Examining Different Noise Scenarios for the Probabilistic Inversion of Seismic Data

Accounting for the noise is a fundamental step in probabilistic inversion approaches as well as a challenge for the practitioners. To investigate a pragmatic approach for noise description in probabilistic seismic inversion, we used a probabilistic sampling-based inversion method to invert seismic data associated with a hard carbonate reservoir in southwest Iran to porosity. We assumed eight different scenarios for the bandwidth and the magnitude of the noise. The posterior statistics assessment shows that ignoring the correlation of the noise samples in the noise covariance matrix generates unrealistic features in porosity realisations. Furthermore, underestimating the noise magnitude leads to overfitting the data and generates a biased model with too little uncertainty. These issues are resolved considerably when the noise bandwidth is considered in the inversion setup. This indicates the tangible effect of the noise bandwidth on the statistics of the posterior realisations. Our analyses showed that constructing the noise covariance matrix using extracted seismic wavelet is a practical solution. Our tests also show that the error propagated to the posterior realisations by using imperfect wavelet frequency spectrum in construction of the noise covariance matrix is insignificant.