Historical setting
Starting with a direct connection back to the original work on Minimum Curvature at the then Bureau of Mineral Resources, now Geoscience Australia by Ian Briggs, the gridding algorithms continue to honour the physical nature of the quantity that you wish to interpolate.
Much progress has been made on geophysical survey design, with major new insights coming in 2011, reflecting the year's of working on this issue.
Alan Reid made an early, often quoted contribution to the art, for magnetics and gravity and their gradients in the early 1980's. In this work, the power spectra are used to deduce that for a given flying height and line spacing, just what resolution might be expected, once you interpolate the profile data on to a grid. The generally held view that interpolating to a grid for a scalar field, can only support grid cells no finer than one quarter the line spacing, derives from this work.
Gradient Gridding
Recording horizontal gradient data that is transverse to the profile data, has long been recognized as being an advantage to the ability to resolve finer detail in an interpolated grid, provided the algorithm can be tuned to use this extra vector data effectively. The two most popular methods are both implemented in Intrepid:
a. Akima bi-spline with gradient constraints across the lines
b. East and North horizontal derivatives added in the Fourier domain, and then added to a TMI grid, also in the Fourier domain
Vector/Tensor Gridding
Since 2004, the challenge to properly support vector and tensor data in a natural "field" notation, as it is represented in all text books, has prompted a full object oriented addition to the underlying Intrepid database structure. Natively, all arithmetic associated with tensors and vectors, especially the magnetic and gravity field gradients, is pushed right down into the bowels of the Application Programmers Interface for all persistent data representations of the "field". As a consequence, variations on how different organisations measure the "field", in terms of Coordinate System Orientation must also be recorded, so that algorithms that are vector and tensor aware, can make the correct decisions about how to interpolate, smooth, and integrate the measurements. So, East North Up or ENU, is a natural system for mathematicians, but rarely used in geophysics, as the practise is common that gravity is represented as being positive with depth. North East Down or NED, as well as the left handed system, East North Down or END, are much more commonly used.
The invention of the "Invariant" transform for potential field tensor gradient data, leads to the Spherical Linear Interpolation algorithm, to smoothly interpolate both FTG and Falcon data. This algorithm has now been shown to support 1.5 times the resolution that older scalar interpolation can support (Brewester, SEG 2011).
This is not surprising and tests would indicate that an even finer cell size could be warranted, once the natural successor to Minimum Curvature, MITRE or Minimize Tensor Residuals has also been applied.
Given the line cost of acquiring FTG data, the benefit of a purpose built algorithm to extract optimum use of the geophysical signal, should be self evident.
Mixed Surveys
Another interpolation problem that is very practical to solve, is that of combining geophysical surveys, of differing vintage, and specifications, with the purpose of creating a representation of the field that captures coherently, and perhaps variably, the frequency content of each survey.
The Intrepid gridding tool has already been used to combine into one grid over 5000 individual off-shore surveys or cruises. This process generates a "super-grid".
Similarly, you can make the choice of gridding many surveys into a checkerboard of regular intermediate grids, then merging them, as is done by Geoscience Australia to produce and maintain the super-grids of radiometrics, magnetics and gravity for Australia. About 600 intermediate grids are maintained in readiness for each update.
Or, the "variable density" algorithm may also be used. This is a multi-grid algorithm, that starts with a coarse cell size, to honour the regional sampling, and automatically transfers that signal into finer representations of the field, where no higher frequency data is available, but opens up the finer grids to be influenced by survey data where this is available. Typically, this finds use with random or semi-random gravity surveys in a regional setting.