Cyclic noise can complicate interpretation of open-hole log data, cased-hole log data, and pressure transient data, especially when its amplitude becomes large relative to the primary measurement of interest. Sources of cyclic noise include the following: winch magnetism that affects the spontaneous potential measurement; cyclic (spiral or threaded) bore holes that cause variable standoff on bulk density, neutron porosity, and pad-type resistivity measurements; drill ship and floating platform vertical movement from wave action that can affect the absolute velocity of flow meter tools, reciprocating tool movement from logging-while-tractoring that affects the absolute velocity of flow meter tools; and tidal effects on long time pressure transient tests.
Depth (time) domain filtering of log data affected by cyclic noise is not suitable in most cases because the filter length required to treat the problem causes severe reduction in the vertical resolution of the filtered log measurement. Frequency domain filtering using fast Fourier transforms has been used in the past to eliminate random noise using low pass filters and to determine the vertical resolution of logging measurements. Frequency domain filtering using fast Fourier transforms is readily amenable to treating cycle noise using notch filter(s) centered around the frequency (or frequencies) of the cycle noise. This approach has been used in the electronics industry for decades. Although these techniques are simple to implement, they seldom are used for logging data because stable filter application usually requires interactive filter design.
This paper will review the methodology of applying fast Fourier transforms, designing frequency-domain filters, and applying them. Examples applying this approach to several of the types of cyclic noise listed above will be presented. Issues associated with non-zero mean cyclic noise such as is the case for log measurements made in spiral bore holes and its impact will be addressed.
Before the early 1980s filtering of log data was accomplished by running the voltage produced from a logging instrument through a resistance-capacitance (RC) circuit before running it to a chart recorder. This type of filter was asymmetric in time (depth) and was designed primarily to remove random noise from the measurement. The advent of digital logging units led initially to application of simple digital filters in the depth domain. Most of these filters were nonrecursive filters of the form:
where cj are the filter weights, xi is the measurement at depth increment i, yi is the filtered measurement at depth increment i, and 2n+1 is the total number of sample points. These filters were generally symmetric about n=0. Most filters were equal-weight or boxcar filters such as 1–1–1 or 1–1–1–1–1. These filters also were primarily used to remove the effects of random noise on logging measurements. The values of the coefficients were often chosen to make the new digital logs have about the same appearance as the older analog logs.
Before 1980 most wells were vertical but some were already deviated. Although random noise was the most common type of noise apparent in logging measurements, cyclic noise such as that caused by a magnetized winch were known, especially on the SP. Cyclic noise produced by cyclic boreholes had not yet become a frequently encountered problem. By the 1990s highly deviated wells were the predominant type of wells drilled offshore and horizontal wells were becoming very common. Steering these wells to reach multiple objectives or to keep within a given reservoir interval led to drilling practices using bent subassemblies that often produced cyclic boreholes having a period of about 1–3 meters (3–10 feet). This created periodic variations in borehole diameter such as shown in the caliper log in Figure 1. The impact on other measurements such as bulk density and photoelectric cross section that have small volumes of investigation is quite noticeable.