[Users] *New features* Recursivity and shift within the mathematics attribute

[Arnaud Huck]

Dear users,

The latest development release 3.1.7 contains two additional 
possibilities in the mathematics attribute:

1- The input volume may be directly used at a different time than the 
time of the current sample: Let us assume that the current position is 
at time t0. Then x0[i] is the input volume designed by x0, but at the 
time t0 + (i)*dt where dt is the sampling rate. The integer "i" may be 
negative or positive.

Application: Using this feature, a centred differentiation (time domain) 
can be coded using the formula (x0[+1]-x0[-1])/(2*c0) where c0 is the 
sampling rate. Please note that for lateral shifts the reference shift 
attribute must still be used.

2- Recursive filters can be created using the syntax "THIS[-i]". The 
most general form of recursive equation is the following:

y[n] = a0*x[n] + a1*x[n-1] + a2*x[n-2] + ...
                        + b1*y[n-1] + b2*y[n-2] + ...

where x[] is the input volume, y[] is the output volume and the a's and 
b's the coefficients.  n is the current sample number.

In the mathematics attribute the current sample index "n" does not need 
to be specified. Therefore the equation above can be entered as:
c0*x0 + c1*x0[-1] + c2*x0[-2] + c3*THIS[-1] + c4*THIS[-2] + ...
where THIS[-1] stands for y[n-1] and THIS[-2] stands for y[n-2]

For each instance of THIS[-i] a starting value must be provided. In the 
development release 3.1.7 the starting value is the output value at the 
first sample of the cube or at the first sample of the display element 
(inline, crossline, random or 2D line). A mathematics attribute with 
THIS[-i] should not be applied to timeslices, horizons or picksets in 
this development release.

Indeed local computations around timeslices, horizons and picksets are 
not valid when using a recursive equation since this would need to 
integrate all values from a fixed time or depth to the current position. 
This restriction will be addressed in the incoming stable release 3.2 by 
providing an absolute time or depth to each starting value.

Two examples of low pass and high pass recursive filters are provided in 
the default attribute set "Evaluate attributes":
"Single pole low pass recursive filter" and "Single pole high pass 
recursive filter". Best results are achieved when providing an input of 
impedance or velocity type.

Best regards,
Arnaud Huck.

-- dGB Earth Sciences B.V.
-- Nijverheidstraat 11-2, 7511 JM Enschede, The Netherlands
-- mailto: arnaud.huck at dgb-group.com, http://www.dgb-group.com
-- Tel: +31 53 4315155 , Fax: +31 53 4315104