# Coherence

Coherence is one of several seismic attributes which is a measure of similarity between waveforms or traces in 2D or 3D seismic volumes. This attribute is designed to emphasize discontinuous events, like faults in structural interpretation . In map view - or time slices - it can also be used to aid in stratigraphic interpretation.

## What is coherence?

Coherence is a measure of similarity between waveforms or traces. The seismic waveform is a response of the seismic wavelet convolved with the geology of the subsurface. That seismic response changes in terms of amplitude, frequency, and phase, depending on the acoustic-impedance contrast and thickness of the layers above and below the reflecting boundary. Since, acoustic impedance is affected by the lithology, porosity, density, and fluid type of the subsurface layers; then strong lateral changes in impedance contrasts give rise to strong lateral changes in waveform character. These lateral changes is what the coherency attribute measures.

The calculated coherence volumes dramatically enhance the ability of the interpreter to observe stractural and stratigraphic discontinuities. Stratigraphic features tend to display best on horizon or time slices, if the dip is not too large. Structural features, like faults, are best seen on time (or depth) slices.

Coherence is also commonly referred to as 'discontinuity' and varies between 0 and 1. Typically, high amplitudes shown with this attribute represent discontinuities is the data, while lower amplitudes represent continuous features. A best practice is to always examine the colorbar, as some seismic softwares may show the inverse.

Coherence can also be referred to as 'semblance', or 'similarity'. These attributes are very similar, with slight variations in the algorithms.

## Common coherence methods

There are a variety of coherence methods. A more detailed discussion of these methods can be found here. Among these are:

### Crosscorrelation

The simplest form, which typically used three neighboring seismic traces. This method takes into account only the shape of the waveform, and not the amplitude of the waveform.

### Semblance (or Variance)

This method needs a 3D analysis window to be defined, as well as a dip and azimuth for each point in the seismic volume. The semblance measures the degree of similarity to each other of all of the traces along the selected dip within the defined 3D window. This method is sensitive to both waveform and lateral changes of the reflector amplitude.

### Variance

Variance indicates how widely the individual points vary. Mathematically, it is similar to 1-semblance.

### Eigenstructure Method

The Eigenstructure coherence is the ratio of the energy of the coherent component of the data to the energy of the original traces within an analysis window. Before this ratio can be calculated, the method calculates a wavelet that best represents all the wavelets in the analysis window. Then this wavelet is scaled to fit each input trace creating the 'coherent component'. This method only measures changes in the reflectors waveform (not amplitude).

### Gradient Structure Tensor-based Coherence

This method uses a larger analysis window, and tends to have lower lateral resolution. This method is sensitive to both waveform and lateral changes of the reflector amplitude.

### Least Squares Coherence

Presented by Bednar (1998) and is based on a least-squares fit technique that fits a plane through a seismic data window, and is solved using an iterative technique.^{[2]}

## Impact of varying analysis windows

The analysis window chosen can have a significant effect of the results. Longer windows tend to mix stratigraphy, which can complicate the geologic image. In areas where there are both structural and stratigraphic features of interest, it is a best practice to create multiple coherence volumes to help visualize all the information included in the seismic volume.

## References

- ↑
^{1.0}^{1.1}Chopra, Satinder, and Kurt J. Marfurt. Seismic Attributes for Prospect Identification and Reservoir Characterization. Society of Exploration Geophysicists, 2007 - ↑ Bednar, J.B. (1998) Least squares dip and coherency attributes,
*The Leading Edge*, 17(6), 777-778. http://dx.doi.org/10.1190/1.1438051

## See also

- Seismic attributes
- Semblance, coherence, and other discontinuity attributes
- Stratigraphic interpretation
- Structural interpretation
- Time slices