Core-log integration: optimal geostatistical signal reconstruction from secondary information

Abstract

This paper deals with the problem of reconstructing a significantly under-sampled signal of interest (primary signal) using the few data available for that signal and an exhaustively sampled secondary signal. This is a typical situation in various geophysical settings, as for example in core-log integration. Core measurements are made in the laboratory and are very precise but, because core recovery may be fragmentary along the borehole, there are large gaps in the information these measurements provide. On the other hand, wireline logging offers a complete set of measurements along the borehole. The variable of interest (e.g. porosity) can be measured directly in the cores (i.e. primary variable) while the logging variables are proxy variables (e.g. neutron porosity, electrical resistivity, sonic velocity). The optimal combination of both types of measurements can improve the assessment of the variable of interest. Geostatistics offers a methodology for merging such different types of information. Assuming a linear relation between the primary and secondary variables, various geostatistical techniques are applicable: simple kriging with an estimated local mean, kriging with an external drift, cokriging and Bayesian integration. These methods are compared in a simulation experiment in which the signal is considered to be discrete with 1024 data values and reconstruction is assessed for the case when 10% of the data are known (i.e. 102 data values) and for the case when 50% of the signal is known (512 data values). The various methods are assessed using statistics of the real error involved in the reconstruction and the ratio between the real error and the estimated error. The methods are ranked according to the values of these statistics and their inference and computational requirements. The methodology is demonstrated on a case study in which a few tens of core samples of effective porosity are integrated with a much more exhaustive set of wireline neutron porosity.