Deconvolution of u channel magnetometer data: Experimental study of accuracy, resolution, and stability of different inversion methods

We explore the effects of sampling density, signal/noise ratios, and position-dependent measurement errors on deconvolution calculations for u channel magnetometer data, using a combination of experimental and numerical approaches. Experiments involve a synthetic sample set made by setting hydraulic cement in a 30-cm u channel and slicing the hardened material into similar to 2-cm lengths, and a natural lake sediment u channel sample. The cement segments can be magnetized and measured individually, and reassembled for continuous u channel measurement and deconvolution; the lake sediment channel was first measured continuously and then sliced into discrete samples for individual measurement. Each continuous data set was deconvolved using the ABIC minimization code of Oda and Shibuya (1996) and two new approaches that we have developed, using singular-value decomposition and regularized least squares. These involve somewhat different methods to stabilize the inverse calculations and different criteria for identifying the optimum solution, but we find in all of our experiments that the three methods converge to essentially identical solutions. Repeat scans in several experiments show that measurement errors are not distributed with position-independent variance; errors in setting/determining the u channel position (standard deviation similar to 0.2 mm) translate in regions of strong gradients into measurement uncertainties much larger than those due to instrument noise and drift. When we incorporate these depth-dependent measurement uncertainties into the deconvolution calculations, the resulting models show decreased stability and accuracy compared to inversions assuming depth-independent measurement errors. The cement experiments involved varying directions and uniform intensities downcore, and very good accuracy was obtained using all of the methods when the signal/noise ratio was greater than a few hundred and the sampling interval no larger than half the length scale of magnetization changes. Addition of synthetic noise or reduction of sampling density decreased the resolution and accuracy of all the methods equally. The sediment-core experiment involved uniform (axial) magnetization direction and strongly varying intensities downcore. Intensity variations are well resolved and directions are accurate to within about 5 degrees, with errors attributable to omission and/or inaccurate calibration of cross terms in the instrument response function.