Methodology

The polarity flip angle depends on both velocity fields and on the reflector's dip. Its determination is of crucial importance for the polarity regularization. This section describes the basic steps of our methodology for the polarity flip angle determination and polarity regularization. The algorithm that we use is:

1.

Migrate common shot gathers to offset-domain CIGs.

2.

Transform offset-domain gathers into angle-domain gathers Sava and Fomel (2000).

3.

Determine the polarity flip angle, $\theta_o$ with equation (9).

4.

Flip negative polarities in the angle domain.

5.

Stack over angle to produce a final structural image.

The first step is to transform the data to the temporal frequency domain; subsequently, we downward continue the shot and receiver wavefields with v_p and v_s respectively, and image the data at zero time. In this way, we obtain the offset-domain CIGs, and if we use the correct velocity models, the energy is focused close to zero offset.

The common angle gathers are evaluated in the Fourier-domain by equation (10). The method involves a radial-trace mapping after migration in the k_h-k_z domain Sava and Fomel (2000). Rickett and Sava (2001) describe how we prepare the offset-domain CIGs with a shot-profile migration algorithm.

 

$$\tan \theta = - \frac{\vert\vec{k_h}\vert}{k_z}.$$ (10)

To determine the structural dip, we apply plane-wave destructors Fomel (2000), which characterize the seismic images as a superposition of local plane waves. With the dip field and the two migration velocity models, we calculate the polarity flip angle using equation (9). Flip the polarity is an easy process after we have the polarity flip angle: we just apply a mask to the common angle gathers that follows the polarity flip angles and multiply the data by -1.