Communications – electrical: acoustic wave systems and devices – Seismic prospecting – Land-reflection type
Reexamination Certificate
2003-04-07
2004-11-16
Moskowitz, Neloson (Department: 3663)
Communications, electrical: acoustic wave systems and devices
Seismic prospecting
Land-reflection type
C367S063000, C367S073000, C175S050000, C166S250010, C702S014000, C702S016000
Reexamination Certificate
active
06819628
ABSTRACT:
FIELD AND BACKGROUND OF THE INVENTION
The present invention relates to seismic migration and particularly its use in imaging and, more particularly, but not exclusively to seismic migration using a Krylov space expansion of the square root operator to approximate a wave equation to allow rapid and accurate modeling of wave propagation between layers.
Geological surveying has widespread applications, for example to locate oil and gas reserves whether on land or offshore. In the past, surveying was carried out by looking at surface geological formations and using the surveyor's knowledge and experience to determine locations of underground or subsurface structures likely to contain reserves. A trial bore was then made at the determined location and tested for the presence of hydrocarbons.
The above process owed much to trial and error, and trial bores are expensive. There is therefore a need to reduce the number of trial bores needed for successful discovery. Thus, more recently methodology has been developed to assist the surveyor by allowing him to learn about the sub-surface structure during the initial survey and prior to making a trial bore. Knowing about the substructure allows for a more educated location of the trial bore and thus improves the efficiency of the surveying process.
One method of finding substructure formations uses satellite imaging. Another method uses seismic imaging. In seismic imaging, a technique similar in principal to radar and sonar is used, in which the time taken by sound waves to travel through the sub-surface structure and return to the surface is measured and used to infer the structure. Seismic data is obtained by sending an energy pulse (basically a sound wave) into the earth and then listening for it to be reflected off rock layers and return to the surface. The time it takes for the pulse to return indicates how far it has traveled. The direction and timing of the received wave indicate where it bounced off a rock layer and allows an image to be constructed indicating the position of those layers.
Seismic imaging can be used in conjunction with software analysis to produce three dimensional images of subsurface rock formations. Seismic imaging thus reduces the trial and error dimension of surveying and provides for greater efficiency.
In more detail, sound waves are produced by a seismic source. The seismic source may for example be a small underground explosion referred to hereinafter as a shot. Dynamite is common on land, and air guns which produce large bubbles are common in water. Another way of producing sound waves is known as Vibroseis, in which a heavy vehicle is shaken in such a way as to produce a set of vibrations. The sound waves subsequently propagate into the earth and partially reflect from interfaces, across which the subsurface velocity or the density varies discontinuously. The reflected waves are recorded by recording devices, known as geophones (or hydrophones in marine surveys), which are usually placed in the vicinity of the surface, or within well bores. The time history of each device, which records the amplitude of the waves detected following a given shot, is stored as a seismic trace. The objective is to deduce the sub-surface structure from the recorded data.
Important in constructing an image from shot data are the relative locations of shot sources and geophones as well as information of the actual energy source used. The relative locations of shot source and geophones dictates the region of the subsurface that is imaged and the resolution level of that image.
Seismic migration or imaging is the process by which the seismic data is mapped to form an image of the subsurface. In general, this mapping requires knowledge of the subsurface velocity. The subsurface velocity is highly variable, depending on the type of material in the subsurface structure. The fact of such velocity variability in the first few kilometers beneath the Earth's surface makes the task of seismic imaging more difficult than other types of acoustical imaging, such as for example ultra-sound and sonar which are carried out through a broadly unified medium. A description of the seismic method and of seismic imaging can be found in standard texts such as M. Dobrin and C. Savit: Introduction to Geophysical Prospecting. McGraw-Hill, New York. 1988, O. Yilmaz. Seismic Data Processing. Society of Exploration Geophysics. 1987, the contents of which are hereby incorporated by reference.
Depth migration refers to a type of imaging which maps the time recorded input seismic traces, that is the time history recorded at each device referred to above, into a subsurface spatial image, taking into account the different velocities at different depths in the structure. Migration is based on solution of a governing wave equation. Most often the acoustic wave equation is used because of its simplicity, and because it produces the correct arrival times of primary (P) waves. However, when more accurate results are required, the elastic equations, or other more elaborate equations may be used. The specific embodiments of the imaging technique disclosed herein use the acoustic wave equation. However the same technique can be applied to imaging based on other types of wave equations, such as the elastic wave equations.
Depth migration methods can be roughly divided into two categories; methods based on direct solution of the wave equation, often termed wave equation migration, and methods based on geometrical optics based approximate solutions to the wave equations. The latter have been termed in the exploration industry as Kirchhoff migration. Kirchhoff migration has been considered faster and more flexible in accepting irregular source-receiver geometry. The downward propagation of the surface data as modeled in wave equation migration is not based on geometrical optics approximations and is thus more realistic although harder to compute. Consequently wave equation migration type approaches are considered to have the potential of producing more accurate results. The embodiments of the present invention described below apply to wave equation migration.
The Basis of Wave Equation Imaging
Considering current art wave equation imaging in greater detail, the surface recorded seismic data can be grouped in different ways, for example, according to shots. In grouping according to shot, all seismic traces produced by a given shot are aggregated together into what is known as a common shot gather. As an alternative, seismic traces may be grouped according to receivers. That is all traces recorded by a surface receiver are aggregated together into a common receiver gather. As a third possibility, grouping according to offsets, all traces for which the shot-receiver separation falls within a specified range are aggregated together into a common offset gather. Each of the above types of data grouping, and other, similar possibilities, has its own imaging method, but the general imaging principles behind all methods are similar. For the sake of clarity and conciseness, the following discussion is limited to acoustic common shot imaging of surface recoded reflection data. The skilled person will appreciate how to apply the principles to the other methods.
Let p(x,y,z=0, t) represent the time history of receivers for a given shot, where (x, y) are the horizontal coordinates of each receiver position. The plane (z=0) defines the surface of the earth, which in the present discussion is assumed to be flat. If needed the scheme can be modified to account for topography. The seismic migration, or imaging, consists of two steps:
1. Extrapolation of the surface data p(x,y,z=0,t) in depth to form p(x,y,z,t).
2. Application of an imaging condition to create the subsurface image P
mig
(x,y,z).
The subsurface image can be calculated according to p
mig
(x,y,z)=p(x,y,z,t=t
d
), where t
d
is the time of arrival of a direct wave from the shot location to the subsurface location, see M. Reshef and D. Kosloff. Migration of common shot gathers. Geop
G.E. Ehrlich (1995) Ltd.
Moskowitz Neloson
Paradigm Geophysical (Luxembourg) S.a.r.l.
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