Example I

For our first data example, we upscale synthetic well log data (Figure 1a) to seismic resolution (Backus, 1962), transform it from depth to time domain, and compute synthetic seismograms. A hydrocarbon-bearing reservoir is easily identified from the well logs at approximately 1900-2025 m. We simulate an injection-assisted production experiment by substituting hydrocarbons with water (Gassmann, 1951) (Figure 1b). Finally, a monitor seismic trace is computed from the updated well logs.

logs1,logs2
Figure 1. Velocity (left), density (middle), and water saturation (right) logs (a) before and (b) after fluid substitution. Velocity and density logs (blue) are upscaled to seismic resolution (red) before computing synthetic seismograms.

Timeshifts between these traces are initially estimated using the local similarity attribute (Fomel and Jin, 2009). This algorithm effectively predicts a low frequency approximation of the true timeshift with most significant deviations at the top the the reservoir interval (Figure 3). In order to estimate a higher frequency solution, traces are decomposed into discrete frequency components using the local-time-frequency transform (Liu and Fomel, 2013) to partially eliminate the problematic spurious timeshifts associated with tuning effects at the reservoir. Timeshifts are computed using amplitude-adjusted plane-wave destruction filtes at each frequency (Figure 2). The previously observed anomalous timeshift estimates are less prominent at high frequencies (Figure 3).

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Figure 2. Timeshifts estimated at each frequency. Timeshifts appear to be strongly dependent on frequency.

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Figure 3. (a) Synthetic baseline (blue), monitor (green), monitor with exact timeshift (purple), and monitor with estimated timeshift (red). (b) Timeshifts estimated using the local similarity attribute (blue) and the proposed LTFT + APWD workflow(red) compared to the exact timeshift (purple).