|OpendTect User Documentation version 4.6|
Similarity -- Multi-trace attribute that returns trace-to-trace similarity properties
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).
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 five different modes of data-driven steering: None, Central, Full, Constant direction Steering and Browse dip.
- None: Only the similarity between the pair of traces defined in 'Trace positions' is calculated.
- Mirror 90 degrees: Two similarities are computed: one for the defined trace pair (as in 'None') and one for the pair obtained by 90 degree rotation. (Not available for 2D data)
- Mirror 180 degrees: Two similarities are computed: one for the defined trace pair (as in 'None') and one for the pair obtained by 180 degree rotation.
- Full Block: Similarities between all possible trace pairs in the rectangle defined by the step-out are computed.
- Cross: Similarities between all possible trace pairs in the '+' -shape defined by the step-out are computed.
- Diagonal: Similarities between all possible trace pairs in the 'x' -shape defined by the step-out are computed.
- All Directions: Similarities between all possible trace pairs in the '' -shape defined by step-out are computed. This is the extension found to be most useful: it gives a degree of accuracy almost equal to that of 'Full Block' but with significantly less processing time (depending on the step-out, up to a factor of 10).
Similarity "None" Steering: This option is used when non steeringcube algorithm is used. This is ok in the case the layering is mainly horizontal (with less dip).
However, in very complex geology, the similarity result using "None" as steering option will deteriorate. Full steering should be used instead. The dip steering plugin is required.
Another steering option to use is the "Browse dip". This is a similarity feature acting as a 'Coherency' attribute.
It enables the calculation of 'Similarity' by comparing one trace with the next trace.
Then a value between 0 (not similar at all) to 1 (completely similar) is awarded. In order to compare traces, two variables should be specified:
The 'Maximum dip' represents the maximum dip in microseconds per metre (μs/m), relative to an event in one trace, in which the algorithm will look for similar events along the neighbouring trace. Default is 250.
The "Delta Dip" is a variable which represents the window in microseconds per metre (μs/m) which is shifted along the neighbouring trace to detect similar events whithin the earlier specified 'Maximum Dip'. The closer the value to 1 the more precise the results will be. The default value is 10. Using this value will result in a good balance between calculation time and quality of the results, this also depends on the quality of the data itself.
Let us assume two vectors X, Y of length N=15 samples:
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).