--> --> Abstract: Accurate Conversion between Offset Image Gathers and Angle Image Gathers, by Jianming Sheng and Chengbin Peng; #90105 (2010)
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AAPG GEO 2010 Middle East
Geoscience Conference & Exhibition
Innovative Geoscience Solutions – Meeting Hydrocarbon Demand in Changing Times
March 7-10, 2010 – Manama, Bahrain

Accurate Conversion between Offset Image Gathers and Angle Image Gathers

Jianming Sheng1; Chengbin Peng1

(1) Nexus Geosciences Inc., Sugar Land, TX.


Most Previous HitmigrationNext Hit methods produce either Previous HitcommonNext Hit-Previous HitoffsetNext Hit-gathers (COG) or common-angle-gathers (CAG) gathers. But none produce both, that is until now. We have developed an accurate and efficient method that converts Previous HitcommonNext Hit Previous HitoffsetNext Hit image gathers to common angle image gathers, or vice versa. The practical uses of the method are for velocity analysis or AVO studies using existing commercial toolkits.


The need for an accurate gather conversion method from Previous HitcommonNext Hit-Previous HitoffsetNext Hit-gathers (COG) to common-image-gathers (CAG), and vice versa, stems from the manifold applications of COGs and CAGs. Uses of COGs of depth migrated Previous HitdataNext Hit include updating the subsurface velocity from residual moveouts, and inversion for rock properties from amplitude variations with offset. CAGs, on the other hand, are partitioned according to opening angles at the subsurface rather than the source-receiver offset at the surface, as is the case with COGs. Hence CAGs have advantages over COGs in that they allow tomography programs to use specular ray pairs more naturally and provide amplitude versus angle information more readily. Sometimes individual angle volumes are more interpretable than either stacked volumes or individual offset volumes. A typical case illustrating this is found in sub-horizontal strata underneath a salt wedge (Helsing and Berman, 2006).

A gather conversion method is developed based on the diplet decomposition technology (Peng, 2006). A 3D seismic volume can be expressed as the superposition of components that we call “diplets”. Each “diplet” carries distinct information about its spatial location (x, y, z), orientation (inline dip and crossline dip), amplitude, wavelet, acquisition configuration (acquisition offset and acquisition azimuth), coherency, and derived attributes such as reflection angle, reflection azimuth, wavelet stretch, beam spread, wavefront curvature etc.

The diplet’s special and unique structure allows for the simultaneous storage of surface acquisition and subsurface reflection information. It makes demigration and remigration more convenient and efficient through the process of transformation of diplets between the unmigrated time-domain and migrated depth-domain using dynamic ray tracing. It also simplifies the gather conversion task: binning and sorting the migrated diplets according to acquisition offsets or local reflection angles is all that is required. The process is not only accurate but also extremely efficient.


Let’s assume COGs are available and they are already decomposed into diplets. As shown in Fig. 1, one such decomposed diplet will have its focal point X coordinates, normal direction of the reflector and acquisition offset and azimuth on the surface. The reflection angle can be calculated by searching for two rays (XS and XR, from image point X to acquisition surface S and R, respectively), and by minimizing the difference between the vector SR and the vector determined by a given acquisition distance and azimuth.
Next, let’s assume CAGs are available and they are already decomposed into diplets. Similarly, a decomposed diplet for a given CAG will have the reflection angle as well as its focal point X coordinates and normal direction of the reflector. The offset can be estimated by searching two rays XS and XR which satisfy Snell’s law at the image point and that make the same reflection angle; the distance of SR provides the approximation of the acquisition offset.

After each diplet obtains a correct offset and reflection angle attribute, it is sorted and binned along with all the other diplets according to acquisition offset or reflection angle - thus COGs or CAGs can be readily produced by diplet syntheses. As a special note, specular ray pairs are obtained during this searching procedure, and thus the diplets can also be sorted according to some other attributes, like reflection azimuth, to get other types of user-defined image gathers.

Since the COGs or CAGs are decomposed into diplets, and the searching procedure is completed by ray tracing, this gather conversion method is very efficient.

Numerical Example

A test of the conversion from COG to CAG and back is performed to demonstrate the efficiency of the method. A total of 40 offsets in the input COGs were used with offsets from 1350ft to 20538ft. Fig. 2 depicts a few extracted common-image-gathers (CIG), in which it appears that far-offset reflections contribute more to the subsalt illumination. The COGs were then converted into CAGs, as shown in Fig. 3. The angles are from 0 - 60 degrees in 2 degree increments. As expected the angular coverage decreases rapidly with depth, especially subsalt.

These CAGs were subsequently converted back to COGs to check the accuracy. The main features are preserved quite well in the roundtrip conversions, as shown in Fig. 4 .


A gather conversion method is developed to provide common angle image gathers when only Previous HitcommonNext Hit Previous HitoffsetNext Hit image gathers are available, or vice versa. Numerical results show that it is accurate, fast and cost effective compared to a full volume depth Previous HitmigrationNext Hit. A practical use of this technology is, by way of example, to convert WEM angle gathers to Previous HitcommonNext Hit Previous HitoffsetNext Hit gathers for velocity updating and AVO analysis. It can be also used to convert Previous HitcommonNext Hit Previous HitoffsetNext Hit image gathers to common angle image gathers for AVO analysis, which is more accurate than the conventional one dimensional offset to angle conversion method (which also assumes constant velocity and flat layering).


The authors thank Nexus Geosciences Inc. for permission to publish the research results.

680347_A.jpgFig. 1 A diplet at subsurface X is demigrated subjected to acquisition offset or azimuth constraints, that is, the source and receiver points are offset by a given distance (for Previous HitcommonNext Hit-Previous HitoffsetNext Hit-gathers), or are along a direction of a given azimuth.