Dr. Ian Jones, Senior Geophysical Adviser, ION GX Technology, London
Title: Extended imaging conditions for shot migration
Held: Thursday 4 October 2018, 11AM–12PM
Wavefield extrapolation migration of shot records involves downward continuing a synthetic source wavefield down into the earth, and at the same time, backward (upward) continuing the actual real recorded wavefield back into the earth.
At each propagation time-step, these two 3D wavefields are multiplied together, and at the end of the extrapolation process (when we’ve exhausted all the useful propagation time) all these hundreds of 3D product volumes are summed together to form the image contribution resulting from this particular shot record.
This summation of wavefield products is referred to as the convolutional imaging condition in shot migration: the image is being formed by what is essentially a correlation of downgoing and upcoming wavefields.
This process is repeated for all available shots, and all these overlapping 3D shot-contribution volumes are summed to form the full migrated image of the study area.
However, each of the elemental sub-images resulting from the migration of an individual shot-record only contains a zero-offset trace: there is no inherent pre-stack gather resulting from this process. The convolutional imaging condition only produces the image, and not gathers. Hence, to create a gather (say for use in subsequent velocity analysis of AVA study) we need to invoke some additional computational tricks.
The most widely used of these methods is called an extended imaging condition. The idea in an extended imaging condition is to shift the downgoing and upcoming 3D wavefield volumes with respect to each other just before they are multiplied together. These shifted product volumes are then summed as before to form the imagine contribution from this particular shot record. This shifting procedure is repeated several times, so that we end-up with many 3D imaged volumes for each shot, rather than a single image volume for the shot.
If we re-sort these shift-volumes into gathers, then we now have a pre-stack gather that can be used to velocity analysis and further post-processing prior to stack. The shifting can be done in four different ways: laterally in inline, laterally in crossline, vertically in depth, or vertically in propagation time. It could also be done in depth with respect to the reflector normal, but that is a bit too demanding. These shifting methods are referred to as extended imaging conditions. Alternatively, the 3D source and receiver wavefields can be preconditioned at each propagation time step prior to multiplication by filtering with respect to propagation direction (Poynting vector filtering: Poon & Marfurt, 2006). The history of these techniques dates back to focussing analysis in 2D preSDM (Faye &Jeannot, 1986; Audebert & Diet, 1990, MacKay & Abma, 1992) through to the more recent works of Sava & Fomel, 2003, 2006, and Biondo & Symes 2004, and others).
The basic shift-gather is not very intuitively useful, but they can be converted into subsurface ‘true’ angle gathers via various transforms. However, all this shifting and transforming suffers from aliasing of the underlying data due to poor sampling (primarily in the crossline direction). Hence we tend to work with angle gathers as a projection on the inline, rather than trying to extract both incident angle and azimuth). If we use a lateral inline or crossline shift, then the extended imaging condition gathers are called sub-surface-offset gathers, and if we shift vertically in propagation time, they’re called time-shift gathers. Either can be converted to angle gathers, ready for RMO picking and velocity update, or post-processing, etc. In the GXT RTM software, as can output most of these extended imaging condition gathers, but currently prefer to use the vertical propagation time delay gathers, as these are thought to be less error prone. These time shift gathers are then converted to angle gathers via a tau-p transform and a velocity scaling procedure.