This section is intended to introduce various aspects of the art, which may be associated with the present technological advancement. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present technological advancement. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
In the oil and gas industry, seismic prospecting techniques are commonly used to aid in the search for and evaluation of subterranean hydrocarbon deposits. A seismic prospecting operation consists of three separate stages: data acquisition, data processing, and data interpretation.
In the data acquisition stage, a seismic source is used to generate a physical impulse known as a “seismic signal” that propagates into the earth and is at least partially reflected by subsurface seismic reflectors (i.e., interfaces between underground formations having different acoustic impedances). The reflected signals (known as “seismic reflections”) are detected and recorded by an array of seismic receivers located at or near the surface of the Earth, in an overlying body of water, or at known depths in boreholes. The seismic energy recorded by each seismic receiver is known as a “seismic data trace.”
During the data processing stage, the raw seismic data traces recorded in the data acquisition stage are refined and enhanced using a variety of procedures that depend on the nature of the geologic structure being investigated and on the characteristics of the raw data traces themselves. In general, the purpose of the data processing stage is to produce an image of the subsurface geologic structure from the recorded seismic data for use during the data interpretation stage. The image is developed using theoretical and empirical models of the manner in which the seismic signals are transmitted into the Earth, attenuated by the subsurface strata, and reflected from the geologic structures. The quality of the final product of the data processing stage is heavily dependent on the accuracy of the procedures used to process the data.
The purpose of the data interpretation stage is to determine information about the subsurface geology of the earth from the processed seismic data. For example, data interpretation may be used to determine the general geologic structure of a subsurface region, or to locate potential hydrocarbon reservoirs, or to guide the development of an already discovered reservoir. Obviously, the data interpretation stage cannot be successful unless the processed seismic data provide an accurate representation of the subsurface geology.
In complex geological environments, wave equation migration is recognized to be a good imaging technique currently available for imaging seismic data. Wave equation migration comes in two forms usually called WEM and RTM. In WEM (“Wave Equation Migration”), energy is back propagated from the receivers using a one-way wave equation, and forward propagated from the corresponding source. The wave fields are cross correlated at each image point to create the subsurface seismic image. This method can produce good images for reflectors whose dip is relatively shallow. In RTM (“Reverse Time Migration”), the wave field at the receivers is back-propagated using a two-way wave equation, and is cross correlated with energy forward propagated from the source. This method can produce good images at all reflector dips, but is more expensive than WEM by a factor typically in the range of 4-10.
Ray-based and wave-based imaging algorithms are often both used for a depth imaging project. A typical ray-based method, such as Kirchhoff migration, is almost always used because of its efficiency and flexibility in forming surface-offset gathers, which are subsequently used for driving tomography or image enhancement. On the other hand, wave-based methods, such as reverse time depth migration (RTM) and one-way wave equation migration (WEM), are frequently used for imaging complex geology. However, wave-based imaging algorithms suffer from inefficiencies associated with forming attribute gathers, such as surface-offset gathers, commonly used for evaluating and updating a migration velocity model because the surface-offset attribute gets mixed and lost during shot record migration.
One expensive way to generate wave-equation based surface offset gathers is to migrate the data bin by bin. This method, due to its huge cost, is hereby referred to as the brute force method. The brute force method involves splitting the seismic data into numbers of offset bins. Then each bin of data is carried through the migration engine. The computation cost is proportional to the number of offset bins desired, which is usually in the orders of 20-30 for wide azimuth data or 80-100 for narrow azimuth data. This method generates the most accurate surface offset gathers at huge computational cost (see reference 1 below).
An inexpensive way to estimate a data attribute, such as surface-offset distance between the source and receiver for RTM and WEM, is the so-called expectation method (see references 2 and 3 below).
The expectation method generally works as follows:    1. Denote the original data as “data 0”;    2. Weight “data 0” by a desired attribute to define “data 1”;    3. Migrate “data 0” and “data 1” separately to obtain “image 0” and “image 1” respectively; and    4. In the image domain, divide “image 1” by “image 0” to obtain an estimate of the desired attribute at each location in the image with regularization to avoid division by very small values.
However, this expectation method suffers from several drawbacks. The method is single-valued. If the data includes multiple reflections or other types of coherent noise, the estimated attribute is going to be biased toward the value appropriate for larger amplitude events, which may or may not be the desired event. The larger amplitude events could be events associated with multiple reflections rather than more desirable primary reflection events. The method for an attribute, such as surface-offset distance, is influenced by the surface-geometry irregularity. Therefore, if no regularized shots are available, an inaccurate estimate of the surface is obtained.
The following references, which are discussed herein, are hereby incorporated by reference in their entirety:    Reference 1—J. Etgen, “3D Wave Equation Kirchhoff Migration,” SEG 2012 Annual Meeting Conference Proceedings, pp. 1-5;    Reference 2—U.S. Patent Publication 2014/0149046;    Reference 3—N. Bleistein, “On the imaging of reflectors in the earth,” Geophysics, Vol. 52, No. 7, July 1987, pp. 931-942; and    Reference 4—Santos et al., “Modeling by demigration,” SEG Technical Program Expanded Abstracts, 1997, pp. 1909-1912.
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