One Step at a Time: The Origins of Sequential Simulation and Beyond

Abstract In the mid-1980s, still in his young 40s, André Journel was already recognized as one of giants geostatistics. Many contributions from new research program at Stanford University had centered around indicator methods that he developed: kriging and multiple kriging. But when second crop graduate students arrived Stanford, lacked an approach to conditional simulation not tainted by what called ‘Gaussian disease’; early simulations went through tortuous path converting all indicators Gaussian variables, running a turning bands simulation, truncating resulting multi-Gaussian realizations. When conceived sequential (SIS), even likely did recognize generality tackled task step time. The enthusiasm for SIS its ability, multiple-indicator form, cure disease build realizations which spatial continuity deteriorate extreme values. Much Stanford’s work 1980s focused on petroleum geostatistics, where values (the high-permeability fracture zones low-permeability shale barriers) have much stronger anisotropy, longer ranges correlation maximum direction, than mid-range With necessarily imparting weaker extremes, important breakthrough. soon recognized, first analogy with multi-variate unconditional achieved using lower triangular matrix LU decomposition covariance multiplier random normal deviates. Modifying so it became gave rise (SGS), algorithm shared common SIS. nagging implementation details like search neighborhood being both methods, improvements either or SGS often other. Almost half contributors this Special Issue classes 1984–1988, several are pioneers SGS. Others who studied later explored developed multipoint statistics procedures, based same concept underlies simulation. Among many significant intellectual accomplishments, cornerstones Journel’s legacy built