Characterization of the Measurement Error in Time-Lapse Seismic Data and Production Data with an EM Algorithm

The characterization of measurement error is important if one uses a Bayesian approach to condition reservoir models to dynamic data, e.g., time-lapse seismic and production data, by automatic history matching . In the literature, the measurement error for each data type is usually estimated by some smoothing technique in the whole data domain, which often over-smoothes the data (particularly around points where the underlying true data changes sharply) and results in over estimation of the measurement error. This paper presents a new procedure for measurement error estimation. The method is based on a modified EM (Expectation-Maximization ) algorithm combined with a moving polynomial fit and provides an estimate of the mean and covariance of measurement errors. The procedure avoids smoothing over discontinuities. The algorithm is applied to both synthetic and field time lapse seismic data as well as production data. The results are compared with more standard moving window smoothing algorithms. For the synthetic example, the EM-based process yields results superior to standard smoothing procedures based on some type of moving average. For the field data, EM also appears to give a reasonable result.

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