Extracting Spatial–Temporal Coherent Patterns in Geomagnetic Secular Variation Using Dynamic Mode Decomposition

Abstract

Observations of the geomagnetic field offer a wealth of information about the dynamics of Earth's deep interior. Historical records from the past 400 years (Jackson et al., 2000) are commonly used to construct models of the geomagnetic field and its first-time derivative, often called secular variation. A large part of the secular variation is attributed to large-scale fluid motion near the surface of Earth's core (e.g., Holme et al., 2015). Other contributions include magnetic diffusion and the effects of unresolved small-scale flow. Recent efforts to account for these effects (Gillet et al., 2019) rely on geodynamo simulations to establish statistical correlations between the predicted flow and the magnetic field. While this approach represents the forefront of current research, it does mean that our ability to recover dynamics from magnetic-field observations is dependent on prior assumptions about the nature of the flow. A complementary approach relies on modern data-driven methods to identify and characterize patterns of change in the observations. One particular technique, known as dynamic mode decomposition (DMD) (Schmid, 2022), is particularly well-suited to the analysis of magnetic-field observations because it allows us to establish modes (waves) in the data before attaching a physical interpretation. There is no requirement for each mode to have a common physical basis or interpretation, although we do expect a common set of background conditions. A primary motivation for this study is to explore the feasibility of using new data-driven approaches to assess the geomagnetic field.Several factors prompt our interest in data-driven approaches. One is the availability of magnetic observations from satellite missions (e.g., Orsted, CHAMP, SWARM), which substantially improve the quality and quantity of information. Satellite-based observations give better spatial coverage and allow greater discrimination between the internal and external sources of the geomagnetic field compared to ground-based measurements (Friis-Christensen et al., 2006

Dynamic Mode Decomposition of the Core Surface Flow Inverted From Geomagnetic Field Models

“…We also introduce the quality factor Q to quantify the decay of each modes (Chi‐Durán & Buffett, 2023) $$${Q}_{k}=\frac{{\omega }_{k}}{\left\vert 2{\sigma }_{k}\right\vert }.$$$ …”

“…We also introduce the quality factor Q to quantify the decay of each modes (Chi-Durán & Buffett, 2023)…”

“…It has been shown that DMD is a powerful tool to extract spatial‐temporal coherent flow structures (Schmid, 2022). Most recently, the DMD method was used to extract spatial‐temporal coherent patterns in core flows (Domingos, 2014) and in geomagnetic variations (Chi‐Durán & Buffett, 2023; Xu & Lin, 2023). Our DMD analysis of the core surface flow reveals that geomagnetic jerks in the Atlantic and Pacific equatorial region are primarily driven by distinct dynamic modes with a 7‐year period.…”