Monday, 28 April 2014

Marine Processing - Part 10 | Migration

This sequence of blog posts will build up into a complete description of a 2D marine processing sequence and how it is derived.
No processing sequence is definitive and techniques vary with   time (and software), however the idea is to provide a practical guide for applying seismic processing theory.

The seismic line used is TRV-434 from the Taranaki Basin offshore New Zealand. It is the same marine line used in our basic tutorial dataset.

The data are available from New Zealand Petroleum and Minerals, under the Ministry of Economic Development under the “Open File” System.
The processing sequence developed so far:

  • Reformat from field data (in this case, SEGY)
  • Apply a combined minimum-phase conversion and anti-alias filter
  • Resample to a 4ms sample interval

  • Assign 2D marine geometry; 12.5m CDP spacing and 60 fold gathers
  • QC shots and near trace plots

  • Amplitude recovery using a T2 Spherical divergence correction
  • Amplitude QC and Edit using peak and RMS amplitude displays

  • Swell noise suppression using projective filtering
  • Interpolation to 6.25m group interval, 480 channels to unwrap spatially aliased dips
  • Tau-p transform 500ms robust AGC "wrap", 960 p-values and transform range from -1400ms -1 to +1400 ms-1
  • Tail mute to remove linear arrivals and linear noise
  • Predictive deconvolution: 32ms gap, 480 ms operator
  • Rho filter for low frequency compensation
  • Inverse Tau-p transfrom
  • Interpolation back to 25m group interval, 240 channels

  • NMO correct with 90% of primary velocity
  • Form 120-fold supergathers
  • Parabolic Radon Demultiple
    • Transform range -300ms to 500ms far-offset moveout;  200 p-values
    • Multiple  removed from +24 to +500ms far-offset moveout
    • Application from 1400ms onwards
  • For 60-fold CDP gathers from supergathers
  • Remove 90% NMO correction

Re-pick Velocities

In practice, we only get coherent reflections (that are in the correct lateral position) when the rock layers are flat and continuous.
One way to think of this is to consider the “zero-offset normal ray” section. This is where the reflected ray-path between a source and receiver at the same location at the surface makes a right-angle with the reflecting layer.

An example of “zero offset normal rays” that illustrates why only flat events will be correctly positioned laterally on a normal ray section.  The recorder at the surface has no directional information, so both reflections will appear on the same trace at different times, as shown on the right

In effect the “zero offset normal ray” section is a stack – we have corrected the source-receiver offset to zero using the  NMO correction on a CDP gather, and then stacked (summed) the traces together.

As well as the “ray path” view we can also think of how waves propagate based on Huygen’s Principle. Where we have discontinuities (such as faults, or intrusions) the secondary wavelets used in Huygen’s construction will not fully constructively or destructively interfere, giving rise to diffractions.

When looking at a stacked section, the key things to remember are that:
  • dipping events will be mispositioned laterally and appear less steep than they really are
  • the steeper the dip the greater the degree of mispositioning
  • discontinuities (such as faults, or intrusions) will give rise to diffractions
  • diffracted events may cross reflected events

In order to resolve these issues we need to migrate the data.

Stacked (left) and migrated (right) portions of the TRV-434 seismic line.  The migrated events are a little steeper and have moved laterally up-dip.  Diffractions caused by faults and events that are not continuous have been collapsed.  Crossing complex events have been resolved.

Migration uses a mathematical model to reposition data to its correct lateral position and collapse diffractions. This usually requires some kind of velocity model; as computation speeds have improved it has become practical to use algorithms that can work with more complex – or realistic – velocity models.

Post stack migrations (of the type shown above) have largely been replaced by pre-stack migration techniques.  In pre-stack migrations the data are formed into offset planes which are migrated to their near-offset position and time, which replaces the NMO correction and the migration stage.

In this case the line we are working on has some fairly steep dips and complex ray-paths; after a couple of rounds of velocity picking you will have come across some situations where the velocities are hard to pick;  this is because we have diffracted events (which do not have hyperbolic moveout) as well as dipping events.
Dipping events cause problems not only because the reflection hyperbola is distorted, but because the “common mid-point” is smeared and shifted up-dip.

Illustration of how the common midpoint (CMP, also called CDP) does not contain information from a single sub-surface location (or bin) when the events are dipping. The green ray paths show what we might assume is happening when collect data by its common mid-points, however the red ray paths show the actual ray paths for the shortest (near) and longest (far) offsets – these are both displaced up dip, by differing amounts

Pre-stack migration resolves this issue allowing better velocities to be picked and improved focussing to be obtained on dipping events. For that reason it is common to create a new velocity field after pre-stack time migration, and, in some cases, run a second iteration of the pre-stack time migration with that new velocity model.

Velocities picked on pre-stack time migrated data are a better approximation to the actual RMS velocity of the sub-surface layers, and so can be more useful as a starting point for depth conversion.

A good way to understand the migration parameters is to look at some impulse response functions; this will show you the shape of the migration operator with different parameters.  You can do this by zeroing all of the traces, and placing some suitable ricker wavelets at different time values then running migrations.

An impulse response function showing the full pre-stack time migration operator for a trace at CDP 1100, with an offset of 1283m, and 35Hz Ricker wavelets at 1000ms, 2000ms, 3500ms, 5000ms.  Since the pre-stack time migration corrects to zero offset, the operators include a correction for normal moveout. The migration was run a “open” parameters and a migration velocity of 1480 ms.-1

The parameters we can vary do two things.  They serve to speed up the migration (by limiting the operator in terms of its spatial extent) as well as reduce or remove artefacts from the data.

The main artefacts we want to eliminate are wavelet stretch, which occurs for the same reason as NMO stretch which picking velocities, and aliasing of the operator shape. The operator becomes aliased because (usually) the vertical sampling of the data (time sample interval converted to distance) is at a much higher resolution than the horizontal sampling (the CDP spacing).

In this case, we have a 4ms sample interval at a constant velocity of 1480ms-1, which corresponds to a 2.96m vertical resolution (remembering we are looking at two-way-time), and the CDP spacing is 12.5m.  As a result the operator will be spatially aliased at high angles.

Impulse response function of a 80Hz Ricker wavelets through pre-stack time migration with a constant velocity (left) with a close up variable-area/wiggle (VAWG) display on the right showing detail of the operator at a high dip angle (right);  note the wavelet  of the operator caused by spatial aliasing.  To migrate this without aliasing we would need to be able to represent the 80Hz wavelet horizontally at 1480 ms-1, which corresponds to a full wavelength of 18.5m.  With two samples per wavelength, this would need a CDP spacing of 9.25m, as opposed to the 12.5m spacing we have

The main controls we usually have in a pre-stack time migration are:

Migration Aperture, or Range
The horizontal distance that a trace is allowed to migrate.  Cuts off the migration operator at a specific distance, usually from the CDP position of the trace pre-migration. 
Reduces how many input traces contribute to each output trace, and so makes the migration run faster.  Reduces the ability to image steep dip, deep events.
Migration Angle
Limits the maximum angle of the migration, usually measured from the vertical trace at the CDP location out to the operator, so that 90 degrees is horizontal.
Reduces how far each trace migrates, so requires less calculation runs more quickly if applied in the algorithm and not as a mute.  Can act as a way of reducing both stretch and aliasing, and is approximately the maximum dip to image.
Anti-Alias Filtering
Acts to limit the operator shape where it might become aliased or distorted spatially;  usually has various degrees (weak, medium, strong) that can be applied
Little impact on speed of migration, as it can be computationally expensive to compute the limits even though less data is migrated;  if applied as a mute can actually slow down the migration.  Avoid artefacts where you have rapid lateral or vertical velocity gradients, and a single dip value is inappropriate.  
Stretch Muting
Acts to limit the operator if the shape of the wavelet is too distorted in time. Similar effect to NMO stretch.
Reduces low-frequency artefacts in the shallow-mid portion of the data.  May cause the near surface to be muted, unless there is a “near angle protection” option.

Pre-stack time migration operators from an impulse response function, with some limits applied.  In this case the red line shows the angle parameter, set to 60o, and the blue vertical line shows the effect of limiting the migration aperture to 2500m, which in this case corresponds to 200 cdps.  The input trace is at CDP 1100.  With a constant 1480ms-1 velocity, the angle parameter cuts of the migration before it is spatially aliased, although the shallow event is still stretched.  No stretch mute was applied

Pre-stack time migration is a zero-offset 'image ray' migration. This means the results will look like data that has zero offset between source and receiver. However, unlike the NMO correction, these will also be corrected for the dip of any reflectors. In the zero-offset 'image ray' migration, the rays are normal to the surface - not the rock interface.

Zero offset ray-paths for the normal ray (red) and images rays (orange) to a complex interface.  The image ray is identical to the normal ray if the interface is horizontal.  Where the interface is dipping, the image ray path starts and ends at a surface position (blue circle) that is above the reflection point on the interface.  The normal ray path for the dipping interface starts and ends at a different surface location (purple circle), which is laterally miss-positioned from the reflection point

The results of a pre-stack time migration will be zero-offset image ray gathers; these will be “flattened gathers” if:
  • the input velocity model was correct
  • we don’t have to worry about anisotropy
  • we don’t have to worry about the ray paths being refracted

In practice, these are all likely to be approximations. The velocities we supplied came from normal-ray gathers, and so as we identified earlier they are contaminated by dip.
Beyond 45° or so, we need to start worrying about anisotropic behaviours; this is where the simple second-order normal moveout equation breaks down and we must pick higher order terms and use anisotropic migrations.

Finally, if we have significant refractions as a result of rapid lateral or vertical velocity gradients, then we need to think about using a pre-stack depth migration.  

When we examine the gathers after migration we can look at whether we need to modify or re-
pick the velocities (sometimes called picking residual moveout or RMO) before making a final stack.

If the residual moveout is large it might be worth using the new velocity field and running a new migration. This could be another iteration of the same algorithm, however if there are non-hyperbolic components to the residual moveout then you might need to consider if it is worth the time and effort to move to a more sophisticated migration algorithm.

Stacked (top), post-stack time migrated (middle) and pre-stack time migrated (bottom) sections from TRV-434, using the same velocity model and with a 500ms robust AGC applied. The key thing to observe is the improved imaging of the steeper dip, strong amplitude events and reduction in noise between the post- and pre-stack migrations (circled); this is typically where a pre-stack time migration offers advantages

By: Guy Maslen

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