2D forward modelling

In 2D the resistivity changes along a profile and with depth, but not along the geological strike. The MT fields then split into two independent modes: TE (electric field along strike) and TM (magnetic field along strike). MTGeophysics.jl solves both with finite differences on a rectangular mesh, including topography and lakes.

In this section we compute the 2D response of a model. A forward run needs three files: a model, a data file giving the stations and frequencies, and a forward control file. It writes data.pred.

Run the example

julia --project=. helpers/benchmarks_2D.jl    # writes examples/data/2D-IV
julia --project=. examples/run_fwd2D.jl       # model.true -> data.pred

To use your own files:

julia --project=. examples/run_fwd2D.jl model.rho data.dat FwdCtrl

The forward control file

fwd.ctrl sets the mode, the strike and the air above the model. The example (examples/ctrl/2D/FwdCtrl) looks like this:

Mode                     : TETM
Strike (deg)             : auto
Air layers               : 10
Air thickness (m)        : 50000
Air growth factor        : 2
Air resistivity (ohm m)  : 1e+09
Write Frechet derivative : no
Dipole length (m)        : 100

Most of the time you only change the first two lines. Mode is TE, TM or TETM. Strike is auto or an angle in degrees; the data are rotated to it before the run (see Rotation and strike).

From Julia

using MTGeophysics

pred = ForwardSolve2D("model.rho", "data.dat", "FwdCtrl")    # writes data.pred next to data.dat
PlotData2D("data.dat"; predicted_path = pred, output_path = "DataFit.png")

The second line plots the observed and predicted apparent resistivity and phase, so you can compare them (see 2D plots).

Working in memory

If you want to change the model in a script, for example inside your own inversion, work with the mesh and resistivity directly:

mesh, ρ = Mesh2DFromInputs(ReadModel2D("model.rho"), load_data2d("data.dat"), ReadFwdCtrl2D("FwdCtrl"))
response = run_mt2d_forward(mesh, ρ; mode = :TETM)

response holds the TE and TM impedances, apparent resistivities and phases, per frequency and station.

Benchmarks

helpers/benchmarks_2D.jl writes four test cases into examples/data/. The stations run east–west near Jyväskylä, Finland, one every kilometre.

Case	Description
2D-I	a thin conductive dyke in a two-layer earth
2D-II	two resistive blocks in a two-layer earth
2D-III	conductors and resistors in a three-layer earth
2D-IV	2D-III under 100–200 m of hills and a 3 km lake, with topo.dat (the default)

julia --project=. helpers/benchmarks_2D.jl 2D-I 2D-II 2D-III 2D-IV

The data of each case are computed on a finer mesh than the one the inversion uses, so an inversion cannot fit them by simply reproducing the forward mesh.