# Vector Field-based Simulation of Tree-Like Non-Stationary Geostatistical Models

## TL;DR

This paper introduces a novel vector field-based simulation method for non-stationary geostatistical models, effectively capturing directional and branching structures like trees in complex geological formations.

## Contribution

It proposes a new algorithm that uses training vector fields to model non-stationary, directional, and branched structures, improving upon traditional pattern-based methods.

## Key findings

- Successfully models complex tree-like structures in geostatistics.
- Captures local directional trends more effectively than previous methods.
- Enhances non-stationary geostatistical simulation accuracy.

## Abstract

In this work, a new non-stationary multiple point geostatistical algorithm called vector field-based simulation is proposed. The motivation behind this work is the modeling of a certain structures that exhibit directional features with branching, like a tree, as can be frequently found in fan deltas or turbidity channels. From an image construction approach, the main idea of this work is that instead of using the training image as a source of patterns, it may be used to create a new object called a training vector field (TVF). This object assigns a vector to each point in the reservoir within the training image. The vector represents the direction in which the reservoir develops. The TVF is defined as an approximation of the tangent line at each point in the contour curve of the reservoir. This vector field has a great potential to better capture the non-stationary nature of the training image since the vector not only gives information about the point where it was defined but naturally captures the local trend near that point.