size. Concretely, we use intercept and gradient attributes derived from amplitude versus angle (AVA) data, apply multilevel discrete wavelet transforms (DWT) to attribute data, and estimate noise level of resulting wavelet coefficients. We then select the wavelet coefficients above a certain threshold value, and history-match these leading wavelet coefficients using an iterative ensemble smoother.
As a proof-of-concept study, we apply the proposed framework to a 2D synthetic case originated from a 3D Norne field model. The reservoir model variables to be estimated are permeability (PERMX) and porosity (PORO) at each active gridblock. A rock physics model is used to calculate seismic parameters (velocity and density) from reservoir properties (porosity, fluid saturation and pressure), then reflection coefficients are generated using a linearized AVA equation that involves velocity and density. AVA data are obtained by computing the convolution between reflection coefficients and a Ricker wavelet function. The multiresolution analysis applied to the AVA attributes helps to obtain a good estimation of noise level and substantially reduce the data size. We compare history matching performance in three scenarios: (S1) with production data only, (S2) with seismic data only, and (S3) with both production and seismic data. In either scenario S2 or S3, we also inspect two sets of experiments, one using the original seismic data (full-data experiment) and the other adopting sparse representations (sparse-data experiment). Our numerical results suggest that, in this particular case study, using production data largely improves the estimation of permeability, but has little effect on the estimation of porosity. Using seismic data only improves the estimation of porosity, but not that of permeability. In contrast, using both production and 4D seismic data improves the estimation accuracies of both porosity and permeability. Moreover, in either scenario S2 or S3, provided that a certain stopping criterion is equipped in the iterative ensemble smoother, adopting sparse representations results in better history matching performance than using the original data set.