Porosity estimation by semi-supervised learning with sparsely available labeled samples

Luiz Alberto Lima, Nico Görnitz, Luiz Eduardo Varella, Marley Vellasco, Klaus Robert Müller, Shinichi Nakajima

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


This paper addresses the porosity estimation problem from seismic impedance volumes and porosity samples located in a small group of exploratory wells. Regression methods, trained on the impedance as inputs and the porosity as output labels, generally suffer from extremely expensive (and hence sparsely available) porosity samples. To optimally make use of the valuable porosity data, a semi-supervised machine learning method was proposed, Transductive Conditional Random Field Regression (TCRFR), showing good performance (Görnitz et al., 2017). TCRFR, however, still requires more labeled data than those usually available, which creates a gap when applying the method to the porosity estimation problem in realistic situations. In this paper, we aim to fill this gap by introducing two graph-based preprocessing techniques, which adapt the original TCRFR for extremely weakly supervised scenarios. Our new method outperforms the previous automatic estimation methods on synthetic data and provides a comparable result to the manual labored, time-consuming geostatistics approach on real data, proving its potential as a practical industrial tool.

Original languageEnglish
Pages (from-to)33-48
Number of pages16
JournalComputers and Geosciences
Publication statusPublished - 2017 Sept

Bibliographical note

Funding Information:
LAL and LEV acknowledge the support of Petrobras. NG was supported by BMBF ALICE II Grant 01IB15001B. He also acknowledges the support by the German Research Foundation through the Grant DFG MU 987/6-1 and RA 1894/1-1. KRM thanks for partial funding by the National Research Foundation of Korea funded by the Ministry of Education, Science, and Technology in the BK21 Program. KRM and SN were supported by the German Ministry for Education and Research as Berlin Big Data Center BBDC, funding mark 01IS14013A. KRM is corresponding author.

Publisher Copyright:
© 2017 Elsevier Ltd


  • Conditional random fields
  • Facies classification
  • Latent variable
  • Porosity estimation
  • Ridge regression

ASJC Scopus subject areas

  • Information Systems
  • Computers in Earth Sciences


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