Migration To Zero Offset Research Articles

Autofocusing of UWB MIMO GPR Images by Using MZO and Entropy Minimization

In this letter, an autofocusing method for ultra-wideband ground-penetrating radar imaging with multiple-input multiple-output (MIMO) configuration is proposed. The proposed method is based on the minimization of the entropy of the images that have been migrated by frequency-wavenumber migration. A particular migration to zero-offset (MZO) operator is applied to reduce the processing complexity for MIMO data. The results on the simulation data show that the computation time of the autofocusing process is reduced significantly with the MZO operator, while some advantages of the MIMO configuration are successfully preserved.

The common reflecting element (CRE) method revisited

The common reflecting element (CRE) method is an interesting alternative to the familiar methods of common midpoint (CMP) stack or migration to zero offset (MZO). Like these two methods, the CRE method aims at constructing a stacked zero‐offset section from a set of constant‐offset sections. However, it requires no more knowledge about the generally laterally inhomogeneous subsurface model than the near‐surface values of the velocity field. In addition to being a tool to construct a stacked zero‐offset section, the CRE method simultaneously obtains information about the laterally inhomogeneous macrovelocity model. An important feature of the CRE method is that it does not suffer from pulse stretch. Moreover, it gives an alternative solution for conflicting dip problems. In the 1-D case, CRE is closely related to the optical stack. For the price of having to search for two data‐derived parameters instead of one, the CRE method provides important advantages over the conventional CMP stack. Its results are similar to those of the MZO process, which is commonly implemented as an NMO correction followed by a dip moveout (DMO) correction applied to the original constant‐offset section. The CRE method is based on 2-D kinematic considerations only and is not an amplitude‐preserving process.

True‐amplitude transformation to zero offset of data from curved reflectors

Transformation to zero offset (TZO), alternatively known as migration to zero offset (MZO), or the combination of normal moveout and dip moveout (NMO/DMO), is a process that transforms data collected at finite offset between source and receiver to a pseudozero offset trace. The kinematic validity of NMO/DMO processing has been well established. The TZO integral operators proposed here differ from their NMO/DMO counterparts by a simple amplitude factor. (The form of the operator depends on how the input and output variables are chosen from among the combinations of midpoint or wavenumber with time or frequency.) With this modification in place, the dynamical validity for planar reflectors of the proposed TZO operators of this paper have been established in earlier studies. This means that the traveltime and geometrical spreading terms of the finite offset data are transformed to their counterparts for zero offset data, while the finite offset reflection coefficient is preserved. The main purpose of this study is to show that dynamical validity of the TZO operator extends to the case of curved reflectors in the 2.5-D limit. Thus, at the cost of a simple additional multiplicative factor in any standard NMO/DMO operator to produce the corresponding TZO operator, the amplitude factor attributed to curvature effects in finite offset data is transformed by this TZO processing to the corresponding curvature factor for zero offset data. This problem has also been addressed in a more general context by Tygel and associates. However, in the generality, some of the specifics and interpretations of the simpler problem are lost. Thus, we see some value in presenting this analysis where one can carry out all calculations explicitly and see specific quantities that are more familiar and accessible to users of DMO. Furthermore, in this paper, we show how processing of the input data with a second TZO operator allows for the extraction of the cosine of the preserved specular angle, a necessary piece of information for amplitude versus angle (AVA) analysis. We then discuss the possibility of using the output of our processing formalism at multiple offsets to create a table of angularly dependent reflection coefficients and attendant incidence angles as a function of offset. This is the basis of a proposed amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of the pseudozero offset traces. Finally, we describe the modifications of Hale DMO and Gardner/Forel DMO to obtain true amplitude output equivalent to ours and also how to extract the cosine of the specular angle for these forms of DMO. This last does not depend on true amplitude processing, but only on processing two DMO operators with slightly different kernels and then taking the quotient of their peak amplitudes.

2.5-D true‐amplitude Kirchhoff migration to zero offset in laterally inhomogeneous media

The proposed new Kirchhoff‐type true‐amplitude migration to zero offset (MZO) for 2.5-D common‐offset reflections in 2-D laterally inhomogeneous layered isotropic earth models does not depend on the reflector curvature. It provides a transformation of a common‐offset seismic section to a simulated zero‐offset section in which both the kinematic and main dynamic effects are accounted for correctly. The process transforms primary common‐offset reflections from arbitrary curved interfaces into their corresponding zero‐offset reflections automatically replacing the geometrical‐spreading factor. In analogy to a weighted Kirchhoff migration scheme, the stacking curve and weight function can be computed by dynamic ray tracing in the macro‐velocity model that is supposed to be available. In addition, we show that an MZO stretches the seismic source pulse by the cosine of the reflection angle of the original offset reflections. The proposed approach quantitatively extends the previous MZO or dip moveout (DMO) schemes to the 2.5-D situation.

Migrating around on hyperbolas and parabolas

The term “migration” in seismic reflection imaging is traditionally used to describe a strategy by which one can transfer primary time‐domain reflections (e.g., as observed in a common‐shot or common‐offset section) into their correct spatial positions on the searched‐for subsurface reflector. It is also employed to describe a strategy to transfer primary reflections into their time‐migrated positions directly in the time domain. More recently, the term migration has also been used to describe the process by which primary reflections, as observed in a common‐offset (CO) section, are transferred to the positions where they would be observed in the zero‐offset (ZO) section. The latter procedure is referred to as migration‐to‐zero offset (MZO). It is the subject to which we want to contribute.