The 3D Forward Model

Model description

For MT3DINV4, the forward model is a sphere in a half-space. This geometry was chosen because a general analytical solution exists for any source-receiver configuration — including magnetotellurics — from Vallée and Moussaoui (2023) (DOI: 10.1080/08123985.2022.2162382), providing a rigorous benchmark against which all numerical results can be compared.

Sphere resistivity
0.1 Ω·m
Host resistivity
1,000 Ω·m
Sphere centre depth
1,000 m
Sphere radius
500 m
Frequency range
10 kHz – 0.001 Hz (1,000 s)
Frequency sampling
10 points per decade
Sphere-in-half-space model schematic
Model geometry — sphere in a half-space

Receiver locations

Preferably, responses are to be computed at 2,025 locations defined by a 45 × 45 grid. All positions are in metres relative to the geographic reference point defined below.

X (45 positions, m):
−5000  −2000  −1500  −1000  −750  −500  −400  −300  −250  −200  −150  −125  −100  −90  −80  −70  −60  −50  −40  −30  −20  −10  0  10  20  30  40  50  60  70  80  90  100  125  150  200  250  300  400  500  750  1000  1500  2000  5000
Y (45 positions, m):
−5000  −2000  −1500  −1000  −750  −500  −400  −300  −250  −200  −150  −125  −100  −90  −80  −70  −60  −50  −40  −30  −20  −10  0  10  20  30  40  50  60  70  80  90  100  125  150  200  250  300  400  500  750  1000  1500  2000  5000
You are at liberty to compute your responses at any locations, as long as you include the centre of the grid directly above the sphere at (0,0), where (Ex,Ey) minimise and (Hx,Hy) maximises, and also the edges of the sphere at (-500,0) and (500,0), where Hz maximises.
Best would be sampling along an E-W profile from (-5000,0) to (5000,0).
Site distribution — full grid
Site distribution — full grid (click to enlarge)
Site distribution — central detail
Site distribution — central detail (click to enlarge)

Geographic reference point (0, 0)

The origin of the site grid corresponds to the location of the Alexander Murray Building (home of Earth Sciences), Memorial University of Newfoundland. Coordinate conversion uses WGS84.

Latitude47.5731° N
Longitude52.7358° W
UTM Zone22N
Easting369,454 m E
Northing5,270,314 m N
DatumWGS84

Submitting your results

Responses are to be submitted in EDI format. Please include the following information in your submission email:

Type of code used (FD, FE, integral equation, etc.)

Mesh dimensions

Computing time

Hardware details (CPU speed, memory, cluster specification)

Sphere source code

The Fortran and Python Windows source codes and executables for the MTSphere program computing the magnetotelluric response of a sphere in a layered earth are now available on GitHub here.

All requests or comments about the forward code should be addressed to mvallee@geodatasolutions.ca