The equivalent offset method of prestack time migration

Abstract

A prestack time migration is presented that is simple, efficient, and provides detailed velocity information. It is based on Kirchhoff prestack time migration and can be applied to both 2-D and 3-D data. The method is divided into two steps: the first is a gathering process that forms common scatterpoint (CSP) gathers; the second is a focusing process that applies a simplified Kirchhoff migration on the CSP gathers, and consists of scaling, filtering, normal moveout (NMO) correction, and stacking. A key concept of the method is a reformulation of the double square‐root equation (of source‐scatterpoint‐receiver traveltimes) into a single square root. The single square root uses an equivalent offset that is the surface distance from the scatterpoint to a colocated source and receiver. Input samples are mapped into offset bins of a CSP gather, without time shifting, to an offset defined by the equivalent offset. The single square‐root reformulation gathers scattered energy to hyperbolic paths on the appropriate CSP gathers. A CSP gather is similar to a common midpoint (CMP) gather as both are focused by NMO and stacking. However, the CSP stack is a complete Kirchhoff prestack migrated section, whereas the CMP stack still requires poststack migration. In addition, the CSP gather has higher fold in the offset bins and a much larger offset range due to the gathering of all input traces within the migration aperture. The new method gains computational efficiency by delaying the Kirchhoff computations until after the CSP gather has been formed. The high fold and large offsets of the CSP gather enables precise focusing of the velocity semblance and accurate velocity analysis. Our algorithm is formulated in the space‐time domain, which enables prestack migration velocity analysis to be performed at selected locations and permits prestack migration of a 3-D volume into an arbitrarily located 2-D line.

Application of the equivalent offset migration method in acoustic log reflection imaging

“…In addition, the acoustic reflection signals inevitably suffer from boreholeguided mode interference leading to very low SNR compared with input traces in surface seismic migration operations (Chabot et al, 2002;Tao et al, 2008a and2008b). Bancroft et al (1998) formally introduced an equivalent offset migration method (EOM). The method forms common scatter point (CSP) gathers and applies a simplified Kirchhoff migration on the CSP gathers.…”

Simultaneous estimation of subsurface properties from CSP gather

“…In a chain of seismic reflection data processing, seismic migration is an essential step to migrate reflection events to right location to visualize an accurate underground structure. Equivalent offset migration (EOM) 1) , which is one of pre-stack migration methods, is known as a simple and effective wave-equation-based method without any interpolation techniques. In our previous study, we noticed the effectiveness to use the horizontal component of Common Scatter Point (CSP) gather produced in the processing of EOM for both the normal moveout velocity and for AVO analyses of S-waves that have been recognized important for lithological interpretation 2) .…”

Numerical Simulation of Ultrasonic Detection for Concrete Structure Based on Equivalent Offset Migration

“…40 . Thus, we can find that this method is essentially Kirchhoff integration scatter imaging, which is called equivalent offset migration (EOM) [14].…”

“…Bancroft and Geiger (2011) introduced an alternative technique initially known as common scatter point (CSP) migration and now is named equivalent offset migration (EOM) [11][12][13][14][15]. This method was also applied in other relative fields due to its advantage in imaging scattered waves [16,17].…”

“…Scattered wave imaging method is based on the concept of equivalent offset and CSP gather [11,14]. We assumed that the concrete material is composed by a large number of single scatter points.…”