Page 81 - Contributed Paper Session (CPS) - Volume 1

CPS1110 Selamawit M. et al.

Bayesian inversion into soil types with Kernel-
Likelihood Models
2
1
Selamawit Moja ; Henning Omre
1 Hawassa University, Hawassa, Ethiopia
2 Norwegian University of Science and Technology, Trondheim, Norway

Abstract
Knowledge of the sub-surface characteristics is crucial in many engineering
activities. Sub-surface soil classes must for example be predicted from indirect
measurements in narrow drill holes and geological experience. In this study
the inversion is made in a Bayesian framework by defining a hidden Markov
chain. The likelihood model for the observations is assumed to be in factorial
form and they are assessed from a calibration well by kernel estimators. The
prior Markov model are defined to be either a traditional stationary Markov
chain or a trend Markov chain. The methodology is demonstrated on one case
study for offshore fundamentation of wind-mills. We conclude that a suitable
choice of kernel likelihood model is of at most importance, and that using a
trend Markov prior model improve the predictions even more.

Keywords
Sub-surface layer prediction; circular uniform kernel; Gaussian kernel

1. Introduction
In the previous study Moja et al. (2018), we constructed a prediction rule
for the sub-surface facies characteristics from well-log observations. This rule
is based on a non-stationary prior Markov chain model with a Gaussian
likelihood model on factorial form. However, the Gaussian likelihood model
does not capture the bimodal nature of our CPT data. In the current study we
define a non-parametric kernel model in order to capture the bimodal nature
of the observations which offers an alternative to traditional parametric
models (Izenman 1991). We define a non-stationary prior Markov chain model
with two different types of kernel likelihood models. These models are circular
uniform kernel likelihood and Gaussian kernel likelihood. Therefore, the
current study allow us to handle the bimodality nature of the data in the
likelihood model. We compare results from the inversion based on the
Gaussian likelihood, and the circular uniform kernel likelihood and Gaussian
kernel likelihood model. The sensitivity of the likelihood model to the choice
of kernel band width is also explored. Thereafter, an estimate of the optimal
band width based on the maximum cross-validation pseudo-likelihood
criterion is obtained, and the corresponding likelihood models and posterior
pdfs are presented.
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