Acceleration Settings

Use the Settings > Acceleration option to speed up the inversion process at the expense of the resolution.

Acceleration Settings dialog options

Maximum Source Data Distances		By default, all model elements, including elements in the padding zone, contribute to the response at each survey point. However, you can limit the maximum domain of influence of the model elements, and thus speed up the calculations while maintaining a negligible impact on the overall outcome.
	Radius of influence	This reduces the size of the inversion matrix that is solved for each element, thus reducing the computation time. By default, the radius of influence is set to a very large constant with the intent to account for all the model elements. See application notes on guidelines for determining the radius of influence.
Computational Error Tolerance		The resolution of the instrument as well as the level of noise in the surveyed response define the floor threshold, beyond which the data cannot be resolved practically.
	Factor	The internal computations need not be performed to an accuracy below this threshold. By increasing this factor, you effectively decrease the computation time. In addition, to focus on solving the regional features at the expense of local features, this threshold can be raised well above the noise and instrumentation threshold.

Application Notes

Radius of Influence

VOXI Inversion is based on solving a system of equations which relate the influence or contribution of each model element to a given set of responses. In theory, all model elements contribute to all responses. To ensure that, the maximum radius of influence is currently set to a constant of 10⁷ meters.

A typical airborne survey can cover areas of 10's of kilometres on a side, which leads to a very large system of equations. However, in practice, solving the full system of equations is unnecessary and inefficient, and can be reduced in size without compromising the precision of the outcome.

By taking into account that the influence of the magnetic response of a contributing voxel element decreased as Distance-3 and that of gravity as Distance-2, the set of equations can be reduced and the solution attained with a small, if not negligible, impact on the outcome.

Furthermore, depending on the exploration economic constraints, the depth of investigation can also be limited. In the mineral exploration field, the interest is primarily focused on the upper 5 kilometres. In Oil and Gas exploration, the study area is generally larger by an order of magnitude and the depth of investigation may cover as much as the upper 12 kilometres of the crust.

Taking into account the extents of the area of interest, the depth of investigation, and assuming a geologically reasonable voxel element size, the radius of influence can be set to as little as 10 km in mineral exploration, and 100km in oil and gas exploration. Imposing a limit on the domain of influence acts as an effective spatial wavelength high pass filter on the model. In addition, the number of cells in the vertical direction can be reduced to further accelerate the inversion.

The table below provides benchmark values for a study area of 10 kilometres by 20 kilometres, with the model reaching a depth of 3.5 kilometres. The voxel model consists of approximately 2.5 million elements. The loss difference in the precision of the three models is marginal.

Domain of influence	Depth of investigation	Matrix Size [GB]	Matrix Generation Time [s]	System Solution Time [s]	Total Elapsed Time [s]
10 Km	3.5 Km	1.19	788	1782	2671
5 Km	3.5 Km	1.09	259	1642	2009
1 Km	1 Km	0.842	66	770	904

Table 1: Statistics for Full Domain Inversion

Computational Error Tolerance

The geophysical inversion practitioner knows that field data are always noisy, and the inversion problem is ill-posed. As a result, it makes little sense to solve the geophysical inversion problem with vastly more accuracy than is supported by the data, the geophysical method, or required by the project. VOXI provides access to a single parameter which control the solution accuracy. Using an appropriate computational error tolerance can significantly speed up the inversion.

In addition, if the intent is to focus on solving the regional rather than the local features, this threshold can be further increased and as a result, decrease the number of iterations and speed up the computation.

The table below provides a benchmark on a study area of 10 kilometres by 20 kilometres, with the model reaching a depth of 3.5 kilometres. The voxel model consists of approximately 2.5 million elements.

Computational error tolerance	Matrix Size [GB]	Matrix Generation Time [sec]	System Solution Time [sec]	Total Elapsed Time [sec]
0.002	1.19	788	1782	2671
0.02	0.227	778	1215	2097

Table 2: Statistics for Computational Error Tolerance