| OpendTect User Documentation version 3.2 |
|---|
| Prev | | Next |
Name
Similarity -- Attribute that returns trace-to-trace similarity properties
Description
Similarity is a form of "coherency" that expresses how much two or more trace segments look alike. A similarity of 1 means the trace segments are completely identical in waveform and amplitude. A similarity of 0 means they are completely dis-similar.
In OpendTect, we favor a different approach. We first try to find the direction of best match at every position, which is a result by itself: the dip. By using this dip we can then calculate the best Similarity between adjacent traces. Similarity is based on fundamental mathematics: the samples of the trace are seen as components of a vector, and the Similarity is defined in terms of distance in hyperspace.
The point about using the Similarity is that it's mathematically simple; it is very clear what is going on. Then, by combining different kinds of similarities and other attributes, you can always get much better results with lots less computing time.
Consider the trace segments to be vectors in hyperspace. Similarity is then defined as one minus the Euclidean distance between the vectors, normalized over the vector lengths.
The trace segments is defined by the time-gate in ms and the positions specified in relative co-ordinates. In case of using input from 2D data, the trace positions are defined by a trace step-out only, not by inline and crossline stepout. The Extension parameter determines how many trace pairs are used in the computation. This is visualized in the image below.
Definition of trace positions relative to the reference point at (0,0).
Extension
With None specified, only the trace pairs specified in Trace positions are used to compute the output. Mirror at 90 degrees (not available when input is 2D data) and Mirror at 180 degrees means that two similarities are computed: for the specified trace pair and for the pair that is obtained by 90 or 180 degrees rotation. When using Full block as extension, all possible trace pairs in the rectangle, defined by Inl/Crl stepout, are computed.
The attribute returns the statistical property specified in Output statistic. The Steering option enables the user to follow the local dip to find trace segments that should be compared instead of comparing two horizontally extracted trace segments. The Steering option supports three different modes of data-driven steering; Central, Full and Constant direction Steering.
Mathematical description
Let us assume two vectors X, Y of length N=15 samples:
Xi, i=1,15
Yi, i=1,15
The similarity is 1 minus the Euclidean distance between the vectors divided by the sum of the length of each vector. Please note that the length of a vector is its L2 norm, also called RMS value:
An example timeslice is highlighting fault structure: (a) Dip-steered Filtered Seismic, (b) Non-Steered minimum Similarity, (c) Steered minimum Similarity. Notice that the definition of faults has been improved with the Similarity attributes. The steered minimum Similarity (c) is highlighting precise fault definitions as compared with the result of non-steered minimum Similarity (b).