Jef Caers, Xiaojin Tan and Pejman Tahmasebi Stanford University, USA

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Presentation transcript:

Jef Caers, Xiaojin Tan and Pejman Tahmasebi Stanford University, USA Comparing multiple-point geostatistical algorithms using an analysis of distance Jef Caers, Xiaojin Tan and Pejman Tahmasebi Stanford University, USA

A simple question Which one is better ? Two algorithm aim to reproduce training image statistics Training image dispat ccsim Which one is better ?

Two fundamental variabilities Target statistics within realization variability “pattern reproduction” between realization variability “space of uncertainty” realization generated by a geostatistical algorithm

Comparing two geostatistical simulation algorithms Target statistics Algo 2 Algo 3 Algo 4 Definition of best: an algorithm that maximizes reproduction of statistics (within) while at the same time maximizes spatial uncertainty (between)

How to quantify this? Statistical science Computer Science x1 x2 x3 Form Matrix of realizations X Statistical science ANOVA Computer Science ANODI C: covariance D: Dot-product E: euclidean distance

Creating a distance multi-resolution view (34 x 34) Multi-resolution g=2 (51 x 51) Multi-resolution g=1 (101 x 101) Pyramid of one single realization

Creating a distance multiple-point histogram (MPH) Realization MPH But works only for binary, small 2D cases and small templates

Creating a distance cluster-based histogram of patterns (CHP) Pattern database Class-prototype Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Cluster patterns into classes based on a measure of similarity (distance)

Illustration case

Creating a distance cluster-based histogram of patterns (CHP)

Creating a distance Jensen-Shannon divergence Basic equation In this context multi-resolution algorithm

MDS visualizing distances

Multi-scale visualization

Ranking with ANODI Definition of best: an algorithm that maximizes reproduction of statistics (within) while at the same time maximizes spatial uncertainty (between) Use ratios

Back to illustration case

Ranking based on MPH algo m algo m algo m dispat ccsim sisim 1 1.15 0.38 * 0.33 dispat ccsim sisim 1 1.63 0.24 * 0.15 dispat ccsim sisim 1 0.70 1.58 * 2.20 algo k MPH approach: 1 : 0.70 : 0.46 (ccsim : dispat : sisim)

Ranking based on CHP dispat ccsim sisim 1 0.88 0.86 * 0.98 dispat ccsim sisim 1 1.31 0.43 * 0.33 dispat ccsim sisim 1 0.67 2.00 * 2.90 CHP approach: 1 : 0.67 : 0.35 (ccsim : dispat : sisim) MPH approach: 1 : 0.70 : 0.46 (ccsim : dispat : sisim)

Trade-off pattern reproduction for uncertainty in MPS

Trade-off Space of uncertainty (“between”) 1.65 : 1 : 1 (ns=10 : ns=50 : ns=200) Pattern reproduction (“within”) 2:75 : 1 : 1 (ns=10 : ns=50 : ns=200) Total (“between/within”): 0.60 : 1 : 1 (ns=10 : ns=50 : ns=200)

CHP works for 3D MPH does not Total (“between/within”): 0.60 : 1 (dispat : ccsim)

Conclusions Need: a repeatable quantitative comparison going beyond visual subjectivity Two fundamental variabilities Pattern reproduction (often the main focus) Space of uncertainty (often considered a by-product) What this presentation does not discuss which statistics to reproduce conditioning to data