Phase and polarity assessment of seismic data
Seismic data can be indicators of many factors such as amplitude, continuity, phase, and polarity of the reflections coming from the subsurface. This article reviews how the last two are used in seismology.
Phase in seismic data is simply known as the lateral time delay in the start of a reflection recording, and because it is amplitude-independent, phase can be used as a good continuity indicator in poor reflectivity areas in the seismic data with a higher sensitivity to reflection discontinuity caused by pinch outs, faults, fractures, and other structural and stratigraphic seismic features.
Furthermore, polarity is compatible to reflection coefficient of the seismic data. In other words, if the beddings’ boundary gave a positive acoustic impedance, it corresponds to a positive polarity and vice versa.
Phase: Assessment and examples
To better understand how phase works in seismology, consider a simple cosine curve for example. If a ‘time shift’ of 90° to the right has been applied, then the cosine equation has a shift of -90° and so on.
Phase Calculations and Correction
For real seismic data, we want to check whether it has zero phase (no phase shift is applied) or minimum phase. Having our data with the former is preferable because it minimizes processing and ambiguity, but the second one might lead to counting false events as true reflections and/or distort actual events (see figure 1). We need to perform seismic picking (choosing a horizon) that connects the primary peaks after ensuring that our data is zero phase. Some of the advanced techniques to do so are autopicking, interpolation, voxel tracking, and surface slicing. Many mathematical operations have been applied by seismic software nowadays to properly time shift the seismic responses into the desired position, and one of them is used in Rost and Thomas. The authors used a method called beam forming that applies mathematical equations to produce a trace with no time delay in their usage of seismic arrays. Starting off with the following time series:
Where xcenter is center of the array, f(t) is the signal, and ni(t) is noise recorded at station i. Since each seismic wave fronts has different arrival times at each station and those times are conditional to slowness and wave front sensor location, the next time series is created:
Having ri as the location vector of station i and uhor as the horizontal slowness. Then, a trace with no time delay is generated:
Finally, the beam trace called “delay and sum” for an array with M elements is estimated with:
The end-product of this system is presented in figure 2 (lower right) that shows a comparison between a simple ‘sum’ and a ‘delay and sum’ approach (see  for more details).
There are various other ways purposed to determine the phase of seismic data, and one of them is [HISTOGRAM MATCHING SEISMIC WAVELET PHASE ESTIMATION].
Another example for employing phase in seismic processing is shown by Mitrofanov and Priimenko. The researchers have given a comparison between amplitude and phase spectra in detecting pinch-outs of the oil and gas spectrum and thin layers in their paper. In summary, the scientists have proven that the second way of viewing seismic traces is more efficient in lowering uncertainty when viewing pinching-out zones’ beds (figure 3).
In addition, Metrofanov and Priimenko have discovered that phase spectrum is also capable of giving more precise elastic parameters for the thin layer pack presented in their research (figure 4) (see  for details).
Polarity: Assessment and examples
Polarity is essentially used in seismology to decide wither to assign a positive polarity to a peak or a trough. It might seem straightforward, but the type of polarity used in seismic display must be known by interpreters to avoid confusion regarding the sign of reflections’ coefficients.
Types of Polarity
There are two definitions of polarity used by seismologists:
- American polarity: positive polarity (impedance) is linked to a peak (positive amplitude)
or ‘hard’ event and vice versa.
- European polarity: opposite of the American one, which means a positive polarity (impedance)
is associated with a trough (negative amplitude) or ‘soft’ event and vice versa.
Figure 5 shows a comparison between the two polarity systems and how they view hydrocarbon sand bright spot. This phenomenon appears when the embedding formation has a higher acoustic impedance than the hydrocarbon itself, so the top of it resembles a decrease in acoustic impedance while the base makes for an increase in acoustic impedance.
A typical soft layer would count as sand and a hard one would be shale (check  for more examples of soft and hard beds and more details). There are some methods that help detect the polarity system used in composite seismic data, and some of them are deconvolution and zero phase processing. Another way of figuring out the polarity is by generating synthetic seismograms from good well logs and correlating them to the real data. Other ways of determining polarity of seismic data has been presented by other scholars such as [Automatic Bayesian polarity determination].
Polarity in Seismic Display
To display seismic data in terms of polarity (impedance), variable wiggle and area display (VWA), variable density display (VD) or a combination of both can be used (figure 6) . The most common VD display is the blue-white-red color scale (figure 6c). Blue color, regarding American standard, is equivalent to a peak in VWA display (figure 6b) and it is the opposite for the European (or Australian) standard.
Polarity characteristics can be good indicators of changes in the subsurface, and polarity reversal, which develops from change in acoustic impedance with depth, is one them (figure 7). On figure 7, the bright spot above depth A is due the large difference of acoustic impedance between gas-sand and shale but a seldom one between those for water-sand and shale. Also, polarity reversal, which is located between depths A and B, generated from water-sand having higher impedance than shale and gas-sand with a lower impedance than shale. Finally, the dim spot shown below depth B results from the three formations converging and thus having only a small difference in impedance between them.
- Niranjan, N. C., 2016, Chapter 2 Seismic Reflection principles: Basics, Seismic Data Interpretation and Evaluation for Hydrocarbon Exploration and Production: A Practitioner's Guide, Springer, 19–35.
- Brown, 1998, found in Avseth, P., Mukerji, T., and Mavko, G., 2005, Common techniques for quantitative seismic interpretation. In Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk, Cambridge: Cambridge University Press, 168-257, doi:10.1017/CBO9780511600074.005; https://pangea.stanford.edu/~quany/QSI_Chapter-4.pdf
- Dorn, 1998, found in Avseth, P., Mukerji, T., and Mavko, G., 2005, Common techniques for quantitative seismic interpretation. In Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk, Cambridge: Cambridge University Press, 168-257, doi:10.1017/CBO9780511600074.005; https://pangea.stanford.edu/~quany/QSI_Chapter-4.pdf
- Rost, S., and Thomas, C., 2002, Array seismology: Methods and applications, Rev. Geophys., 40, no.3, 1008, doi:10.1029/2000RG000100; https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000RG000100
- Mitrofanov, G., and Priimenko, V., Phase spectra in seismic data processing, PETROBRAS, S.A.; http://www.sscc.ru/conf/mmg2008/papers/Priimenko_2.pdf
- Brown, 2001a, 2001b, found in Avseth, P., Mukerji, T., and Mavko, G., 2005, Common techniques for quantitative seismic interpretation. In Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk, Cambridge: Cambridge University Press, 168-257, doi:10.1017/CBO9780511600074.005; https://pangea.stanford.edu/~quany/QSI_Chapter-4.pdf
- Brown, A. R., and William, A. L., 2014, Polarity of zero-phase wavelets. GeoScienceWorld, 2, no.1, 19F; https://pubs.geoscienceworld.org/interpretation/article-abstract/2/1/19F/284781/the-polarity-of-zero-phase-wavelets?redirectedFrom=PDF
- Avseth, P., Mukerji, T., and Mavko, G., 2005, Common techniques for quantitative seismic interpretation, In Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk, Cambridge: Cambridge University Press, 168-257, doi:10.1017/CBO9780511600074.005; https://pangea.stanford.edu/~quany/QSI_Chapter-4.pdf
- Alistar, B. R., 2004, Reservoir identification, AAPG Memoir 42 and SEG Investigations in Geophysics, No. 9, Chapter 5,153-197.
- [Automatic Bayesian polarity determination] — A paper made by D.J. Pugh, R.S. White and Christie for Department of Earth Sciences, University of Cambridge on September 23, 2015.
- [HISTOGRAM MATCHING SEISMIC WAVELET PHASE ESTIMATION] — A thesis made by Jiangbo Yu in partial fulfillment of the Requirements for the Degree Master of Science from the University of Houston.