### Abstract

The geomagnetic ﬁeld is generated in the Earth’s outer core by ﬂuid motions in a process known as the geodynamo. During the past 18 years satellite magnetic measurements have provided new insights into the spatial structure of the ﬁeld and its time variations. Among these observations are the decay of the dipole ﬁeld, the signature of a high latitude jet, pulse-like features in the second time derivative of the ﬁeld at the core-mantle boundary (CMB) and rapid ﬁeld changes called geomagnetic jerks. Theories into the origin and dynamics of these phenomena may begin to converge as numerical dynamo simulations reach more Earth like conditions and magnetic ﬁeld measurements are made continuously spanning longer time intervals. In order to gain further geophysical insights into the geo-dynamo processes, there is a need for robust estimation of the core ﬁeld and its evolution and to quantify the uncertainty and resolution of these estimates. In this thesis two local techniques for estimating the core-generated magnetic ﬁeld are described and implemented using satellite data from the Swarm and CHAMP satellite missions.

The ﬁrst technique is the Virtual Observatory (VO) method, in which time series of the ﬁeld and ﬁeld gradients at pre-speciﬁed locations at satellite altitude, are calculated via a local procedure, such that short-period variations of the core signal can be investigated. These VO time series resembles the time series from ground observatories which have higher temporal resolution. We show that using a reﬁned VO setup together with an im-proved data selection and handling scheme, the VO time series exhibit strong correlation in all three ﬁeld components with time series of nearby ground observatories. Using the VO time series, signs of ﬁeld changes over South America around 2016 and in the Paciﬁc region in 2017 may be the ﬁrst indications of a new geomagnetic jerk taking place. We ﬁnd that ﬁeld models built using both vector and gradient VO data show evidence for secular acceleration activity in the Paciﬁc region.

In order to construct reliable estimates of the ﬁeld tracking its evolution at the CMB, appraisal is crucial. Appraisal consists of spatial resolution and variance estimation. The second technique used builds on a modiﬁed Backus-Gilbert inversion approach called Sub-tractive Optimally Localized Averages (SOLA). Using the SOLA method, localized av-erages of the ﬁeld and its ﬁrst time derivative are estimated at the CMB, determined via spatial averaging kernels, accounting for both internal and external ﬁeld sources. We incorporate information from data error covariance matrices which include along-track serial error correlation. We show an example of a global collection of SOLA estimates for the radial main ﬁeld (MF), with widths of the averaging kernel varying between ∼18° and ∼54° depending on latitude, with a standard deviation of ∼10µT. We present global collections of SOLA estimates for the radial secular variation (SV) at the CMB, based on 2yr data windows, with averaging kernel widths of ∼42°, ∼33° and ∼30° at the equator, with corresponding standard deviations of ∼0.25µT/yr, ∼2.5µT/yr and ∼5µT/yr. We ﬁnd that the morphology of the MF and SV maps agree well with results from spherical harmonic (SH) based ﬁeld models, however our method involves only averaging in time and space and not spectral truncation or temporal regularization. We compute the local accumulated secular acceleration (SA) by subtracting the SV SOLA estimates, based on 2yr data windows, from epochs 2 years apart, which have averaging kernel widths of ∼42° at the equator and standard deviation of ∼0.2T/yr

The ﬁrst technique is the Virtual Observatory (VO) method, in which time series of the ﬁeld and ﬁeld gradients at pre-speciﬁed locations at satellite altitude, are calculated via a local procedure, such that short-period variations of the core signal can be investigated. These VO time series resembles the time series from ground observatories which have higher temporal resolution. We show that using a reﬁned VO setup together with an im-proved data selection and handling scheme, the VO time series exhibit strong correlation in all three ﬁeld components with time series of nearby ground observatories. Using the VO time series, signs of ﬁeld changes over South America around 2016 and in the Paciﬁc region in 2017 may be the ﬁrst indications of a new geomagnetic jerk taking place. We ﬁnd that ﬁeld models built using both vector and gradient VO data show evidence for secular acceleration activity in the Paciﬁc region.

In order to construct reliable estimates of the ﬁeld tracking its evolution at the CMB, appraisal is crucial. Appraisal consists of spatial resolution and variance estimation. The second technique used builds on a modiﬁed Backus-Gilbert inversion approach called Sub-tractive Optimally Localized Averages (SOLA). Using the SOLA method, localized av-erages of the ﬁeld and its ﬁrst time derivative are estimated at the CMB, determined via spatial averaging kernels, accounting for both internal and external ﬁeld sources. We incorporate information from data error covariance matrices which include along-track serial error correlation. We show an example of a global collection of SOLA estimates for the radial main ﬁeld (MF), with widths of the averaging kernel varying between ∼18° and ∼54° depending on latitude, with a standard deviation of ∼10µT. We present global collections of SOLA estimates for the radial secular variation (SV) at the CMB, based on 2yr data windows, with averaging kernel widths of ∼42°, ∼33° and ∼30° at the equator, with corresponding standard deviations of ∼0.25µT/yr, ∼2.5µT/yr and ∼5µT/yr. We ﬁnd that the morphology of the MF and SV maps agree well with results from spherical harmonic (SH) based ﬁeld models, however our method involves only averaging in time and space and not spectral truncation or temporal regularization. We compute the local accumulated secular acceleration (SA) by subtracting the SV SOLA estimates, based on 2yr data windows, from epochs 2 years apart, which have averaging kernel widths of ∼42° at the equator and standard deviation of ∼0.2T/yr

^{2}. Comparison of the SOLA based SA and SH ﬁeld models show good agreement, however we have direct control over the chosen time window length and spatial averaging kernel. Investigating the time evolution of the SA along the geographical equator and pushing towards higher temporal resolution, we compute 1 year SV diﬀerences, based on 1yr data windows. We are able to track coherent structures of the SA and their evolution in time-longitude plots. In particular, we ﬁnd a distinctive SA ”cross-over” event having adjacent and strong oppositely signed SA features, at longitude 25°W in mid 2007. The SOLA technique proves to be well suited for high resolution local studies of the rapidly evolving SA, while at the same time providing the necessary means of appraisal.Original language | English |
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Place of Publication | Kgs. Lyngby |
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Publisher | Technical University of Denmark |

Number of pages | 257 |

Publication status | Published - 2018 |

## Cite this

Hammer, M. D. (2018).

*Local Estimation of the Earth's Core Magnetic Field*. Technical University of Denmark.