Hi Mohammed,
The reference for the Naudy filter is:
Naudy, H., and H. Dreyer, Essai de filtrage non-lineaire applique aux
profiles aeromagnetiques, Geophys. Prosp., 16, 171-178, 1968.
I will have a copy FAXed to you.
The "non-linear" concept of the filter comes from the ability of the filter
to make a decision about whether a particular data point is noise or not.
If a point is considered noise, it is removed and replaced by an
interpolated value using the method described in the paper. If a point is
not noise, it is not changed at all. So, it is best to think of the Naudy
filter as having two parts - a noise test, and an interpolation.
The Naudy and Dreyer noise test uses a 5-point criterion that evaluates the
center data value from a sequence of 5 consecutive values. However, this
test is only sensitive to features with a width the size of the test sample
interval, which is why it works so well with spikes. The Geosoft
implementation has extended this concept so that it can be applied to test
for noise at any width (greater than the sample interval, obviously). We do
this in an iterative fashion as follows:
Say we want to remove features that are 12 points wide and exceed a certain
amplitude.
1. We pass the filter using every 6th point - points (1,7,13,19,25),
(2,8,14,20,26), (3,9,15,21,28), etc., each time evaluating the center point.
If is noise, we replace it.
2. We then reduce the filter width by half plus 1. In this case 6/2+1 to a
width of 4 and repeat the process. This reduction continues until the
separation is 1 (in our example, 6,4,3,2 and 1).
3. After the first time through steps 1 and 2, we have removed most of the
big things, but a lot of noise will have been introduced between points in
areas that have been changed. So we iteratively repeat steps 1 and 2 until
nothing changes, or up to a reasonable maximum number of iterations.
An important feature of the non-linear filter is that if a data point is not
considered noise, it is not changed at all. This means that if you do not
like the Naudy interpolation, you can still apply the filter just to find
out what points were changed. You can then use the math functions to dummy
these points out:
"(new-old!=0)?dummy:old"
The dummies can then be interpolated using the minimum curvature, Akima or
B-splines, or just be left as holes in the data.
Regards,
Ian
_______________
Geosoft Inc.
Ian MacLeod
[EMAIL PROTECTED]
(416) 369 0111 x323
Geosoft: Spatial Data Processing and Analysis Solutions
http://www.geosoft.com
-----Original Message-----
From: Mohammed A. Kidwai [mailto:[EMAIL PROTECTED]]
Sent: Thursday, September 09, 1999 10:03 AM
To: GEOSOFT USER GROUP
Subject: [geonet]: NON-LINEAR FILTERING.
Hello All,
I am trying to understand the mechanics and behavior of Geosoft's Non
Linear filter. I have used it on airborne magnetic and gravity data for
noise reduction etc.. I would appreciate any information I can get
regarding the design and behavior of this filter. I would appreciate if
I can get some references to papers where I can find more information. I
am also trying to get my hands on Naudy's paper, any uggestions/comments
where I can get it from. Thanks.
Mohammed Kidwai
Carson Services Inc.
Aerogravity Division
Perkasie, PA 18944
Ph 215-249-3535
Fax 215-249-0726
E-mail [EMAIL PROTECTED]
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