Magnetotelluric Deep Target (2D): Layered-Earth Sounding Curves

Hidden earth scenarios

My model (3 layers)

Probe

Live readouts

What to try

1. Pick "Deep conductive target": the apparent resistivity drops at long periods. 2. Tune my layers until the model curve passes through the dots; the misfit shows RMS error. 3. Press Auto-fit, then Reveal to compare with the truth. 4. Turn on noise: several different models now fit equally well, which is why real MT inversion is ambiguous. 5. Move the period marker to see the skin depth reach the target.

Independent numerical checks

The science

Method. Magnetotellurics measures the ratio of the horizontal electric to magnetic field of natural waves (solar wind, lightning). The impedance is Z = E_x/H_y; apparent resistivity and phase are ρ_a = |Z|²/(ωμ₀) and φ = arg Z. For a uniform half-space ρ_a = ρ and φ = 45°; a phase above 45° means resistivity is falling with depth.

Layered earth. Wait's recursion from the bottom up: Z_j = Z⁰_j (Z_j+1 + Z⁰_j tanh(k_jh_j)) / (Z⁰_j + Z_j+1 tanh(k_jh_j)) with k = √(iωμ₀/ρ) and Z⁰ = iωμ₀/k.

Depth of investigation. Skin depth δ = √(2ρ/ωμ₀) ≈ 503√(ρT) m; Bostick depth D = δ/√2 is a better estimate of the depth a given period senses. Long periods see deeper, but conductive layers shield what lies below.

Simplifications. One-dimensional horizontally layered earth, plane-wave source, no static shift, no anisotropy, no topography or 2D/3D structure, and a simple coordinate-descent fit rather than a full regularised inversion. Real data inversion is non-unique; the noise toggle shows why.