Boxplots of RMSEs of log PERMX (1st column) and PORO (2nd column) as functions of iteration step, with <i>c</i> being 1 (top) and 5 (bottom), respectively (scenario S3).

<p>Boxplots of RMSEs of log PERMX (1st column) and PORO (2nd column) as functions of iteration step, with <i>c</i> being 1 (top) and 5 (bottom), respectively (scenario S3).</p

Boxplots of RMSEs of (a) log PERMX and (b) PORO as functions of iteration step (scenario S1).

<p>Boxplots of RMSEs of (a) log PERMX and (b) PORO as functions of iteration step (scenario S1).</p

As in Fig 9, but for scenario S3 with <i>c</i> = 1.

<p>As in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198586#pone.0198586.g009" target="_blank">Fig 9</a>, but for scenario S3 with <i>c</i> = 1.</p

Boxplots of RMSEs of log PERMX (1st column) and PORO (2nd column) as functions of iteration step, with <i>c</i> being 1 (top) and 5 (bottom), respectively (scenario S2).

<p>Boxplots of RMSEs of log PERMX (1st column) and PORO (2nd column) as functions of iteration step, with <i>c</i> being 1 (top) and 5 (bottom), respectively (scenario S2).</p

The proposed 4D seismic history matching framework.

<p>The proposed 4D seismic history matching framework.</p

Boxplots of seismic data mismatch as functions of iteration step (scenario S2).

<p>Case (a) corresponds to the results with <i>c</i> = 1, for which choice the number of leading wavelet coefficients is 178332, roughly 2.5% of the original data size; Case (b) to the results with <i>c</i> = 5, for which choice the number of leading wavelet coefficients is 3293, more than 2000 times reduction in data size.</p

Boxplots of production data mismatch as a function of iteration step (scenario S1).

<p>The horizontal dashed line indicates the threshold value (4 × 1400 = 5600) for the stopping criterion <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198586#pone.0198586.e051" target="_blank">(24)</a>. For visualization, the vertical axis is in the logarithmic scale. In each box plot, the horizontal line (in red) inside the box denotes the median; the top and bottom of the box represent the 75th and 25th percentiles, respectively; the whiskers indicate the ranges beyond which the data are considered outliers, and the whiskers positions are determined using the default setting of MATLAB R2015b, while the outliers themselves are plotted individually as plus signs (in red).</p

Illustration of sparse representation of a 3D AVA far-offset trace using slices at <i>X</i> = 40, 80, 120 and at <i>Z</i> = 50, 100, 150, 200, respectively.

<p>(a) Reference AVA trace; (b) Noisy AVA trace obtained by adding Gaussian white noise (noise level = 30%) to the reference data; (c) Reconstructed AVA trace obtained by first conducting a 3D DWT on the noisy data, then applying hard thresholding (using the universal threshold value) to wavelet coefficients, and finally reconstructing the data using an inverse 3D DWT based on the modified wavelet coefficients; (d) Wavelet sub-band <i>HHL</i>₁ corresponding to the reference AVA data; (e) Wavelet sub-band <i>HHL</i>₁ corresponding to the noisy AVA data; (f) Wavelet sub-band <i>HHL</i>₁ corresponding to the reconstructed AVA data; (g) Reference noise, defined as noisy AVA data minus reference AVA data; (h) Estimated noise, defined as noisy AVA data minus reconstructed AVA data; (i) Noise difference, defined as estimated noise minus reference noise. All 3D plots are created using the package <i>Sliceomatic (version 1.1) from MATLAB Central (File ID: #764).</i></p

As in Fig 8, but for the production data profiles in scenario S3 with <i>c</i> = 1.

<p>As in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0198586#pone.0198586.g008" target="_blank">Fig 8</a>, but for the production data profiles in scenario S3 with <i>c</i> = 1.</p

Efficient big data assimilation through sparse representation: A 3D benchmark case study in petroleum engineering - Fig 12

<p>Top row: slices of the observed far-offset AVA attributes at <i>X</i> = 80, with respect to the base survey (1st column), the 1st monitor survey (2nd column) and the 2nd monitor survey (3rd column), respectively. Middle row: corresponding reconstructed slices at <i>X</i> = 80 using the leading wavelet coefficients at <i>c</i> = 1 (while all other wavelet coefficients are set to zero). Bottom row: corresponding reconstructed slices at <i>X</i> = 80 using the leading wavelet coefficients at <i>c</i> = 5 (while all other wavelet coefficients are set to zero).</p