Stochastic simulation of porosity and acoustic impedance conditioned to seismic data and well data

Abstract

this paper the approach is generalized to cover nonlinear relations between the acoustic impedance and the reflection coefficients. Integration of seismic data is particularly important since it gives good spatial coverage of the reservoir. Acoustic impedances have been included trough cokriging (Doyen 1988) and indicator models (Zhu and Journel 1993). These methods assume that acoustic impedance is available from conventional inversion methods, hence the uncertainty in the inversion process and the ambiguity of the seismic data are not properly accounted for. Bortoli, Alabert, Haas and Journel (1993) and Haas and Dubrule (1994) suggest using stochastic models at an earlier stage in the inversion process. To account for the nonlinear relationship between seismic amplitude and acoustic impedance, ad hoc sampling techniques are used. Abrahamsen, Buland, Bølviken, Hauge, Hektoen and Skorstad (1996) use a more formal approach and improve the efficiency of the sampling methods by utilizing a linearized model. In our model, the reflection coefficients are linearly related to seismic amplitude under a convolution model. Under a Gaussian based model, the stochastic model for the reflection coefficients conditioned to seismic amplitude data can be obtained analytically. Realizations from this conditional model of the reflection coefficients can then be nonlinearly transformed to give acoustic impedance realizations. Finally, porosity realizations conditioned to seismic amplitude data are obtained via the acoustic impedance realizations. Observations of porosity and acoustic impedance in wells are also included.