A GEOSTATISTICAL FRAMEWORK FOR INCORPORATING SEISMIC TOMOGRAPHY AUXILIARY DATA INTO HYDRAULIC CONDUCTIVITY

A geostatistical approach is presented for the inclusion of seismic to mography data and sonic log data into the estimation of hydraulic cond uctivity. The procedure accounts for the errors in seismic tomography inversion and for the correlation of such errors, The proposed methodo logy consists of two steps: (1) the cross-variogram inference is carri ed out using only the data at the wellbore (both hydraulic and seismic ); (2) a co-kriging procedure takes the cross-well data into account t o interpolate between boreholes. No postulated a-priori relationship i s needed. In order to illustrate the methodology a synthetic data set is generated on the basis of evidence from published case studies and simplified physical considerations. The numerical experiments show tha t the choice of the excitation frequency is critical. A trade-off exis ts between the need for a high-resolution survey (asking for higher fr eqencies) and the need for a good correlation between hydraulic conduc tivity and seismic properties (asking for frequencies below the squirt frequency of the medium). In the simulation using seismic data with t he best excitation frequency (1 kHz in this case), the mean squared er ror of the hydraulic conductivity estimate is two-thirds lower than us ing hydraulic data alone. It is important to note also that only a par t of the interwell region is adequately sampled by the tomographic exp eriment, Such a region can be readily identified by calculating the en ergy of the quasi-null space, through singular value decomposition of the tomographic matrix, In planning this type of experiments, it is ne cessary to carefully verify case by case whether the adopted range of high frequencies does not prevent the seismic energy from propagating effectively from sources to receivers. (C) 1998 Elsevier Science B.V. All rights reserved.