Constraining Stochastic Images to Seismic Data

Abstract

Selection of conditional simulations of acoustic variables is done by matching the simulated values with a series of actual seismic vertical sections. This is done by forward convolution of the simulated acoustic models. The proposed algorithm allows an iterative adjustment of the convolved simulated vertical section to the original seismic data: first impedances along a vertical trace are simulated, then this impedance trace is convolved into a synthetic trace at the seismic scale. An acceptance/rejection criterion based on a correlation function is applied to compare the synthetic with the actual trace. If accepted, the algorithm proceeds and builds the synthetic image by simulating an impedance trace at the next node, otherwise another simulation of the same trace is drawn. Particular attention is given to calibration of the synthetic seismograms at well locations and calibration of acoustic variables to porosity at the log scale. Once the adjustment of the vertical section is obtained, the stochastic impedance image -i.e. the adjusted section before convolution- is easily converted into a porosity image. This image can directly be used for interpretation or flow simulator processing. The method is developped and tested on a real field, a shaly/sand formation covered by an 3D seismic survey.