During logging operations and especially in oceanic environments such as those encountered during ODP legs, the logging tool string experiences more or less regular vertical (tool displacement, stick-slip, and heave) and horizontal (rotation and shock) movements. These movements are complex functions of the external conditions (hole shape, heave compensation, logging speed, cable length, etc.) and the tool itself (length, weight, and number of points of contact with the formation: centralizer and pads). In order to better assess the frequency spectrum of these movements, we inspected the normalized vertical and horizontal tool string accelerations recorded by the GPIT accelerometers in Hole 1203A (see "Downhole Measurements" in Shipboard Scientific Party, 2002). Analysis was performed using the continuous wavelet transform (WT), an alternative and generalization to the basic windowed Fourier transform for space-scale analysis.
Wavelet analysis (Morlet et al., 1982a, 1982b) provides an automatic localization of specific behaviors such as cyclic patterns or discontinuities, both in time and frequency (e.g., Daubechies, 1992; Torrence and Compo, 1998). In contrast to classical Fourier transform or windowed Fourier transform, which decomposes the original signal on the basis of an infinite periodic function depending on a unique parameter (frequency), the wavelet transform allows a "depth-scale" representation that depends on the (a) scale and (b) translation parameters. A reading of the wavelet power spectrum can be obtained by constructing a color diagram with the depth on the vertical axis, the scales on the horizontal axis and the modulus of the wavelet transform represented by patches of varying color (Torrence and Compo, 1998).
Applied to the normalized vertical and horizontal accelerations recorded at Site 1203 (Fig. F2A, F2C), this type of diagram reveals the frequency nature of ocean drilling tool string movements by deciphering the multiscale components of tool acceleration (Fig. F2B, F2D). The full normalized vertical acceleration record (191.0–916.2 meters below seafloor [mbsf]) is characterized by (1) a high-frequency component (<5 m) associated with heave and (2) localized stick-slip displacement over intervals of small (<20 m) and intermediate (~40–60 m) scale. Whereas the high-frequency component could be explained by incomplete heave compensation, the other components are directly linked to hole conditions, in particular hole shape (Fig. F2E). In contrast, the horizontal record (Fig. F2D) is very simple and is characterized by a component of distinct low frequency within the ~40–160 m range. A comparison of the wavelet representations of the horizontal acceleration with hole shape shows that the intervals where tool acceleration changes are limited by the tool string length (~40 m) and correspond to changes in hole diameter (Fig. F2E). Whereas vertical movements are often "jerky," the horizontal component of the tool is smooth and characterized by a low-frequency content with a wavelength about one-half the tool string length.
Using raw magnetic records, tool string orientation (rot) in the borehole is indirectly estimated by comparing the declination measured in the tool frame (tdec) (i.e., angle between the horizontal component of the total field and the tool housing reference line [x-axis]) and the tabulated declination of the geomagnetic field (DEC) (Fig. F1) (Barton, 1997). Whereas the discrepancy between the measured local field and the tabulated field at seafloor never exceeds ±5°, rapid changes in magnetic properties with depth can locally add anomalous field components that can in turn perturb the estimated value of the tool rotation (Fig. F1D). In that case, the horizontal component of the local total magnetic field (Fx and Fy) logs integrates (1) a low-frequency rotational component, as has been demonstrated above, and, possibly, (2) a high-frequency perturbed "declination" component associated with highly magnetized/permeable materials such as oxide-rich layers. Because of the frequency difference between these two components, a simple frequency filtering algorithm was developed to isolate the rotational component necessary to properly orient the FMS images from the indirect raw magnetic records of the GPI modules.