The amplitude / phase treatment of full tensor gradiometry

Summary

For each observation of the potential field full tensor gradient (FTG), a rotation from world coordinates to principal components space is made. The two independent gradient magnitudes together with a succinct ‘quaternion’ representation of the rotation is termed the amplitude / phase representation of the signal.

This separation of concern isolates aspects that are invariant to rotation from the coordinate system. Benefits that flow from this approach are many and include: (1) Full tensor gridding from observed profiles is achieved using SLERP techniques (spherical linear extrapolation). Model studies show this method to correctly estimate intermediate tensors. (2) Applications of the technique to the Frequency Method also show required abilities to deliver low pass filtered data. (3) Just 3 independent power spectra are derived using this approach. This contrasts with the previous ‘best’ practice of 5 power spectra and 15 cross spectra. Obviously this previous practice mixed the rotational and signal strengths aspects.

Practical applications allow the treatment of the full tensor gradient as the signal, maintaining all the correct properties. Visualisation and interpretation aspects of this signal are illustrated.

Key Words::

• Interpolation
• Fourier
• Error
• Quaternion
• Correlations
• Rotations