In the present paper, we address symmetry issues in the context of the so-called giant gaussian process (GGP) modelling approach, currently used to statistically analyse the present and past magnetic field of the Earth at times of stable polarity. We first recall the principle of GGP modelling, and for the first time derive the complete and exact constraints a GGP model should satisfy if it is to satisfy statistical spherical, axisymmetrical or equatorially symmetric properties. We note that as often correctly claimed by the authors, many simplifying assumptions used so far to ease the GGP modelling amount to make symmetry assumptions, but not always exactly so, because previous studies did not recognize that symmetry assumptions do not systematically require a lack of cross-correlations between Gauss coefficients. We further note that GGP models obtained so far for the field over the past 5 Myr clearly reveal some spherical symmetry breaking properties in both the mean and the fluctuating field (as defined by the covariance matrix of the model) and some equatorial symmetry breaking properties in the mean field. Non-zonal terms found in the mean field of some models and mismatches between variances defining the fluctuating field (in models however not defined in a consistent way) would further suggest that axial symmetry also is broken. The meaning of this is discussed. Spherical symmetry breaking trivially testifies for the influence of the rotation of the Earth on the geodynamo (a long-recognized fact). Axial symmetry breaking, if confirmed, could hardly be attributed to anything else but some influence of the core-mantle boundary (CMB) conditions on the geodynamo (also a well-known fact). By contrast, equatorial symmetry breaking (in particular the persistence of an axial mean quadrupole) may not trivially be considered as evidence of some influence of CMB conditions. To establish this, one would need to better investigate whether or not this axial quadrupole has systematically reversed its polarity with the axial dipole in the past and whether dynamo simulations run under equatorial symmetric CMB conditions display additional transitions (mirror transitions, which we describe) only allowed in such instances. This remains to be fully investigated.
Geophys. J. Int.ISI Document Delivery No.: 935OXTimes Cited: 4Cited Reference Count: 38Cited References:CARLUT J, 1998, GEOPHYS J INT, V134, P527CONSTABLE CG, 1988, J GEOPHYS RES, V93, P11569CONSTABLE CG, 1999, PHYS EARTH PLANET IN, V115, P35GARDNER WA, 1990, INTRO RANDOM PROCESSGLATZMAIER GA, 1995, PHYS EARTH PLANET IN, V91, P63GLATZMAIER GA, 1996, PHYSICA D, V97, P81GLATZMAIER GA, 1997, CONTEMP PHYS, V38, P269GLATZMAIER GA, 1999, NATURE, V401, P885GUBBINS D, 1993, NATURE, V365, P829GUBBINS D, 1993, PHYS EARTH PLANET IN, V75, P225HATAKEYAMA T, 2001, EARTH PLANETS SPACE, V53, P31HATAKEYAMA T, 2002, PHYS EARTH PLANET IN, V133, P181HONGRE L, 1998, PHYS EARTH PLANET IN, V106, P311HULOT G, 1994, PHYS EARTH PLANET IN, V82, P167HULOT G, 1996, PHYS EARTH PLANET IN, V95, P37HULOT G, 2002, NATURE, V416, P620JACKSON A, 2000, PHILOS T ROY SOC A, V358, P957JOHNSON CL, 1996, PHILOS T ROY SOC A, V354, P89JOHNSON CL, 1997, GEOPHYS J INT, V131, P643KHOKHLOV A, 2001, GEOPHYS J INT, V145, P157KONO M, 1995, J GEOMAGN GEOELECTR, V47, P115KONO M, 2000, J GEOPHYS RES-SOL EA, V105, P5817KORTE M, 2003, PHYS EARTH PLANET IN, V140, P73LANGEL RA, 1987, GEOMAGN AERON, V1, P249LANGLAIS B, 2003, PHYS EARTH PLANET IN, V135, P77LOVE JJ, 2003, GEOPHYS J INT, V152, P515MCELHINNY MW, 1996, J GEOPHYS RES-SOL EA, V101, P25007MCELHINNY MW, 1997, GEOPHYS J INT, V131, P240MCFADDEN PL, 1988, J GEOPHYS RES, V93, P11583MERRILL RT, 1988, J GEOPHYS RES, V93, P11589MERRILL RT, 1996, MAGNETIC FIELD EARTH, P527QUIDELLEUR X, 1994, GEOPHYS RES LETT, V21, P1639QUIDELLEUR X, 1996, PHYS EARTH PLANET IN, V95, P55SCHNEIDER DA, 1988, J GEOPHYS RES, V93, P11621SCHNEIDER DA, 1990, REV GEOPHYS, V28, P71TANAKA H, 1995, GEOPHYS J INT, V120, P97TAUXE L, 2004, AM GEOPHYS UN MONONG, V145, P101VILENKIN NJ, 1969, FONCTIONS SPECIALES, P626