# 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.

## Overview

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.[1]

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.[1]

## 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.

Figure 1:Comparison between minimum (leggy) (a) and zero phase (b). side lobes are minimized, and the main amplitudes are more emphasized in (b). Also, multiple close reflections are easier to distinguish in zero phase data. Courtesy to Sheriff, 1973.[1]

### Phase Calculations and Correction

as For real seismic data, we care to know whether they have zero phase (no phase shift is applied) or minimum phase. Having our data in the first condition 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.[2] Some of the advanced techniques to do so are autopicking, interpolation, voxel tracking, and surface slicing.[3] 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.[4] 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:

${\displaystyle [x_{center}=f(t)+n_{i}(t)]}$

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:

${\displaystyle [x_{i}(t)=f(t-r_{i}.u_{hor})+n_{i}(t)]}$

Having ri as the location vector of station i and uhor as the horizontal slowness. Then, a trace with no time delay is generated:

${\displaystyle {\bar {x}}_{i}(t)=x_{i}(t+r_{i}.u_{hor})=f(t)+n_{i}(t+r_{i}.u_{hor})}$

Finally, the beam trace called “delay and sum” for an array with M elements is estimated with:

${\displaystyle [B(t)={\frac {1}{M}}\sum _{i=1}^{M}n_{i}(t+r_{i}.u_{hor})=f(t)+{\frac {1}{M}}\sum _{i=1}^{M}n_{i}(t+r_{i}.u_{hor})]}$
Figure 2: Comparison between plain sum (top right) and delay and sum (lower right) for an event collected in an array from the Lake Tanganyika (October 2nd, 200) (original data at left). Notice how the delay and sum method gave higher amplitudes for the main events and ‘deleted’ the noise in it (small wiggles). Courtesy to [4].

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 [4] for more details).

Figure 3: Possible pinching-out zone with result of real date processing. (a) original data. (b) result of interpretation using amplitude and phase spectra. Courtesy to [5].

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.[5] 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).

Figure 4: Numerical modeling result on the evaluation of the elastic parameters of the thin layer package. (a) model and first estimation. (b) two parts of synthetic seismogram made for selecting the reflected signal of converted wave. (c) The changed structure of model (amplitude) with parameters. (d) Phase spectrum-based estimation result. Courtesy to [5].

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 [5] 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 types of polarity used be seismologiests:

• American polarity: positive polarity (impedance) is linked to a peak (positive amplitude)

or ‘hard’ event and vice versa.[6]

• 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.[6]

Figure 5: Comparison between American (left) and European (right) polarities in showing hydrocarbon synthetic seismogram bright spot. Courtesy to [7].

Figure 5 shows a comparison between the two polarity systems and how they view hydrocarbon sand bright spot.[7] 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.[7]

A typical soft layer would count as sand and a hard one would be shale (check [8] 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.[3] Another way of figuring out the polarity is by generating synthetic seismograms from good well logs and correlating them to the real data.[6] Other ways of determining polarity of seismic data has been presented by other scholars such as [Automatic Bayesian polarity determination].

### Polarity in Seismic Display

Figure 6: Types of seismic data display modes: (a) Wiggle. (b) Wiggle and variable area. (c) Variable density. (d) Combination of (a) and (c). Courtesy to [1].

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) [1]. 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.[6]

### Polarity Reversal

Figure 7: Acoustic impedance change with depth for gas sands, water sands, and shales. The right sketch shows a generalized curve of the behavior of acoustic impedance for those materials, and left pictures show variable density display examples of the three situations presented on the right. Courtesy to AAPG Memoir 42(sixth edition).[9]

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).[9] On figure 7, the bright spot above depth A happened with immense difference between acoustic impedances of gas-sand and shale but a seldom one between those for water-sand and shale.[9] 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.[9] Finally, the dim spot shown below depth B resulted from the three formations converging and them having slight differences in impedance between each other.[9]

## References

1. 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.
2. 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
3. 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
4. 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
5. Mitrofanov, G., and Priimenko, V., Phase spectra in seismic data processing, PETROBRAS, S.A.; http://www.sscc.ru/conf/mmg2008/papers/Priimenko_2.pdf
6. 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
7. 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
8. 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
9. Alistar, B. R., 2004, Reservoir identification, AAPG Memoir 42 and SEG Investigations in Geophysics, No. 9, Chapter 5,153-197.