Imaging methods for potential fields (fatiando.gravmag.imaging)¶

Imaging methods for potential fields.

Implements some of the methods described in Fedi and Pilkington (2012). Most methods convert the observed data (gravity, magnetic, etc) into a physical property distribution (density, magnetization, etc). Most methods require gridded data to work.

• geninv: The Generalized Inverse solver in the frequency domain (Cribb, 1976)
• sandwich: Sandwich model (Pedersen, 1991). Uses depth weighting as in Pilkington (1997)
• migrate: 3D potential field migration (Zhdanov et al., 2011). Actually uses the formula of Fedi and Pilkington (2012), which are comprehensible.

References

Cribb, J. (1976), Application of the generalized linear inverse to the inversion of static potential data, Geophysics, 41(6), 1365, doi:10.1190/1.1440686

Fedi, M., and M. Pilkington (2012), Understanding imaging methods for potential field data, Geophysics, 77(1), G13, doi:10.1190/geo2011-0078.1

Pedersen, L. B. (1991), Relations between potential fields and some equivalent sources, Geophysics, 56(7), 961, doi:10.1190/1.1443129

Pilkington, M. (1997), 3-D magnetic imaging using conjugate gradients, Geophysics, 62(4), 1132, doi:10.1190/1.1444214

Zhdanov, M. S., X. Liu, G. A. Wilson, and L. Wan (2011), Potential field migration for rapid imaging of gravity gradiometry data, Geophysical Prospecting, 59(6), 1052-1071, doi:10.1111/j.1365-2478.2011.01005.x

fatiando.gravmag.imaging.geninv(x, y, z, data, shape, zmin, zmax, nlayers)[source]¶

Generalized Inverse imaging in the frequency domain (Cribb, 1976).

Calculates a physical property distribution given potential field data on a regular grid.

Note

Only works on gravity data for now.

Note

The data must be leveled, i.e., on the same height!

Note

The coordinate system adopted is x->North, y->East, and z->Down

Warning

The Generalized Inverse does not use depth weights. This means that the solution will tend to be concentrated on the surface!

Parameters:

• x, y

  : 1D-arrays

  The x and y coordinates of the grid points

• z

  : float or 1D-array

  The z coordinate of the grid points

• data

  : 1D-array

  The potential field at the grid points

• shape

  : tuple = (ny, nx)

  The shape of the grid

• zmin, zmax

  : float

  The top and bottom, respectively, of the region where the physical property distribution is calculated

• nlayers

  : int

  The number of layers used to divide the region where the physical property distribution is calculated

Returns:

• mesh

  : fatiando.mesher.PrismMesh

  The estimated physical property distribution set in a prism mesh (for easy 3D plotting)

fatiando.gravmag.imaging.migrate(x, y, z, gz, zmin, zmax, meshshape, power=0.5, scale=1)[source]¶

3D potential field migration (Zhdanov et al., 2011).

Actually uses the formula of Fedi and Pilkington (2012), which are comprehensible.

Note

Only works on gravity data for now.

Note

The data do not need to be leveled or on a regular grid.

Note

The coordinate system adopted is x->North, y->East, and z->Down

Parameters:

• x, y

  : 1D-arrays

  The x and y coordinates of the grid points

• z

  : float or 1D-array

  The z coordinate of the grid points

• gz

  : 1D-array

  The gravity anomaly data at the grid points

• zmin, zmax

  : float

  The top and bottom, respectively, of the region where the physical property distribution is calculated

• meshshape

  : tuple = (nz, ny, nx)

  Number of prisms in the output mesh in the x, y, and z directions, respectively

• power

  : float

  The power law used for the depth weighting. This controls what depth the bulk of the solution will be.

• scale

  : float

  A scale factor for the depth weights. Simply changes the scale of the physical property values.

Returns:

• mesh

  : fatiando.mesher.PrismMesh

  The estimated physical property distribution set in a prism mesh (for easy 3D plotting)

fatiando.gravmag.imaging.sandwich(x, y, z, data, shape, zmin, zmax, nlayers, power=0.5)[source]¶

Sandwich model (Pedersen, 1991).

Calculates a physical property distribution given potential field data on a regular grid. Uses depth weights.

Note

Only works on gravity data for now.

Note

The data must be leveled, i.e., on the same height!

Note

The coordinate system adopted is x->North, y->East, and z->Down

Parameters:

• x, y

  : 1D-arrays

  The x and y coordinates of the grid points

• z

  : float or 1D-array

  The z coordinate of the grid points

• data

  : 1D-array

  The potential field at the grid points

• shape

  : tuple = (ny, nx)

  The shape of the grid

• zmin, zmax

  : float

  The top and bottom, respectively, of the region where the physical property distribution is calculated

• nlayers

  : int

  The number of layers used to divide the region where the physical property distribution is calculated

• power

  : float

  The power law used for the depth weighting. This controls what depth the bulk of the solution will be.

Returns:

• mesh

  : fatiando.mesher.PrismMesh

  The estimated physical property distribution set in a prism mesh (for easy 3D plotting)