Local multi-polar expansions in potential field modeling

B Minchev,M Mandea,I Panet,G Ramillien,M Holschneider,A Chambodut,E Schöll

doi:10.1186/bf03352965

Abstract

AbstractThe satellite era brings new challenges in the development and the implementation of potential field models. Major aspects are, therefore, the exploitation of existing space- and ground-based gravity and magnetic data for the long-term. Moreover, a continuous and near real-time global monitoring of the Earth system, allows for a consistent integration and assimilation of these data into complex models of the Earth’s gravity and magnetic fields, which have to consider the constantly increasing amount of available data. In this paper we propose how to speed up the computation of the normal equation in potential filed modeling by using local multi-polar approximations of the modeling functions. The basic idea is to take advantage of the rather smooth behavior of the internal fields at the satellite altitude and to replace the full available gravity or magnetic data by a collection of local moments. We also investigate what are the optimal values for the free parameters of our method. Results from numerical experiments with spherical harmonic models based on both scalar gravity potential and magnetic vector data are presented and discussed. The new developed method clearly shows that very large datasets can be used in potential field modeling in a fast and more economic manner.

Highlights

Our knowledge of the Earth’s system is far from being complete, and gaining deeper insight into global processes and their interactions is one of the most urgent challenges in geo-sciences
Our method uses a 3D tiling of the space and it is based on local harmonic polynomial approximations of the modeling functions inside each space segment
Introducing such local approximations is shown to be equivalent on replacing the original dataset with a set of local moments of various orders

Summary

Introduction

Our knowledge of the Earth’s system is far from being complete, and gaining deeper insight into global processes and their interactions is one of the most urgent challenges in geo-sciences. In Maus et al (2007), the authors use a least-square collocation method to combine different surveys of near-surface data and merged the obtained grid with marine and aeromagnetic line-leveled tracks For both gravity and magnetic applications, the main drawback of the gridding approach, is that the local interpolations and reduction to a sphere modify the stochastic properties of the data in a complex way and lead to a loss of information. We design our method based on two main requirements: (i) the data should be pre-processed in a compact and reasonable way; (ii) the inversion scheme should allow fast and local computations In this context, we develop local multipole approximations of the modeling functions at satellite altitude. We replaced each model function by a power series of local multipolar expansion, around a defined point inside each volume of the discretized space In this way, we obtain a piecewise decomposition of the potential field at the altitude of the measurements. The advantage of this definition is related to a better spatial distribution of the residuals, the disadvantage comes from the fact that the local coefficient matrix (see section) can not be precomputed independently from the dataset used in the model

General Development into Local Multi-polar Expansions

Conclusion and Prospects

Findings

Real case