Determination of Significant Structure

Studies such as Bendjoya [2] determine the significance of structure in a given area of an image by finding the maximum wavelet transform coefficient expected in that area from a set of pseudo-random images which are based on the large-scale structure of the original. In the current study only the strongest feature in each wavelet transform is noted owing to the number of dimensions over which the structure is spread and the strength of the sporadic sources. Two wavelet size-scales are used in order to enhance features with different spatial extents: a 3° probe size is assumed to probe at the scale expected from a shower source embedded in the sporadic background while a 6° probe is used to detect showers which occur closer to the size-scale of the background itself. Because the sporadic source regions specified above differ markedly, their regimes are examined separately.

All orbital data from the vernal equinox of 1995 through to the end of July 1999 were combined to produce a virtual equinoctial year for study—the assumption here is that coherent showers must occur year after year to some degree in order to be detected and verified within the amor data set. In total 64 different wavelet transform sets are created for all combinations of the two time window sizes, two wavelet probe sizes, four speed partitions and four sporadic source regions. Each of these sets contains 360 wavelet transforms of selected radiant region images; the data extracted from each transformed image are the maximum wavelet transform coefficient (Wm), the position of the latter in

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Solar Longitude J2000, d

Figure 2. A normalised amplitude profile containing the Southern <5 Aquarids peak about the A0 ~ 125° point is shown on the left, with the background, determined by a 60° sliding median window overlaid (dashed line). On the right the distribution of normalised amplitude values measured throughout the virtual equinoctial year is shown.

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Solar Longitude J2000, d

Figure 2. A normalised amplitude profile containing the Southern <5 Aquarids peak about the A0 ~ 125° point is shown on the left, with the background, determined by a 60° sliding median window overlaid (dashed line). On the right the distribution of normalised amplitude values measured throughout the virtual equinoctial year is shown.

radiant space ((A — Aq)m,Pm) and the total number of meteors recorded in the sporadic source region under study, with no speed constraints, during the corresponding time window (Ns). Ns is used to normalise WM for fluctuations in the background meteor rate based on the assumption that a meteor shower constitutes only a small part of the overall population in a sporadic source region at a given time: this is found to be reasonable for the amor data set where, as shown in Figure 1, only the Southern 5 Aquarids show a slight hint of existence in the night-time activity profiles.

A typical profile obtained from the current antihelion region data is shown in Figure 2 where the antihelion region is probed in the 40 ± 10 km s_1 speed partition, using the 3° wavelet probe and a 2° wide time window. The normalised (maximum) transform coefficient amplitude shows a clear maximum about A© ~ 125°; there are a number of less clearly significant peaks in this diagram, however, whose reality must be determined. The assumption made is that the normalised maximum transform coefficient will describe a Gaussian noise distribution for most of the year with occasional unexpectedly strong signal strength corresponding to the presence of a shower. There are some long term background trends in the profile: these are determined by means of a 60° wide sliding median window, producing the background level shown. The latter figure also shows the distributions obtained from both the original set of normalised maximum transform coefficients and from that set corrected for the background trend. It is clear that the detrended distribution is approximately Gaussian but with some very far outlying points which are attributed to shower presence. Points further than 3a from the mean in the detrended distribution are removed in order to diminish the effect of much of the shower structure and the standard deviation of the truncated distribution resulting is then determined which is assumed to correspond to the noise distribution spread (a^)- Tests on profiles such as that shown in Figure 2 are applied at the 2>gn and 4an levels in order to determine shower significance at the 99% and 99.99% levels respectively.

4.2. Application Example

An example of the results obtained from a typical search is shown in Figure 3. This is from the same antihelion region search shown in Figure 2. The upper two sub-plots in this figure show the radiant position coordinates at which the maximum transform coefficient occurred in each 1° time step. The lower sub-plots show the maximum coefficient amplitude in both original and background normalised forms. The twin dotted lines in these amplitude profiles correspond to the 99% and 99.99% significance levels: amplitude peaks rising above these are considered significant at the respective levels.

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