Scaling

Name

Description

• Using a time/depth variant weighting function
• Using weight(s) extracted in static time/depth window(s)
• Using Automatic Gain Control (single dynamic window)

1. Z^n scaling
   
   
   
   The weight function is defined by Z^n where Z is the time/depth of the current sample and n is a user-defined exponent:
   
   w(i) = Z(i)^-n where is Z is the time or depth of the i^th sample.
   
   The exponent is a float and thus it can be negative, positive and equal to zero (unity operator). An exponent larger than zero will apply a correction proportional to the depth, while an exponent smaller than zero will apply an inversely proportional correction with depth. The output amplitude is the normalized sum of the input amplitude using a weight equal to Z^n.
   
   
2. Window(s) scaling
   The weight function is a step function: w(i) is constant over a static time/depth window, equal to the "basis" value than is computed from the input amplitudes using the following mathematical definitions:
   
   • The Root Mean Square (RMS)
   • The arithmetic mean
   • The maximum
   • A user-defined value (float)
   Please note that the window time/depths are float and do not need to be on a sample. The time/depths will be round to the nearest sample when defining the extraction window. Unlike most of the window definitions in the attribute engine you must provide in this scaling attribute absolute time/depths values and not values relative to the actual sample. A weight of 1 (no scaling) will be given to the samples not covered by a user-defined time gate. The weights are cumulative: If several windows overlap the output weight will be the sum of the "basis" output for the samples belonging to multiple windows.
   
   
   
3. Automatic Gain Control scaling
   The AGC is a special case of the window scaling. In this case the window is defined relative to the actual sample and the "basis" is the energy value in that sliding window. The window width is a total size, i.e. the relative width corresponds to +/- half of the total window width. The low energy mute will mute the output samples that have an energy lower than a ratio of the trace energy distribution: The energy of the input trace is computed and the output values are sorted per increasing energy value. Given 1000 samples the energy of sample 250 (for a low energy mute at 25%) corresponds to the mute level: If the energy computed in the AGC window is lower than this level the value 0 will be output. Otherwise the sum of the squares over the number of (valid) samples will be output. Undefined values are not used for the computation and a zero is output if all values of a time window are undefined.
   
   
   
4. Squeeze
   The purpose is to put a limit to the value range of the input. Rather than clipping the value (which would be equivalent to a simple Mathematics formula like 'x0 > c0 ? c0 : x0'), the value can be squeezed into a range.
   
   The first parameter is the 'Value range'. it defines the hard limits to the value range. One of these limits may be empty, signifying 'unlimited'.
   
   The second parameter is the 'Untouched range'. If no limits are entered there, Squeeze will degrade to a simple clipping operation. If specified, it will squeeze rather than clip, constraining the squeezing to the ranges outside this range.
   
   For example, Value range [0,10] and untouched range [2,8]. Values outside the [2,8] range will be modified to fit between [0,10]. This means the values in the range [-infinitiy,2] will be squeezed into the range [0,2] via a hyperbolic function. That function is continuous in value (and first derivative) at 2. Similarly, values higher than 8 will go somewhere between 8 and 10.
   
   Example application: predicted porosities. Predictions of porosity tend to have values below 0. To counter this, you could squeeze all values below 1%. Use value range [0, ] and untouched range [1, ]. If you also want a more fuzzy upper limit, starting at 25% to absolute maximum 30, you may specify [0,30] and [1,25].
   
   This is shown in the attribute set below: