Posted by Tomas Snyder

Breakthroughs in distributed optical fiber sensing have enabled continuous recording of seismic data (strain/strain rate) and temperature, resulting in unparalleled spatial resolution and coverage at a more affordable cost in remote areas. However, distributed electromagnetic sensing systems are still in the prototype stage. This project explores a novel multiphysics optic fiber that records seismic and magnetic wavefields simultaneously. The magnetostrictive effect formulates the basic measurement principle of the proposed distributed magnetic sensing. Two-dimensional (2D) and three-dimensional (3D) modeling of the magnetic fiber based on micromagnetic dynamics and magnetostriction are explored in this project to ensure data can be reliably modeled, even in the face of nonlinearity.

Magnetostriction is the strain induced in a ferromagnetic material (e.g., iron, nickel, cobalt)

by an effective magnetic field **H**_{eff}. Domains within ferromagnetic materials have magnetization magnitudes at the saturation magnetization value M_{s}. When a ferromagnetic material is in an ideal demagnetized state (i.e., all magnetic domain orientations are of the same volume), the material exhibits a net zero external magnetic field. When * H* is applied to the material, the domain magnetic moments

*experience a torque per volume which aligns the overall magnetic moment of the material in the direction of*

**M***if ||*

**H****H**|| is large enough to saturate the material. The Landau-Lifshitz-Gilbert (LLG) equation

describes the dynamics of the total magnetic moment of a ferromagnetic material, accounting for damping of the domain motion. In the LLG equation, the constant γ =ge/2mc, where e and m are the charge and mass of the electron; c is the speed of light; and g is the spectroscopic splitting factor (g = 2 for electron spin). The damping term α = λ/γM, where λ is an adjustable damping parameter.

The 2D and 3D models iteratively solve the LLG equation using the Dormand-Prince method (a fifth order Runge-Kutte numerical method). The 2D method provides an understanding of the strain response from a single domain to an external magnetic field, which the 3D model expands upon through the addition of multiple domains and induced magnetic fields within the material. The 3D model outputs signals similar to what is seen in the lab, giving us the ability to predict the signal given a known magnetic field strength. The figure below shows an example of the 3D model mesh with one domain element highlighted in orange along with an example output signal from that generated mesh.

*Left: Mesh of 3D cells defined in Ubermag. Right: 3D model results for a 100Hz**source with an amplitude of 13 kA/m.*

The predictive capability of the model is invaluable when considering possible applications of the magnetic sensing fiber. Understanding whether the fiber can measure the magnetic field from a source, and the appearance of the magnetic fiber, signal an application will give us the capability to determine appropriate applications and distinguish the magnetic signal from seismic ones. In addition, future modeling of the signal temperature dependence will provide valuable insight into the application of the fiber in environments with large variations in temperature (e.g., geothermal applications).

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