# A general approach to the assessment of uncertainty in volumes by using the multi-Gaussian model

## TL;DR

This paper introduces a general, non-simulation-based method for assessing uncertainty in volumes conditioned on sampling data, using an extended multi-Gaussian model and Kriging to derive local distributions.

## Contribution

It develops a numerical tool that explicitly relates volume uncertainty to data grades, spatial correlation, and conditioning values, applicable to any probabilistic distribution.

## Key findings

- Provides explicit formulas for local uncertainty measures.
- Enables straightforward computation of local distributions.
- Applicable to arbitrary probabilistic data distributions.

## Abstract

The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for any probabilistic distribution of the sample data. For this, we have worked with an extension of the traditional multi-Gaussian model, allowing us to obtain a formulation that makes explicit the dependence of the uncertainty in the arbitrary volume from the grades within the volume, the spatial correlation of the data and the conditioning values. A Kriging of the Gaussian values is the only requirement to obtain not only conditional local means and variances but also the complete local distributions at any support, in an easy and straightforward way.