Deconvolution of long‐core paleomagnetic data of Ocean Drilling Program by Akaike's Bayesian Information Criterion minimization

Abstract

Deconvolution of long‐core paleomagnetic data of the Ocean Drilling Program (ODP) was developed based on Bayesian statistics. Samples of deep‐sea sediments obtained by drilling with an advanced piston corer are subjected to pass‐through measurements by a cryogenic magnetometer aboard the ODP's research vessel (Joides Resolution) which provide continuous paleomagnetic records. Deconvolution of the magnetometer output was developed in order to obtain more detailed variations of the magnetization than permitted by the spatial resolution of the pickup coil (approximately 11 cm). The magnetization vector was modeled as a smoothly changing sequence parametrized by L2 norm of second‐order difference and then deconvolved using a matrix calculation as a smoothness constrained least squares method. The optimum smoothness was obtained by minimizing Akaike's Bayesian Information Criterion which is a measure of the logarithm of the likelihood. This deconvolution scheme was applied to pass‐through data artificially produced by convolving synthetic reversal record and adding a Gaussian noise. The amplitude of the noise was estimated and the variations shorter than the spatial resolution of the sensor were obtained. The deconvolution also was applied to the real pass‐through data from Holes 769A and 769B measured at intervals of 5 mm. The deconvolution revealed variations of the magnetizations with a maximum spatial resolution of about 2 cm. The magnetizations after deconvolution were in good agreement with magnetization values measured separately on cube samples taken at intervals of 5 or 10 cm.

Explanatory Notes

“…These are narrower than ~11 cm measured from the old magnetometer (Oda and Shibuya, 1996). As the radial distance from the center of the pick-up coil increases, the half widths of the response curves become narrower and the peak value increases.…”

“…Deconvolution of paleomagnetic data using the sensor-response curves was conducted on pass-through data at Site 1071 using the method of Oda and Shibuya (1996). The spatial resolution of the paleomagnetic signal was enhanced from the original half width of the magnetometer (~7 cm) to ~3 cm after deconvolution.…”

UDECON: deconvolution optimization software for restoring high-resolution records from pass-through paleomagnetic measurements

“…Flux jumps are sudden changes in magnetic moment along particular measurement axis, after which the magnetic moment levels do not go back to that prior to the flux jump. Flux jumps in measurement could dramatically distort paleomagnetic direction and intensity estimation after drift correction (e.g., Oda and Shibuya 1996). In general, two types of flux jumps have been known to occur in SQUID magnetometers.…”

“…Type 2 flux jumps may originate from a trapped fluxon hopping between two positions within the SQUID or flux transformer's structure (see Clark and Braginski 2004). A type 2 flux jump was reported by Oda and Shibuya (1996) and referred to as "unknown jumps".…”

“…Deconvolution is necessary to overcome the convolution effect and obtain more accurate and significantly higher-resolution data comparable to that measured using back-to-back discrete samples (see Guyodo et al 2002). Various algorithms have been presented for deconvolution of pass-through paleomagnetic data acquired on either whole-core or u-channel SRMs (e.g., Dodson et al 1974;Constable and Parker 1991;Oda and Shibuya 1994;1996;Jackson et al 2010). Oda and Xuan (2014) recently developed an improved deconvolution algorithm based on the Akaike's Bayesian Information Criterion (ABIC) minimization method introduced by Shibuya (1994, 1996).…”