Fix Flat-Ground TM Receiver Sampling in 2D Forward Solver

[pankajkmishra]

Fix flat-ground TM receiver sampling in the 2D forward solver

What was wrong

On flat ground, TM Ey at a station was interpolated between the cell-centre Ey values of the neighbouring cells. Those values leave out the lateral ∂Ez/∂y term. Ey is also discontinuous at a vertical resistivity contact, so interpolating it across a contact mixes the two resistivities. The computed TM field was correct; only the value read at the station was wrong. 1D models are unaffected, which is why half-space and layered checks never caught it. Near lateral contrasts the TM impedance error was large and depended on the mesh: up to 218% on a coarse mesh and 12.6% on a fine mesh for a surface conductor.

What was fixed

• TM Ey at a station is now the nodal normal current Jy, which is continuous across a contact, interpolated to the station and multiplied by the station cell's own ρ. The nodal Jy comes from the complete surface Ey reconstruction, including ∂Ez/∂y.
• The rule lives in one helper, _mt2d_tm_receiver_ey, used by both _mt2d_station_impedance and compute_fields_at_receivers_tm.
• TE responses and the step-dipole treatment next to topography are unchanged.
• The Fréchet derivatives differentiate the same station function, so they stay consistent.

Validation

• New test in test/TestForward2D.jl: the exact field at a 10/100 Ωm contact, on uniform and nonuniform cells, with stations on the contact and on nodes. The old code was off by 225% and 327%; the new code matches to 1e-10 relative.
• The existing forward, Fréchet, topography and inversion tests pass.
• Against an independent 2D finite-difference reference, TM impedance now agrees within 0.000006% across 5 models, 3 mesh refinements and 2 station layouts. TE output is unchanged.

Note

Stored TM responses near lateral contrasts that were generated with the old sampling will change.