Seismic terrain displays


A couple of years ago I stumbled in a great 2001 paper by Beyer [1] on The Leading Edge. Being interested in visualization techniques I was drawn by the display in Figure 1 (which is a low resolution copy from Figure 2 in the paper). But what really amazed me was the suggestion that a display like this could be created in a few minutes, without doing any interpretation, by just manipulating instantaneous phase slices. With the only condition of having data of fair quality, this promised to be an awesome reconnaissance tool.


Figure 1 – Copyright SEG

The theory

The idea that instantaneous phase is a great attribute for interpretation has been around for a long time. There is, for example, a 1989 Exploration Geophysics paper by Duff and Mason [2]. These two authors argue that amplitude time slices are a suboptimal choice, and that instantaneous phase slices should be preferred. They give three reasons:

1) on amplitude time slices only relatively strong events remain above the bias level after gain and scaling. Weak events are submerged below the bias and remain unmappable.  Although it is the topic of a future post, it is worth mentioning I think this effect is exacerbated by the common but unfortunate choice of a divergent color palette with white in the middle. White is so bright (I call it white hole) that even more low amplitude events become indiscernible.

2) discrete boundaries corresponding to unique positions on the wavelet are displayed on instantaneous phase slices – this intra wavelet detail is lost on amplitude slices.

After-Duff-Mason 2

Figure 2 – after Duff and Mason, Figure 2

3) instantaneous time slices give DIRECTLY the sense of time dip for dipping events. In Figure 2 I show 2 parallel dipping reflectors, represented by 5 (non consecutive) traces, and 2 (non-consecutive) instantaneous phase slices (at arbitrary t1 an t2). I marked 5 discrete phase events for the top dipping reflector. The sense of time dip is given (with appropriate color palette) by the sense of color transition. Conversely, this intra wavelet detail would be lost on the amplitude time slices, with amplitudes between the black center trace and the red traces, and amplitudes between the red traces and the green traces lost within a single broad zone. The difference is probably not as dramatic nowadays with the increase in dynamic ranges available, but using instantaneous phase slices still remains advantageous for detailed mapping.

Beyer’s seismic terrain is just a natural extension of the instantaneous time slice as ( quoted from [1]):”… it then follows that the instantaneous phase (-180 deg to +180 deg) can simply be rescaled to the wavelength in ms of pseudoseismic two-way time… Seismic terrain can be thought of as a type of instantaneous wavelength generated from instantaneous phase along a time slice”. With reference to the top dipping reflector in Figure 3, the method allows generating converting the brown phase segment to the dipping blue segment (and similarly the yellow phase segment to the dipping green segment for bottom dipping event).


Figure 3

The practice – Petrel

Let’s see how we can create a terrain display similar to that in Figure 1 using Petrel.

Raw data

The process starts with migrated seismic data, from which we need generate both the phase and frequency component to get us the instantaneous wavelength.

For this tutorial I use a public seismic dataset (BPA9901) available on the Norwegian Public Data Portal. In Figure 4 below I am showing an amplitude time slice (above the Chalk) from the migrated seismic volume.


Figure 4

Step 1 – generate phase component

The first step is to generate an instantaneous phase attribute volume. This is found in the volume attributes. In Figure 5 below I am showing the instantaneous phase slice corresponding to the amplitude time slice of Figure 4.

*** N.B. *** If significant regional dips are observed in the seismic data, care should be taken in some cases  it may be beneficial (please see comment section) to remove them through flattening prior to the terrain generation.

Figure 5

Figure 5

Step 2 – generate frequency component

This is the trickiest part. In theory to get the instantaneous wavelength we would have to calculate the instantaneous frequency and divide the  instantaneous frequency attribute can be very noisy and can have spurious values in areas of low amplitude in the input data. A good practical alternative is to measure a single value of the dominant wavelet period T in an area of relatively flat reflections near the zone of interest as I am showing in Figure 6.

For the more avid readers, this is all explained quite nicely in Beyer (quoted from [1]): “Complex trace relationships dictate that the wavelength is the phase component divided by the frequency component. Thus one may be compelled to derive the seismic terrain by dividing the extracted instantaneous phase by the  extracted instantaneous frequency (carefully applying unit conversion of 1000 ms/ 360 deg or 2.78). However extracted instantaneous frequency tends to include spurious values in low amplitudes (approaching infinity according to literature and practice which correspond to poor data quality zones. Instantaneous frequency or even averaged instantaneous frequency renders the seismic terrain noisy, unrealistic, and misleading. Years of extensive use have shown that  single value of visually estimated dominant wavelet period (i.e. cycles per second) produces a very high-quality seismic terrain that closely fits the seismic events over wide areas”.


Figure 6

Step 3 – generate the instantaneous wavelength (seismic terrain)

Having estimated the dominant wavelet period T (in ms) , I can now use it to generate the instantaneous wavelength. We are essentially converting the data from the range [-180 180] deg to the range [-T/2 T/2] ms.

In Petrel I do it in the calculator with a formula of the type:

terrain=(((instantaneous phase +180)*T/2)/180)

The actual formula used is shown on the top row of Figure 7 below. You will notice that it isn’t exactly the same as the above formula. I added 1 to 180 to avoid division of zero values, e.g.:

(([-180 180]+180)*28/180) = ([0 180]*28/180) = ([0 5040]/180) % not good!


(([-180 180]+181)*28/180) = ([1 181]*28/180) = ([28 5068]/180) % good!

Once the division is performed I subtract T/2 again.

Notice from Figure 7 that because we added 181 but divided by 180 there is a small adjustment to be made by hand. I get this small adjustment by double clicking on the output volume to get the statistics. In this case it is +-0.16 ms, so I run a second time the formula (bottom row, Figure 7), this time subtracting T/2 +0.16 instead of just T/2.


Figure 7

Step 4 – display seismic terrain.

There are two options in Petrel to display the resulting seismic terrain volume:

Option 1 – display bump mapped terrain slices in 2D or 3D window

This is my preferred option for scanning up and down through the terrain slices. The bump mapping effect is done by double clicking on the terrain survey with a 2D or 3D window open and selected, in the Style tab>Intersection  tab. In Figure 8 I am showing the bump mapped terrain slice corresponding to the instantaneous phase time slice of Figure 5.


Figure 8

Option 2 – display selected horizons of interest in 3D window

One may want to create a display such as the one in Figure 1, which for me is intended for a later stage, when integrating perhaps with extracted amplitude or attribute anomalies highlighting hydrocarbon presence.

As often in Petrel there are different ways of achieving the same result. This is how I do it. First, I create a flat surface, with a TWT value corresponding to the slice I am interested in (as in Figure 9, left panel). Then I extract and append to this surface the terrain values from that slice of interest (as in Figure 9, right panel).

Figure 9

Figure 9

Figure 10

Figure 10

Finally, in the calculations tab, I add a constant time shift corresponding to the time associated with the slice  of interest: notice the difference in Z value between the left panel in Figure 10 (before the calculation), and the right panel (after the calculation). It is also necessary to use the extracted value as visual vertical position as illustrated in Figure 11.

Figure 11

Figure 11

I am showing the result in Figure 12. This is the same terrain slice as in Figure 8.

terrain_slice extracted

Figure 12


As a quick QC I am displaying in Figure 13 a vertical section (corresponding to the thick black line in Figure 12) from the input seismic data, with the extracted surface drawn as a thin black line.

The terrain deteriorates to the far left as we approach the edge of the survey, with fold decreasing and noise increasing, and there is a cycle skip towards the far right. But all in all I think  this is a very good result: it captures the faults well, and the whole process took less than 20 minutes with no picking.


Figure 13


This method has one limitation: the maximum fault throws or stratigraphic relief (in milliseconds) that can be mapped is equal to the period T.


I wish to thank DONG Energy for agreeing to the publication of the seismic images, which were generated using company licensed Petrel.

** UPDATE **

A few readers asked clarifications on what the benefits and potential uses are of using this attribute. The short answer is that this is in fact a pseudo-horizon that tracks dipping  seismic events accurately within the range of the period of the dominant frequency period (as seen in Figure 13), which makes it an excellent reconnaissance tool.  A good quality first pass map can be made in minutes in areas where detailed mapping can take days.  An excellent example is Figure 16 in the original paper [1].  More details can be found in the last two paragraphs of the paper:  Reservoir-scale structural data from seismic terrain and Fast 3-D screening. 


[1] Beyer, L. (2001). – Rapid 3-D screening with seismic terrain: deepwater Gulf of Mexico examplesThe Leading Edge, 20 (4), 386–395.

[2] Duff, B.A., and Mason, D.J. (1989) – The instantaneous-phase time slice: A crucial display for enhancing 3-D interpretationExploration Geophysics 20 (2) 213 – 217

8 thoughts on “Seismic terrain displays

  1. A couple of questions:

    1 Did you flatten the volume and then generate the attributes? Reason I ask is don’t you want to display resulting attributes along the regional dip?

    2) 56ms = one way or two way time?

    Thanks! I am having fun trying this out in Petrel in my spare time.

    • Hi Maitri

      2) Good question. 56 ms is TWT. I should add vertical scale to both Figure 6 and Figure 13.
      1) This is a very astute observation. Yes, I flattened the input volume and then created the terrain. In this particular case the regional dip increased the fault throws I was trying to map, so flattening helped bring them back to within the range of the dominant frequency period. Your comment makes me realize I generalized something that is not general. Does it make sense?
      I will correct my nota bene!


  2. Thanks for the replies so far, Matteo.

    So, your process is : flatten along horizon of interest –> measure TWT between successive peaks –> generate instantaneous phase and terrain attributes. After that, did you paint your flattened terrain attribute on your unflattened surface?

    Example: I have a sand reservoir (top is a seismic trough) in a steeply-dipping anticline (this qualifies as regional dip, correct?) that I want to generate this terrain attribute over. So, would I flatten on that trough or on the peak above it?

    Thanks again! I’ve seen this paper before but it is so interesting when someone has actually implemented it in everyday workflow software.

    • First question: I flattened on a shallow horizon that was easy to pick to remove the regional dips. Then I measured successive peaks in the vicinity of the zone of interest, where the reflectivity was really flat. Then I generated the terrain. I then painted the flattened attribut on flattened input data (Figure 13). You could also paint on unflattened input data but then you would have to add not just the constant time shift but also the horizon used for flattening.

      For your specific case I am not sure, I’d say trial and error is your best bet.

      I am starting to think I may have lead readers astray with this flattening by generalising a 1 in 10 cases when flattening helps. So I owe you one for pointing that out right away.

      Please also read the 2 last paragraphs in the paper (I added an update at the botom of the post based on questions by other readers).

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  4. @Matteo,
    I am skeptical of this, which might mean there are some things I don’t understand. First, in your theory section, you used the term ‘phase event’. I know what you mean in spirit, but I have a hard time pulling the word ‘event’ away from ‘amplitude’. I don’t really know what a ‘phase event’ is, though I follow your story. The instantaneous phase would have to be relative to some envelope, No? See my post on E is for Envelope, Moreover, Is your sketch merely just the same ‘event’ just shifted in time. And if so, then travel time is another instantaneous attribute…a measure of overburden velocity heterogeneity, or structural relief / typography for instance.

    Come to think of it, an interesting attribute would be the the travel-time difference (delta T in ms), between the maxima on the envelope, and the maxima on the real part of the seismic trace. I am not sure if that is mathematically equivalent to what you are showing here. but I can imagine phase shifts relative to an ‘event envelope’, without the need for a travel-time shift.

    The features, and general ‘informationness’ shown in the amplitude time slice, (your figure 4), does not look all that much different from the from the instantaneous phase (your figure 5). Does placing them on a different color palette misconstrue? Instantaneous phase slice suffers from an wrapping problem, but are there actually features that are enhanced here?

    No matter what, you’ve done creative work here, and put Petrel’s calculators to good use. Kudos for that! Maybe a co-rendering of amplitude (grayscale) and phase (yellow-green-black) would curb my skepticism.

    • Evan

      Thank you so much for your feedback and great comments.
      You do well to be skeptical on the theory section. I went through it and I realize it is unclear and can use a major rewrite, which I plan to do in a followup post. In short for now, with reference to figure 1, this is indeed a schematic sketch, where I repeated for simplicity the same trace over 5 times. These are amplitude traces and the dipping events are in fact dipping reflections. t1 and t2 are time slices, and can represent either amplitude or phase slices. When amplitude slices, then the intersections of traces are peaks, zero crossing, or trough events, corresponding to phase ‘events’ (I know it is perhaps an unfortunate choice of term, but I kept it for consistency with the original paper) of 0 degrees, +/- 90 degrees, and +/-180 degrees respectively. I think both the sketch and the explanation must be improved. I am still waiting to hear back about permission to reuse the figures from the original Duff and Mason paper; once I do I will either use them or improve my sketch.

      I take your point and your tweet ( on envelope. This is something that is worthwhile spending some time experimenting on, and perhaps writing a separate post on. I’ll follow-up.

      On the ‘informationness’ of Figure 4, and 5: there are a few considerations here. Firstly, in my eagerness to use a perceptual color palette for the instantaneous phase time slice (Figure 5) I forgot to make it a cyclical one to account for the wrapping of the attribute. I will correct this. And I think a zoom in on an area with some features of interest would be good. But I do believe the instantaneous phase is an enhancement. The best description I found of it is in the book 3-D Seismic Interpretation ( “…the instantaneous phase display looks like a seismic display with a very short gate AGC applied; amplitude information is suppressed…then the instantaneous phase section makes it easier for the interpreter to spot angular relationship in low amplitude parts of the seismic section”. I think this is not something I want to take as gospel, in fact I’d like to do some modelling to put the idea to the test, in addition to real data. Hopefully I will be able to follow up on that too.
      By the way, I just found today this recent two-part series on phase on AAPG Explorer.
      Now, mind you, let’s beware of Explorer papers (as you reminded me today I haven’t finish reading the papers yet but I find the figure on unwrapping phase and the discussion intriguing.

      Now to go back to the seismic terrain, I do believe in its value as a very fast reconnaissance tool, for both volume scanning and for reservoir scale detailed mapping, at least preliminary. As I wrote in the UPDATE at the end of the post, this is really well exemplified in Beyer’s paper. Perhaps you can take a look and let me know what you think.

      I look forward to continuing the discussion.

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