Geophysical migration is the process by which geophysical events (changes in energy) are geometrically re-located in either space or time to the location the event occurred in the subsurface rather than the location that it was recorded at the surface, thereby creating an accurate image of the subsurface. This process is necessary to overcome the limitations of geophysical methods imposed by areas of complex geology, such as: faults, salt bodies, folding, etc. The end result is that the migrated image typically resolves these areas of complex geology much better than non-migrated images. Consequently, a form of migration is one of the standard data processing techniques for certain geophysical methods (seismic and ground penetrating radar). Computational migration needed for large datasets acquired today is extremely demanding on modern computers and is the subject of intense research, both within the geophysical industry as well as academic circles.

Need for Migration

A zero-offset non-migrated data set. Raw zero-offset data for a simple syncline in a constant velocity world. Notice the signature bow-tie effect in the image. This is the result of reflections occurring from both sides of the syncline, and arriving at the same receiver at different times. Migration can correct this effect.

Seismic waves are elastic waves that travel through the Earth with a finite velocity, which is governed by the material properties of the rocks. When the waves reach a rock unit with a different velocity some of the seismic energy is either absorbed, transmitted to the next layer, or reflected back towards the surface by the reflector (new rock layer). The reflected energy from these velocity contrasts arrive at the surface, and are recorded by Geophones that are placed at certain location away from the source of the waves. When a Geophysicist views the recorded energy from the Geophone, the geophysicist can only view the energy that was recorded at that location, but has no way of determining where it came from in the subsurface because (unlike Sonar), the seismic energy is not directed in the Earth. In the case that the source and receiver are at the same location (referred to as Zero-offset, where offset is the distance between the source and receiver), the geophysicist can guess at the event's location by (in the constant velocity world) using the relationship$d = (1/2)r*t$ where d is the distance, r is the velocity (or rate of travel) and t is the measured time from the source to the receiver. In this case, the distance is halved because it can be assumed that it only took one-half the time from the reflector to the receiver, rather than the full measured time from the source to the receiver.

A zero-offset migrated data set of the File:SimpleSyncline.jpg data. This data was migrated using a time-migration referred to as phase-shift which operates in the Fourier domain. The migration has replaced all events in their correct locations, successfully reconstructing a syncline. However, there are erroneous events (swinging arcs) throughout the image which are migration induced noise.

The result is troubling though, because it gives us only a singular value (a scalar). Therefore, the event could have come anywhere that has the same distance to the receiver. The result is that a half-sphere (a half-sphere, because we can ignore all possibilities that occur above the surface as unreasonable) represents all the possible locations that the event could have come from. This leads to zero-offset migration, wherein it can be assumed that the event came from somewhere on the sphere at that distance.

Zero-offset data is important to a geophysicist because the migration operation is much simpler, and can be represented by spherical surfaces. When data is acquired at offsets, the sphere becomes an ellipsoid, which is much more complex to represent (both geometrically, as well as computationally). Therefore, geophysicists would like to get their data to zero-offset before migrating it, because zero-offset migration is faster.

Zero-offset migration is more commonly referred to as Post-stack migration, wherein zero-offset traces are moved about in an image. Typically post-stack migration does a good job at imaging, but may fail in areas of complex geology due to some broad simplifications in the algorithms. Also, it is important to note, that in practical surveys data is almost always collected at offset, and then converted to zero-offset data. In doing so, much information is discarded for simplicity's sake.

For all intents and purposes, complex geology is defined as anywhere there is an abrupt or sharp contrast in lateral and/or vertical velocity (e.g. a sudden change in rock type or lithology which causes a sharp change in seismic wave velocity). Some examples of what a geophysicist considers complex geology are: faulting, folding, (some) fracturing, salt bodies, and unconformities.

In these situations a form of migration is used that is referred to as pre-stack migration (PreSM), in which all traces are migrated before being moved to zero-offset. Consequently, much more information is used, which results in a much better image, along with the fact that PreSM honors velocity changes more accurately than post-stack migration.

Graphical Migration

The simplest form of migration is that of graphical migration. Graphical migration assumes a constant velocity world and zero-offset data, in which a geophysicist draws spheres or circles from the receiver to the event location for all events. The intersection of the circles then form the reflector's "true" location in time or space. An example of such can be seen in.

An example of simple graphical migration. Until the advent of modern computers in the 1960s and 1970s this was a method used by geophysicists to primitively 'migrate' their data. This method is obsolete with the advent of digital processors, but is useful for understanding the basic principle behind migration.

Types of Migration

Migration operators can be applied in both the time and space domains. The main difference between the two is how well the operator respects the velocity model. Time migrations typically use average values for velocity in computations, and as a result tend to poorly image overly complex areas. Time migrations are quick, and sufficient for areas with minor structural complexity. Depth migrations use the full velocity model, which leads to a (typically) much better image than time migration. However, depth migrations are substantially more expensive computationally than time migrations.

Time Migration

There are many formulations of Time migrations. Some of the more famous time migrations are: Stolt migration, Gazdag, and Finite-difference migration.

Depth Migration

There are many formulations of Depth migrations. Some of the more prominent depth migrations are: Kirchoff migration, Reverse Time Migration (RTM), Gaussian Beam Migration, and Wave-equation migration.

Technical Details

Migration of seismic data is the correction of the flat-geological-layer assumption by a numerical, grid-based spatial convolution of the seismic data to account for dipping events (where geological layers are not flat). There are many approaches, such as the popular Kirchoff migration, but it is generally accepted that processing large spatial sections (apertures) of the data at a time introduces fewer errors, and that depth migration is far superior to time migration with large dips and with complex salt bodies.

Basically, it repositions/moves the energy (seismic data) from the recorded locations to the locations with the correct common midpoint (CMP). While the seismic data is received at the proper locations originally (according to the laws of nature), these locations do not correspond with the assumed CMP for that location. Though stacking the data without the migration corrections yields a somewhat inaccurate picture of the subsurface, migration is preferred for better most imaging recorder to drill and maintain oilfields. This process is a central step in the creation of an image of the subsurface from active source seismic data collected at the surface, seabed, boreholes, etc., and therefore is used on industrial scales by oil and gas companies and their service providers on digital computers.

Explained in another way, this process attempts to account for wave dispersion from dipping reflectors and also for the spatial and directional seismic wave speed (heterogeneity) variations, which cause wavefields (modelled by ray paths) to bend, wave fronts to cross (caustics), and waves to be recorded at positions different from those that would be expected under straight ray or other simplifying assumptions. Finally, this process often attempts to also preserve and extract the formation interface reflectivity information imbedded in the seismic data amplitudes, so that they can be used to reconstruct the elastic properties of the geological formations (amplitude preservation, seismic inversion). There are a variety of migration algorithms, which can be classified by their output domain into the broad categories of Time Migration or Depth Migration, and Pre-Stack Migration or Post-Stack migration (orthogonal) techniques. Depth migration begins with time data converted to depth data by a spatial geological velocity profile. Post-Stack migration begins with seismic data which has already been stacked, and thus already lost valuable velocity analysis information.