Calculation of the bin size and migration aperture in a 3-D seismic survey design using a linear velocity model: A case study of Ahwaz Oil Field

In oil exploration, because of the anisotropy of the earth, the velocity of the waves in horizontal and vertical directions are not uniform; however, with a good accuracy in exploration procedures, we can assume that in a layer, velocity changes are limited as a results of slow variations in density as well as the elastic properties of the layers in these horizontal directions. In general, variations of the above mentioned parameters in horizontal directions are much slower than in vertical ones. For this reason, the acquisition area is often divided into smaller areas; horizontal variations are neglected while the same vertical velocity distributions are applied in any sub-area.
There are basically two methods in calculation of the bin  size and migration aperture in a 3-D seismic survey design. The first method is based on using a constant velocity model which is not compatible with real conditions. In this model, we assume that the medium between the surface of the earth and the target layer is replaced with supposed layer and ascribe a constant amount velocity to this layer that is equal to the average velocity in medium between the surface and the target layer. The second method uses the model wherein the velocity changes with depth and therefore a linear velocity model is assumed which is more compatible with reality in comparison with the previous method. Whereas the linear velocity method can include all important wave propagation effects, it involves a certain circular logic. This method, involves building a detailed subsurface velocity model and uses ray tracing or other simulation techniques to customize the survey for the local subsurface.
In Ahwaz Oil Field, the main target was Asmari Formation and the deep target was Fahlian Formation. The 3-D seismic survey design of Ahwaz Oil Field was performed on the main target located in the depth of 2900 m and the deep target located in the depth of 5000 m from the mean sea level. Ground level was about 15 to 40 m higher than the sea level in this area. By considering the check shot, VSP and sonic log data from 14 well logs, the image area was divided into 14 parts, so that the variations of the horizontal velocity could be neglected in each part and the constant contribution for the vertical velocity could be used. Finally, using the velocity values at the desired vertical depth to the reflection point (target depth), the dip angles of the target horizon (dip of reflector at the reflection Point) and the maximum frequency reflected from the main target, we were able to calculate the bin size and migration aperture in each part. At last, we could select a value for the bin size in this project.
In this study, we examined the parameters of the velocity-dependent 3-D seismic survey design. These parameters included the bin size and migration aperture. Conventional formula for the bin size and migration aperture for Ahwaz Oil Field was carried out based on the linear model between the velocity and depth. As an intermediate between constant velocity and interval velocity model, we have given expressions valid for a linear velocity function. By using the linear velocity model, the design parameters incorporated first-order ray bending. Hence, this method was adjusted to the reality and led to better results compared to a constant velocity model.
Linear V(z) is an attractive approximation for three reasons. First, this kind of velocity variation captures the first-order effect of the pressure and the temperature increases with depth. It does not require detailed knowledge of the subsurface velocities. Second, analytical expressions are available for the ray path geometry and travel times in such a medium. Third, the linear V(z) propagation allows turning waves which have potential for imaging dips beyond 90 degrees.
Migration aperture is overestimated by constant velocity calculations, whereas the bin size is underestimated and this results in an increase in costs. On the other hand, calculations based on a linear velocity model require a less migration aperture and a larger bin size. The bin size and migration aperture are two sensitive economy parameters. Hence, using a larger bin size and a smaller migration aperture obtained from a linear velocity model, the cost of a 3-D seismic survey design will be decreased.