Forward Modelling

A data type for a layered-earth conductivity model.

Members:

• σ::Vector{<:Real}: conductivity of each layer
• d::Vector{<:Real}: thickness (not depth) of each layer. Length must be one less than length of σ, as the bottom layer is an infinite half-space.

Data type for forward modelling 1D magnetic resonance sounding (MRS) experiments.

Members: -kernel::Matrix{<:Number}: pre-computed linear kernel matrix for the forward problem. May be complex. -qgrid::AbstractVector{<:Real}: pulse moments used in the experiment. -zgrid::AbstractVector{<:Real}: depth grid for forward modelling (as cell boundaries). -dz::AbstractVector{<:Real}: cell thickness of the depth grid.

MRSForward(R::Real, zgrid::AbstractVector{<:Real},
qgrid::AbstractVector{<:Real}, ϕ::Real, Be::Real,
condLEM::ConductivityModel; nrvals = 200, temp=300.0,
qwe=true)

Returns an MRSForward forward modelling object, with the kernel computed for a circular loop.

Parameters:

• R: loop radius in metres
• zgrid: depth cell boundaries, in metres below surface.
• qgrid: pulse moments used for the experiment, in Ampere-seconds.
• ϕ: magnetic field inclination in radians.
• Be: Earth field magnitude in Tesla.
• condLEM: layered-earth conductivity model, as a ConductivityModel object.

Optional parameters:

• nrvals: number of radial points to use to evaluate the horizontal integration of the kernel.
• temp: temperature in Kelvin, affects the magnitude of equilibrium magnetisation.
• qwe: whether to use quadrature with extrapolation (QWE) to evaluate Hankel transforms for the kernel.

This is slower, but more accurate at shallower depths, than the alternative 801-point digital filter.

MRSForward_square(L::Real, zgrid::AbstractVector{<:Real},
qgrid::AbstractVector{<:Real}, ϕ::Real, θ::Real, Be::Real,
condLEM::ConductivityModel; nxpoints = 128, temp=300.0)

Returns an MRSForward forward modelling object, with the kernel computed for a square loop.

Parameters:

• L: loop radius in metres
• zgrid: depth cell boundaries, in metres below surface.
• qgrid: pulse moments used for the experiment, in Ampere-seconds.
• ϕ: magnetic field inclination in radians.
• θ: horizontal angle between loop orientation and magnetic north, in radians.
• Be: Earth field magnitude in Tesla.
• condLEM: layered-earth conductivity model, as a ConductivityModel object.

Optional parameters:

• nxpoints: number of points to use in each dimension for the horizontal integration of the kernel.
• temp: temperature in Kelvin, affects the magnitude of equilibrium magnetisation.

forward(F::MRSForward, m::Vector{<:Real})

Computes the complex response amplitude of a water content model for a given FID experiment setup, described by an MRSForward object. Returns response as a complex vector, in units of volts, one element per pulse moment.

Parameters:

• F: an MRSForward object containing the kernel for modelling
• m: a vector containing water saturation at each depth in F.zgrid.