Similarity measure of sedimentary successions and its application in inverse stratigraphic modeling

Taizhong Duan

doi:10.1007/s12182-017-0174-1

Abstract

This paper presents a unique and formal method of quantifying the similarity or distance between sedimentary facies successions from measured sections in outcrop or drilled wells and demonstrates its first application in inverse stratigraphic modeling. A sedimentary facies succession is represented with a string of symbols, or facies codes in its natural vertical order, in which each symbol brings with it one attribute such as thickness for the facies. These strings are called attributed strings. A similarity measure is defined between the attributed strings based on a syntactic pattern-recognition technique. A dynamic programming algorithm is used to calculate the similarity. Inverse stratigraphic modeling aims to generate quantitative 3D facies models based on forward stratigraphic modeling that honors observed datasets. One of the key techniques in inverse stratigraphic modeling is how to quantify the similarity or distance between simulated and observed sedimentary facies successions at data locations in order for the forward model to condition the simulation results to the observed dataset such as measured sections or drilled wells. This quantification technique comparing sedimentary successions is demonstrated in the form of a cost function based on the defined distance in our inverse stratigraphic modeling implemented with forward modeling optimization.

Highlights

Quantitative study of sedimentary successions unavoidably involves the formal description of discrete or symbolic properties such as facies, rock texture, or structure, and until recent our ability has been still very limited on how to quantify such type properties, for instance, the difference or similarity between sedimentary facies successions from measured sections in outcrop, or drilled sections
In order to quantify the distance or similarity between sedimentary facies successions, it is essential to define what a sedimentary facies succession is and what is the distance between the sedimentary facies successions or the sedimentary facies successions distance (SFSD) formally and quantitatively
To define a distance or similarity measure between sedimentary facies successions, it is important to understand what characters are essential in distinguishing different sedimentary facies successions and what would be fundamental requirements for a distance definition mathematically

Summary

Introduction

Quantitative study of sedimentary successions unavoidably involves the formal description of discrete or symbolic properties such as facies, rock texture, or structure, and until recent our ability has been still very limited on how to quantify such type properties, for instance, the difference or similarity between sedimentary facies successions from measured sections in outcrop, or drilled sections. Geostatistical methods currently dominate, to large extent due to their data conditioning capacity, that is, the model can honor the observed dataset . Forward stratigraphic modeling is geological process based and is more relevant to petroleum reservoirs (Bosence and Waltham 1990; Granjeon and Joseph 1999; Griffiths et al 2001), and this method has been developed since the 1960s (Harbaugh and Bonham-Carter 1970), compared to the geostatistics developed since the 1960s (Matheron 1962, 1989). In current version of ISM as shown, among others, a critical technique needed to enhance the procedure is how to quantify the similarity or distance between simulated results and the observed dataset.

Formal representation of sedimentary facies successions

Definition of distance between sedimentary facies successions

Conclusion