Seismic migration
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Seismic migration is the process by which seismic events 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 a more 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. Migration moves dipping reflectors to their true subsurface positions and collapses
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
s, resulting in a migrated image that typically has an increased
spatial resolution In physics and geosciences, the term spatial resolution refers to distance between independent measurements, or the physical dimension that represents a pixel of the image. While in some instruments, like cameras and telescopes, spatial resolutio ...
and resolves areas of complex geology much better than non-migrated images. A form of migration is one of the standard data processing techniques for reflection-based geophysical methods (
seismic reflection Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismi ...
and
ground-penetrating radar Ground-penetrating radar (GPR) is a geophysical method that uses radar pulses to image the subsurface. It is a non-intrusive method of surveying the sub-surface to investigate underground utilities such as concrete, asphalt, metals, pipes, cables o ...
) The need for migration has been understood since the beginnings of seismic exploration and the very first seismic reflection data from 1921 were migrated. Computational migration
algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing c ...
have been around for many years but they have only entered wide usage in the past 20 years because they are extremely resource-intensive. Migration can lead to a dramatic uplift in image quality so algorithms are the subject of intense research, both within the geophysical industry as well as academic circles.


Rationale

Seismic waves are elastic waves that propagate through the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
with a finite velocity, governed by the elastic properties of the rock in which they are travelling. At an interface between two rock types, with different
acoustic impedance Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The SI unit of acoustic impedance is the pascal-second per cub ...
s, the seismic energy is either
refracted In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
, reflected back towards the surface or attenuated by the medium. The reflected energy arrives at the surface and is recorded by
geophone A geophone is a device that converts ground movement (velocity) into voltage, which may be recorded at a recording station. The deviation of this measured voltage from the base line is called the seismic response and is analyzed for structure of ...
s that are placed at a known distance away from the source of the waves. When a
geophysicist Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...
views the recorded energy from the geophone, they know both the travel time and the distance between the source and the receiver, but not the distance down to the reflector. In the simplest geological setting, with a single horizontal reflector, a constant velocity and a source and receiver at the same location (referred to as zero-offset, where offset is the distance between the source and receiver), the geophysicist can determine the location of the reflection event by using the relationship: :d=\frac, where d is the distance, v is the seismic 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 of the total travel time to reach the reflector from the source, then the other half to return to the receiver. The result gives us a single
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...
value, which actually represents a half-sphere of distances, from the source/receiver, which the reflection could have originated from. It is a half-sphere, and not a full sphere, because we can ignore all possibilities that occur above the surface as unreasonable. In the simple case of a horizontal reflector, it can be assumed that the reflection is located vertically below the source/receiver point (see diagram). The situation is more complex in the case of a dipping reflector, as the first reflection originates from further up the direction of dip (see diagram) and therefore the travel-time plot will show a reduced dip that is defined the “migrator’s equation” : :\tan \xi_a = \sin \xi, where is the ''apparent dip'' and is the ''true dip''. 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 non-zero offsets, the sphere becomes an
ellipsoid An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a surface that may be defined as the ...
and is much more complex to represent (both geometrically, as well as computationally).


Use

For a geophysicist, 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 The lithology of a rock unit is a description of its physical characteristics visible at outcrop, in hand or core samples, or with low magnification microscopy. Physical characteristics include colour, texture, grain size, and composition. Lit ...
which causes a sharp change in seismic wave velocity). Some examples of what a geophysicist considers complex geology are:
faulting In geology, a fault is a planar fracture or discontinuity in a volume of rock across which there has been significant displacement as a result of rock-mass movements. Large faults within Earth's crust result from the action of plate tectonic ...
, folding, (some) fracturing, salt bodies, and
unconformities An unconformity is a buried erosional or non-depositional surface separating two rock masses or strata of different ages, indicating that sediment deposition was not continuous. In general, the older layer was exposed to erosion for an interval ...
. In these situations a form of migration is used called 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 honours velocity changes more accurately than post-stack migration.


Types of migration

Depending on budget, time restrictions and the subsurface geology,
geophysicists Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' so ...
can employ 1 of 2 fundamental types of migration algorithms, defined by the domain in which they are applied: time migration and depth migration.


Time migration

Time migration is applied to seismic data in time coordinates. This type of migration makes the assumption of only mild lateral
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
variations and this breaks down in the presence of most interesting and complex subsurface structures, particularly salt. Some popularly used time migration algorithms are: Stolt migration, Gazdag and Finite-difference migration.


Depth migration

Depth Migration is applied to seismic data in depth ( regular Cartesian) coordinates, which must be calculated from seismic data in time coordinates. This method does therefore require a velocity model, making it resource-intensive because building a seismic velocity model is a long and iterative process. The significant advantage to this migration method is that it can be successfully used in areas with lateral velocity variations, which tend to be the areas that are most interesting to
petroleum geologists Petroleum, also known as crude oil, or simply oil, is a naturally occurring yellowish-black liquid mixture of mainly hydrocarbons, and is found in geological formations. The name ''petroleum'' covers both naturally occurring unprocessed crude ...
. Some of the popularly used depth migration algorithms are Kirchhoff depth migration, Reverse Time Migration (RTM), Gaussian Beam Migration and Wave-equation migration.


Resolution

The goal of migration is to ultimately increase spatial resolution and one of the basic assumptions made about the seismic data is that it only shows primary reflections and all noise has been removed. In order to ensure maximum resolution (and therefore maximum uplift in image quality) the data should be sufficiently pre-processed before migration. Noise that may be easy to distinguish pre-migration could be smeared across the entire aperture length during migration, reducing image sharpness and clarity. A further basic consideration is whether to use 2D or 3D migration. If the seismic data has an element of cross-dip (a layer that dips perpendicular to the line of acquisition) then the primary reflection will originate from out-of-plane and 2D migration cannot put the energy back to its origin. In this case, 3D migration is needed to attain the best possible image. Modern seismic processing computers are more capable of performing 3D migration, so the question of whether to allocate resources to performing 3D migration is less of a concern.


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 the diagram.


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 Kirchhoff 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 Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
) 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 In geophysics (primarily in oil-and-gas exploration/development), seismic inversion is the process of transforming seismic reflection data into a quantitative rock-property description of a reservoir. Seismic inversion may be pre- or post- stack, d ...
). 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.


See also

*
Reflection seismology Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismi ...
* Seismic Unix, open source software for processing of seismic reflection data


References

{{Reflist Geophysics Seismology