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In a previous work \citep{luo2016sparse2d_spej}, the authors proposed anensemble-based 4D seismic history matching (SHM) framework, which has somerelatively new ingredients, in terms of the type of seismic data in choice, theway to handle big seismic data and related data noise estimation, and the useof a recently developed iterative ensemble history matching algorithm.  In seismic history matching, it is customary to use inverted seismicattributes, such as acoustic impedance, as the observed data. In doing so,extra uncertainties may arise during the inversion processes. The proposed SHMframework avoids such intermediate inversion processes by adopting amplitudeversus angle (AVA) data. In addition, SHM typically involves assimilating alarge amount of observed seismic attributes into reservoir models. To handlethe big-data problem in SHM, the proposed framework adopts the followingwavelet-based sparse representation procedure: First, a discrete wavelettransform is applied to observed seismic attributes. Then, uncertainty analysisis conducted in the wavelet domain to estimate noise in the resulting waveletcoefficients, and to calculate a corresponding threshold value. Waveletcoefficients above the threshold value, called leading wavelet coefficientshereafter, are used as the data for history matching. The retained leadingwavelet coefficients preserve the most salient features of the observed seismicattributes, whereas rendering a substantially smaller data size. Finally, aniterative ensemble smoother is adopted to update reservoir models, in such away that the leading wavelet coefficients of simulated seismic attributesbetter match those of observed seismic attributes.  (The rest of the abstract was omitted for the length restriction.)

Efficient big data assimilation through sparse representation: A 3D benchmark case study in seismic history matching