I’m Building a Solver to Follow Electromagnetic Energy Through Earth

The ocean conducts electricity.

When Earth’s magnetic environment changes, electric currents can start moving through seawater. Those currents create their own magnetic fields. The conducting Earth responds to those fields, and that response changes the electric field driving the ocean currents.

Then the currents change again. That feedback loop’s what I’m building my electromagnetic induction solver to calculate.

Why do I need my own solver?

I’m ultimately trying to answer a pretty simple question:

When electromagnetic energy enters the Earth system from the atmosphere, where does it go?

Existing observations can tell us about magnetic fields around Earth. Ocean datasets can tell us what’s happening in the water. I still need the physics connecting those pieces if I want to calculate where electromagnetic energy’s actually deposited in the ocean.

That’s where the solver comes in.

Phase 1 started with a simpler Earth made of spherical conducting layers.

Phase 2 adds a conductive ocean wrapped around it.

I’m using the Sun-Egbert thin sheet formulation as the bridge between those two pieces. It lets the model take the electromagnetic response of the layered Earth and connect it to an ocean whose electrical conductance changes from place to place around the planet.

Then the solver finds a self consistent answer where the ocean currents, induced magnetic fields, solid Earth response, and surface electric field all agree.

Where we’re at now

We’ve validated the core Phase 2 physics.

We’ve checked the ocean Earth coupling, reconstructed the induced fields, tested the solution against an independent method, and verified that an increasingly thin conducting layer converges toward the thin ocean shell model.

One of those tests even exposed a scary numerical instability in the original reference calculation. I rebuilt that part using a stable radial method and checked it independently at high precision.

It’s converging now. ;)

Phase 2 still has its final production and convergence tests ahead, including the full SeaSigma ocean conductance map and real SWARM magnetic forcing.

What’ll this eventually answer?

Questions like:

• How much electromagnetic energy is deposited in the ocean?

• How much goes into the crust and mantle?

• Where on Earth does the strongest ocean heating occur?

• How does the answer change with different magnetic field frequencies?

• What happens during stronger magnetic disturbances?

• How strongly do the ocean and solid Earth affect each other?

• Once the depth-resolved ocean model’s added, how deep does the energy actually reach?

• How much electromagnetic energy is actually dissipated in the ocean?

• Does the ocean materially change how electromagnetic energy enters the Earth?

• Are ocean currents and telluric currents really separate systems?

• Would heating preferentially occur near tectonic or volcanic structures?

• Can an external magnetic disturbance deliver enough energy to power a proposed geophysical effect?

• Could the calculated heating ever become large enough, deep enough, and geographically aligned enough to matter for the observed abyssal warming signal?

That last question is the reason I started building this thing.

We’re getting closer….