Application of artificial intelligence for Euler solutions clustering

Abstract

Results of Euler deconvolution strongly depend on the selection of viable solutions. Synthetic calculations using multiple causative sources show that Euler solutions cluster in the vicinity of causative bodies even when they do not group densely about the perimeter of the bodies. We have developed a clustering technique to serve as a tool for selecting appropriate solutions.The clustering technique uses a methodology based on artificial intelligence, and it was originally designed to classify large data sets. It is based on a geometrical approach to study object concentration in a finite metric space of any dimension. The method uses a formal definition of cluster and includes free parameters that search for clusters of given properties.Tests on synthetic and real data showed that the clustering technique successfully outlines causative bodies more accurately than other methods used to discriminate Euler solutions. In complex field cases, such as the magnetic field in the Gulf of Saint Malo region (Brittany, France), the method provides dense clusters, which more clearly outline possible causative sources. In particular, it allows one to trace offshore the main inland tectonic structures and to study their interrelationships in the Gulf of Saint Malo.The clusters provide solutions associated with particular bodies, or parts of bodies, allowing the analysis of different clusters of Euler solutions separately. This may allow computation of average parameters for individual causative bodies. Those measurements of the anomalous field that yield clusters also form dense clusters themselves. Application of this clustering technique thus outlines areas where the influence of different causative sources is more prominent. This allows one to focus on these areas for more detailed study, using different window sizes, structural indices, etc.

Tensor deconvolution: A method to locate equivalent sources from full tensor gravity data

“…Thus, these methods should best be combined to better identify the sources and estimate their depths. Clustering of solutions, as proposed by Mikhailov et al ͑2003͒, is indeed a powerful tool, especially useful for noisy data or if signals from various sources interfere.…”

On Inversion of Gradient Magnetic Data for Detection of Multiple Buried Metallic Objectives

“…Geometrically, Euler solutions form broad clouds rather than dense clusters, making it difficult to outline causative sources. We utilize a post processing technique, the Rodin algorithm (V. Mikehailov et al, 2003), to eliminate some unrealistic solutions. Based on the spatial separation of the buried objectives, we then apply a technique to split the solutions thus obtained into groups, each of which forms a dense cluster which clearly outline possible causative sources.…”

The Study of Time Series Using the DMA Methods and Geophysical Applications

“…Due to the randomness of the time series f, its local anomalous nodes LA can comprise a subset in T which demands extra work (preliminary topological filtering ) and further clustering (Mikhailov et al 2003;Agayan et al 2004;Soloviev et al 2005)). The point is that the connected side-by-side and sufficiently large excesses of the measure µɛ f over the anomaly level 0.75 are of the main interest as it is them what should be considered expressions (traces) of global anomalies of f from the perspective of ɛ.…”