ALGORITHM VALIDATION USING THE GBM DIRECT ROTATION RECORD

To validate the algorithm we developed, we determine the GBM rotational component (rot) indirectly (Fig. F3H) by filtering the equivalent raw magnetic records (tdec obtained from Fx, Fy, and Fz) as it was obtained by a GPI module (Fig. F3H) and compare our results with the direct GBM rotation data (Rot) (Fig. F3G).

Various low-filtered versions of the data can be obtained by convolving various type and width of filters with the original data. The boxcar, cosine arch, and Gaussian filters are all linear operators, and their effect on the frequency content of the data (the transfer function) can be calculated (Fig. F5). The boxcar filter is a simple running average, whereas the cosine, Gaussian, and Hamming filters are weighted running averages. In the following, we tested these four types of filters for width ranging from 2 m (approximate heave) to 20 m (about one-half of the tool string length). As an example, the residual (rot) between the filtered component using a cosine filter of 4 m width (rot; Fig. F3H) and Rot (Fig. F3G) is shown in Figure F3I. This comparison shows a good match (residuals mostly <10°) between the indirect (magnetometer based) and direct (optical-gyro based) records and thus validates our filtering algorithm. Quality of the filtering algorithm can also be estimated by comparing the resulting declination with that measured by the GBM (Fig. F4C). The difference between the two records is mostly within 10° and does not impair the computation of the tool orientation. Similar results were found with other combinations of types and widths of filters.