Normal moveout for long offset in isotropic media using the Padé approximation

The normal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-depth ratio and thus fails at large offset-to-depth ratios. We approximate the long-offset moveout using the Padé approximation. This method is superior to typical methods and flattens the seismic gathers over a wide range of offsets in multilayered media. For a four-layer model, traditional methods show traveltime errors of about 5 ms for offset-to-depth ratio of 2 and greater than 10 ms for offset-to-depth ratio of 3; in contrast, the maximum traveltime error for the [3, 3]-order Padé approximation is no more than 5 ms at offset-to-depth ratio of 3. For the Cooper Basin model, the maximum offset-to-depth ratio for the [3, 3]-order Padé approximation is typically double of those in typical methods. The [7, 7]-order Padé approximation performs better than the [3, 3]-order Padé approximation.