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