ISSN:
1365-246X
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Geosciences
Notes:
A new form of electromagnetic tensor response function suitable for modelling the 3-D electrical conductivity structure of the spherical Earth was introduced by Zhang & Schultz (1992). The 3-D response tensor ζ can be directly estimated from coefficients of the spherical harmonic expansion of the time variations in the geomagnetic field. Physically, ζ depends both on the horizontal components of B, as well as the horizontal gradient of the vertical component. For conventional spherical harmonic analysis, the aggregate effects of sparse irregularly spaced observations, truncation of the expansion, and noise, results in potentially unbounded oscillatory field behaviour at locations in-between observation points. Such an effect destroys the reliability of estimates of the horizontal gradient in the geomagnetic field derived from resulting spherical harmonic coefficients and impacts our ability to calculate ζ with confidence. We present here a regularized inverse formulation for solving for the spherical harmonic coefficients such that the B field, and its horizontal gradient, are maximally smooth. We examine the l2 norms of the surface integrals of the Laplacian of vertical and horizontal components of B. We find the field that fits the data to a prescribed tolerance such that these norms are simultaneously minimized. The effects of noise and spacing of observation points on the stability of resulting field models and response functions are examined using a synthetic data set produced by the 3-D forward solution of Zhang & Schultz (1992). The trade-off between model misfit and smoothness is emphasized. This formulation involving both vertical and horizontal field components at the surface, termed ‘holomorphically regularized spherical harmonic analysis’ (HRSHA), is relatively insensitive to truncation level.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/j.1365-246X.1994.tb02133.x
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