Leveling aerogeophysical data using a moving differential median filter

Transcription

1 GEOPHYSICS, VOL. 71, NO. 1 (JANUARY-FEBRUARY 2006); P. L5 L11, 14 FIGS / Leveling aerogeophysical data using a moving differential median filter Eirik Mauring 1 and Ola Kihle 1 ABSTRACT We describe a new technique that can be used to level data collected along regular and irregular line patterns with or without tie-line control. The technique incorporates a moving differential median filter to minimize line-level errors, to level survey-line data, and to microlevel data with no tie-line control. This overcomes the problem of standard leveling methods that lose their effectiveness with irregular flight patterns. To validate the method, we use it to level very-lowfrequency (VLF) electromagnetic (EM) data from a helicopter survey where flight lines are parallel. Leveling is also performed on a set of vintage aeromagnetic data from the North Sea, gathered from nonparallel flight lines. Results show that the differential median filter leveling technique is superior to the standard leveling method because it results in fewer line errors and less distortion of high-wavenumber anomalies when processing irregular survey lines, making the method suitable for a wide variety of data sets. INTRODUCTION Aerogeophysical data often suffer from line-level errors (corrugations), which are data inconsistencies between adjacent flight lines arising from a variety of unavoidable acquisition-related circumstances. This problem is partly solved by flying in a grid pattern with lines and tie lines and then resolving the inconsistencies during data processing. However, data collected during difficult conditions [e.g., timevarying fluctuations in the earth s magnetic field, rough terrain, unstable very-low-frequency (VLF) transmitters] may still show corrugations after various corrections and tie-line leveling. The last step in the leveling procedure may be to apply a microleveling routine to remove the remaining line-level errors. Such routines are based on the assumption that line errors appear as elongated artifacts along flight lines (Urquhart, 1989; Minty, 1991; Luyendyk, 1997; Ferraccioli et al., 1998). Their crossline wavelength is often twice the flight-line spacing (Minty, 1991). Most microleveling or decorrugation routines involve filtering a grid of data that is orthogonal to the line direction to detect remaining errors along lines (Luyendyk, 1997). A common approach used by major software vendors combines a 2D high-pass filter and a directional filter to microlevel data (Ferraccioli et al., 1998). A similar microleveling technique for gridded data is described by Urquhart (1989). The disadvantages of this approach are that resolution is lost during the preliminary gridding step, and the approach is not designed for survey data with irregular lines and line spacings. This paper introduces a microleveling/leveling technique that can be applied to data collected along both irregular and regular line patterns with or without tie-line control. The technique is a modification of a technique suggested by Liukkonen (1996), who uses it to process radiometric data. Both directional and differential median filtering can be used for leveling and microleveling aerogeophysical data. Microleveling is normally the term used for small line-error corrections applied after tie-line leveling (Luyendyk, 1997). None of the examples in this paper have tie-line control, so leveling is the most appropriate term to use for the differential median filter leveling technique. LEVELING TECHNIQUES This section compares a standard leveling technique with the differential median filter leveling technique. Our proposed technique is shown to be superior to standard leveling. Standard leveling technique (directional filtering) The directional filtering technique uses sampled values from an error grid that (ideally) shows line errors attributable to insufficient leveling. A grid data set is generated that best describes line-level errors in survey data. Traditionally, this is done by applying a high-pass filter and a directional filter to gridded data that have first been subjected to various corrections and tie-line leveling (Luyendyk, 1997; Ferraccioli et al., 1998). It is customary to use a high-pass filter length of four times the line spacing on the preprocessed grid and subsequently to apply a carefully designed directional filter to Manuscript received by the Editor January 31, 2003; revised manuscript received March 22, 2005; published online December 19, Geological Survey of Norway, 7491 Trondheim, Norway. eirik.mauring@ngu.no. c 2006 Society of Exploration Geophysicists. All rights reserved. L5

2 L6 Mauring and Kihle ensure that only energy nearly orthogonal to the lines is passed. Using this combination of high-pass and directional filters is known as directional filtering. The combination of the high-pass and directional filters enhances short-wavelength features across the line direction, which are considered to be line errors. The resulting grid is sampled along the survey lines. The sampled values are then smoothed using a nonlinear filter followed by low-pass filter convolution (Fraser et al., 1966) to avoid removing any remaining geologic signal. These correction values are then subtracted from the preprocessed values to produce the final leveled data. Differential median filter Figure 1 shows 1D and 2D windows for different line patterns used in median filtering. A circular window with radius r is used to determine the 2D median. A corresponding 1D filter with window length d is placed over the central line segment in the middle of the 2D median window. The point to be processed is centered within the line segment. The windows pass over the data set in unison, station by station, generating level-correction values, one at a time. For the 1D filter, the median is defined as the midpoint in an array of numbers sorted in ascending order. The median is denoted The technique is based on filtering line data, as opposed to filtering grid data when using directional filtering. For a given line, the 1D median is determined at each station based on data values along the line within a given distance d/2fromthe station (see Figure 1). In a similar way, the corresponding 2D median value is determined from nearby data values in the current line and inside the circle that intersects neighboring lines. The difference between the 2D and 1D median values is taken to be the leveling error, and the level correction is made by adding this value to the data value at the current station. With the directional filtering technique, it is important that the corrections are smoothed to avoid removing any remaining geological signal (see Figure 3). For stable results with median filtering, a regional trend must first be removed from some types of data (Smith and Wessel, 1990). Two standard methods are 2D high-pass filtering and trend removal based on a polynomial function. After median (X 1,X 2,...,X n ). The 1D median filter of size n (odd) in the sequence {X i, i Z} is defined as (Justusson, 1981) y i = median x i = median (x i v,...,x i,...,x i+v ), i Z, n where v = (n 1)/2 andz denotes all natural numbers. The nonlinear median filter has two very important properties: It acts as a noise filter, and it is particularly efficient in removing spikes. Although it is a smoothing filter, it preserves sharp edges in a data set (Gallagher and Wise, 1981; Justusson, 1981; Stewart, 1985). Both properties are illustrated in Figure 2. The figure also outlines the 1D median filtering procedure. A 2D median filter is a simple extension of the 1D filter to an array of numbers contained within an area. A 2D median filter with window A in a data set {X ij (i, j) Z 2 } is defined by y i = median A x ij = Median [xi+r,j+s ; (r, s) A], i, j Z 2. (1) Figure 2. Procedure for the median filtering of lines using a five-point filter (after Stewart, 1985). Note the removal of spikes and the preservation of edges in the data. Figure 1. The 1D and 2D windows used in differential median filtering for different line patterns. The length of the 1D filter is d, and the radius of the circular 2D window is r. Figure 3. Smoothing raw correction values using a Naudy filter preceding the application of a low-pass filter.

3 Moving Differential Median Filter L7 determining correction values, we add the smoothed correction values to the preprocessed anomaly field line data. These data are then regridded. TESTING LEVELING TECHNIQUES ON AEROGEOPHYSICAL DATA In this section, two survey examples are presented to evaluate the quality of the differential median filter in comparison to directional filtering. Neither survey includes tie lines. The two examples demonstrate cases in which (1) lines are parallel but the area is irregular and (2) lines are irregular in spacing and direction. The parallel-lines example uses VLF EM data from a helicopter survey. The example of irregularly flown lines uses vintage offshore aeromagnetic data acquired by the Geological Survey of Norway over the North Sea in the 1970s (Figure 4). Helicopter survey A map of the flight lines is shown in Figure 5. The purpose of the survey was to provide information for mineral exploration. The methods used were electromagnetic, VLF EM, radiometric, and magnetic. The line spacing was 200 m. The flying height was 60 m, and lines were flown in south and north directions (Figure 5). A minimum curvature routine (Briggs, 1974) using a grid-cell size of 50 m was applied when gridding the data. We have chosen the results from leveling the VLF EM data. The VLF instrument receives the magnetic component of fields radiated from one or two VLF transmitters (used around the world for navigation and to communicate with submarines). The change in total field (real component) is measured. The instrument has a sensor comprised of three mutually orthogonal antennas that record signals from transmitters radiating from different directions. This provides good coupling with ground conductors of any orientation (RMS Instruments, 2002). In this paper we show the real-component results from the inline antenna that couples maximally with a field in the nominal direction of flight (inline with flight). This field was transmitted from a 16-kHz VLF station transmitter in Rugby, England. The power output could not be predicted or controlled during the survey. Therefore, a constant base level was estimated and removed, leaving lines containing modified anomaly magnitudes. The grid-cell size was 50 m, and the sampling interval was approximately 5 m. Gridded, base-removed data are shown in Figure 6a. Line-level errors are evident. These are mainly caused by fluctuations in the VLF EM data from unaccounted elevation changes in the flight patterns. The percentage values on the legend bar are deviations from a nominal 100% primary magnitude determined in an anomaly-free zone (RMS Instruments, 2002). The data were leveled using both directional microleveling and differential median leveling. Directional leveling was performed using a pass angle of 0. The line-error grid is shown Figure 4. Overview map with flight lines for the vintage aeromagnetic survey. Figure 5. Map of the survey area with flight lines for the helicopter survey with the direction of the traditional leveling filter. Figure 6. (a) Grid of helicopter survey data after preprocessing but before leveling. (b) Line-error grid after 800-m Butterworth high-pass and 0 directional filtering.

4 L8 Mauring and Kihle Figure 7. Curves showing differences in correction values for varying 2D filter radii. The 1D filter length is kept constant (200 m). in Figure 6b. An 800-m Butterworth high-pass filter was applied to the grid to remove trends in the differential median leveling. Here, we used a 1D filter length of 200 m and a 2D filter radius of 450 m. We tried 2D filter radii of 250 m (1.5 times the maximum line spacing), 450 m (2.5 times the maximum line spacing), 650 m (3.5 times the maximum line spacing), and 850 m (4.5 times the maximum line spacing). The absolute difference between the correction values for the different radii were 0.51, 0.21, and 0.13 nt, respectively, while the 1D filter length was kept constant (200 m). Figure 7 shows these differences as curves for one of the survey lines. The differences between the 450 to 650-m and the 650 to 850-m radii are negligible. The absolute differences indicate that using a 2D window larger than 650 m (3.5 times the line spacing) has little effect on the quality of the final leveled result. Comparing the two grid images in Figure 8 reveals practically no line errors, neither for the traditional leveled data nor for the differential median leveled data. To highlight possible line errors, the first vertical derivative of the anomalies is shown in Figure 9. Presenting the first vertical derivative of the VLF magnetic component can be justified because the magnetic field is a potential in the air in the quasistatic approximation (Pedersen and Oskooi, 2004). The grids of the first vertical derivative show no remaining line errors, only highwavenumber anomalies from electrical conductors (geologic structures or manmade installations such as power lines and fences). Comparing anomaly profile curves did not reveal any distortions of anomalies either. Thus, there appear to be no noticeable differences in the performance of the two leveling techniques for this survey area. Figure 8. (a) Grid of directionally leveled data. (b) Grid of differential median leveled data with a 1D filter length of 200 m and a 2D filter radius of 650 m. The correction values for both techniques were smoothed using a 100-point Naudy filter and a 1-km low-pass convolution filter applied to the preprocessed data. Figure 9. (a) First vertical derivative of the VLF anomalies of (a) directionally leveled data and (b) differential median leveled data. On both grids there appear to be no remaining level errors. Vintage offshore magnetic survey A detailed map of the survey area with flight lines is shown in Figure 10. No tie lines were flown, but adjustment was made for base magnetometer data, despite the fact that the area is situated too remotely from the base magnetometer station for the station readings to be used to reduce of line errors. According to Reeves (1993), the most remote part of the survey area should be within 50 km distance from the base magnetometer station to be used in this way. The fan-shaped line pattern results from the use of Decca lanes for navigation. The survey was carried out using a maximum line spacing of 8 km. The sampling interval along the lines is 150 m and the flight altitude is approximately 500 m. In addition to base magnetometer corrections, preprocessing included spike removal and IGRF (1975) corrections. Gridded preprocessed data are shown in Figure 11a; line-level errors (corrugations) are evident.

5 Moving Differential Median Filter L9 The data were leveled using both directional leveling and differential median leveling. First, a 35-km Butterworth highpass filter was applied to the grid. This is equivalent to about four times the maximum line spacing. This high-pass filtered grid is the basis for both leveling techniques. For the median filtering this was done for trend removal. Directional leveling was performed using a pass direction at an angle of 30 clockwise from the south. This is the average direction of the survey lines. The resulting line-error grid for directional leveling is shown in Figure 11b. For differential median leveling, the 1D filter length is 20 km and the 2D filter radius is 28 km (3.5 times the maximum line spacing). We tried radii of 12, 20, 28, and 34 km while keeping the 1D filter length constant. The absolute average differences between the correction values were 4.4, 1.5, and 0.9 nt, respectively, for all of the flight lines. As for the helicopter survey, using a filter radius larger than 3.5 times the maximum line spacing seemed to have negligible effect on the quality of the final, leveled result. Further processing steps were carried out as depicted in the earlier sections discussing leveling techniques. Comparing the two grid images in Figure 12 reveals obvious line-level errors, especially in the northwestern part of the directionally filtered grid (Figure 12a). This is best seen in the corresponding high-pass filtered grid image of Figure 13 (35-km Butterworth high-pass filter). This is from the large angle deviation from the 30 directional filter. Also, some highwavenumber anomalies are attenuated on the directionally leveled grid (see circled areas in Figure 12a). However, small corrugations can also be seen in the southeastern part of the differential median leveled grid (Figure 13b), although less prominent than for the directionally leveled grid. Figure 14 shows magnetic anomaly values for lines P4 and P58 (see Figure 10 for location) before and after leveling with the two techniques. The figure reveals severe distortion of high-wavenumber anomalies for the directional leveling technique in areas where the line direction deviates from the optimal direction for the filter. The distortions are most prominent between 55 and 70 km on line P4. On line P58, the distortions are most severe between 40 and 60 km and between 120 and 140 km. It is evident that the differential median filter is superior to the directional filter in leveling the vintage data with less distortion of anomalies and independence of line direction. A disadvantage of the differential median filter is that the parameter settings (especially the 1D filter) need some trial-anderror adjustments to work properly. Some guidelines for setting these parameters are outlined below. The length of the 1D filter along the lines (distance d in Figure 1) should be less than twice the length of any level errors along the line, according to Liukkonen (1996). However, removing all level errors can distort anomalies (shape and Figure 10. Map of the survey area with flight lines for the vintage aeromagnetic survey with the direction of the traditional leveling filter and the positions of lines in Figure 14. DISCUSSION This section discusses how to set 1D and 2D parameters. It also gives examples of computing time for the case histories presented. Parameter settings Figure 11. (a) Grid of vintage data after preprocessing (spike removal, base magnetometer, and IGRF corrections) before leveling is applied. (b) Line-error grid of vintage data after 35-km Butterworth high-pass and 30 pass angle filtering.

6 L10 Mauring and Kihle Figure 12. (a) Grid of directionally leveled data. (b) Grid of differential median leveled data with a 1D filter length of 20 km and a 2D filter radius of 28 km. For both techniques the level correction values are smoothed using a 20-point Naudy filter and a 10-km low-pass convolution filter applied to the preprocessed data. Note attenuation of high-wavenumber anomalies on (a) (circled areas). amplitude). Subsequent modeling of these anomalies (e.g., calculations of depth to magnetic basement) may then become erroneous. The gridded data may, however, look smooth when displayed on a map. It is crucial that we find the optimal parameters for the 1D and 2D filters. In addition, the optimal parameters may vary within the survey area. The challenge is to find the parameters that preserve the shape and amplitudes of the anomalies while giving a smooth appearance to the gridded data. A trial-and-error approach can be done for the 1D filter length. For the 2D filter, we suggest that its radius (r in Figure 1) should be larger than the maximum distance between at least three neighboring lines to each side of the line being processed. For the two survey examples presented, the corrections converge toward similar values as the 2D radius increases beyond three times the maximum line spacing. This is a rule of thumb derived by comparing the leveling correction values for different sizes of the 2D window while the length of the 1D window is kept constant. It is imperative that the corrections be smoothed to avoid removing any remaining geological signal (see Figure 3). The variety of parameter settings gives more flexibility for skilled processing personnel than the standard technique, which is quite straightforward and does not allow for much variation of processing parameters. Figure 13. (a) Residual grid of directionally leveled data. (b) Residual grid of differential median leveled data. There are fewer remaining corrugations on the differential median leveled data. Both grids are produced after applying a 35-km Butterworth high-pass filter. Computational time The new technique requires longer processing time on a computer than the traditional microleveling method, and it involves sorting a 1D and 2D array for each data point to be processed. Computing time is dependent on the number of data points, data-sampling intervals, and size of the 1D and 2D filters. However, with everfaster computers developing, this should not be an obstacle for using the technique. To filter the data for the helicopter survey, it took 7 minutes and 45 seconds to process points with a sampling interval of 5 m using a 1D filter length of 200 m and a 2D filter radius of 650 m. For the vintage offshore survey, it took 1 minute to process points with a sampling interval of 150 m using a 1D filter length of 20 km and a 2D filter radius of 28 km.

7 Moving Differential Median Filter L11 helicopter survey with a regular line pattern and vintage aeromagnetic data collected in a fan-shaped irregular line pattern. For the vintage survey, the new technique effectively removes line-level errors with less anomaly distortion than the directional filtering technique. We suggest that the new technique can be used for many types of data. Figure 14. Magnetic anomaly values before and after leveling lines P4 and P58 of the vintage data. Distortion of high-wavenumber anomalies on the directional filtered data are evident. General remarks We have applied the technique with success on a wide variety of data, from small helicopter surveys to large gravity and magnetic compilations. While the directional filter works on regular, parallel lines, the differential median filter seems to work also on irregular and nonparallel lines with less distortion of anomalies. CONCLUSIONS Two leveling techniques applied to remove line errors (corrugations) from a set of aerogeophysical data are compared. These are based on directional filtering and on a new technique built on differential median filtering. The first technique is widely used in the geophysical data-processing industry. It involves the combined use of 2D high-pass and directional filters, and it requires that lines be parallel. An alternative leveling technique is suggested that utilizes a moving differential median filter. As opposed to traditional leveling techniques, the alternative technique can be used for nonparallel flightlines and irregular flight-line patterns. For some data types, the technique requires removing a regional field before it can be applied. We have tested the new technique on a wide variety of data sets with success, two of which are presented as examples: a ACKNOWLEDGMENTS The authors thank Mark A. Smethurst for valuable comments and corrections to this paper. They are grateful to Crew Development Corporation for data from the helicopter survey. Thanks also go to V. J. S Grauch and R. O. Hansen for reviewing this paper and providing suggestions for improving it. REFERENCES Briggs, I. C., 1974, Machine contouring using minimum curvature: Geophysics, 39, Ferraccioli, F., M. Gambetta, and E. Bozzo, 1998, Microlevelling procedures applied to regional aeromagnetic data: An example from the Transantarctic Mountains: Geophysical Prospecting, 46, Fraser, D. C., B. D. Fuller, and S. H. Ward, 1966, Some numerical techniques for application in mining exploration: Geophysics, 31, Gallagher, N. C., and G. L. Wise, 1981, A theoretical analysis of the properties of median filters: IEEE Transactions in Acoustics, Speech and Signal Processing, 29, Justusson, B. I., 1981, Median filtering: Statistical properties, in T. S. Huang, ed., Two-dimensional digital signal processing I. Transforms and median filters: Springer-Verlag. Liukkonen, J., 1996, Levelling methods for aerogeophysical data: 10 August liukkonen/public/publications. html. Luyendyk, A. P. J., 1997, Processing of airborne magnetic data: Journal Australian Geology and Geophysics, 17, no. 2, Minty, B. R. S., 1991, Simple micro-levelling for aeromagnetic data: Exploration Geophysics, 22, Pedersen, L. B., and B. Oskooi, 2004, Airborne VLF measurements and variations of ground conductivity: A tutorial: Surveys in Geophysics, 25, Reeves, C. V., 1993, Limitations imposed by geomagnetic variations on high quality aeromagnetic surveys: Exploration Geophysics 24, RMS Instruments, 2002, HERZ TOTEM-2A VLF electromagnetic system user s guide: GRMS Instruments. Smith, W. H. F., and P. Wessel, 1990, Gridding with continuous curvature splines in tension: Geophysics, 55, Stewart, R. R., 1985, Median filtering: Review and a new F/K analogue design: Journal of Canadian Society Exploration Geophysicists, 21, Urquhart, T., 1989, Decorrugation of enhanced magnetic field maps: 59th Annual International Meeting, SEG, Expanded Abstracts,

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