Mantle electrical conductivity estimates from geomagnetic jerk observations

Abstract

The electrical conductivity of the Earth’s mantle has been a subject of much debate in the last few years. Induction studies agree mainly in the first 1000 km of the mantle, however in the lower mantle the conductivity is still very uncertain. Experimental studies of mineral physics simulating the conditions of the deep mantle have been performed and results disagree by 3 orders of magnitude depending, for example, on the considered geotherm and composition of the lower mantle. As a complement to mineralogical and induction studies, time variations of the magnetic field in the core can also contribute towards a better understanding of mantle conductivity. Geomagnetic jerks involve abrupt temporal changes in the secular variation of Earth’s magnetic field and are believed to be due to motions in the fluid core. In this thesis we use geomagnetic jerk observations to constrain information about the mantle electrical conductivity. We modelled the secular variation, around the time of a jerk, by two straight-line segments; their intersection defines the jerk occurrence time and the difference between the two slopes defines the jerk amplitude. The jerk’s morphology was obtained by data analysis of observatory annual means from which we built a spherical harmonic model. The innovative aspect of the data analysis was the evaluation of error bars in both jerk occurrence time and amplitude. We detected global jerks occurring at 1969, 1978, and 1991 that show different time arrivals at the surface of the order of 3 years. There are two possible hypotheses to explain the different occurrence jerk times at the Earth’s surface: the first is to consider these differential time delays generated by dynamical processes in the core which do not occur simultaneously; the second is to consider jerks generated instantaneously in the core and the time delays caused by a conducting mantle. In this thesis we analyze the second hypothesis so that the geomagnetic field observed at the surface will correspond to a filtered version of the original field generated in the core. We developed the forward approach to this problem using Backus’ [1983] mantle filter theory, in which a 1D mantle conductivity model acts as linear, causal and time-invariant filter. The jerk is simulated as an impulse in time at the CMB and its morphology in the core obtained by a global spherical harmonic model. The key point is that the mantle filter is different for each harmonic degree. Therefore, as the mixing of harmonics varies with location at the Earth’s surface, distinct time delays will exist in different location at the Earth’s surface and for different jerk events and components of the magnetic field. We have demonstrated, by simple examples, exactly how different emergence times can occur at the Earth’s surface. However, in order to constrain some information about the electrical conductivity of the mantle one needs to solve the inverse problem. A very interesting aspect is that the same mantle electrical conductivity would generate different delay times in different global jerks (as the 1969, 1978 and 1991 jerks). We used Veliimsky and Martinec’s [2005] approach to solve exactly the diffusion equation for 1D mantle models to calculate the Impulse Response Functions (IRFs). The 1-D mantle conductivity model of Kuvshinov & Olsen (2006) was adopted up to 700 km depth and below that four simulations were performed with electrical conductivities varying from