Technical Information
Radon DMO
A Superior Method for Irregularly Sampled 3D Surveys
In 1995 Vector introduced a new dip-moveout (DMO) processing method in the Radon domain called Radon DMO. Radon DMO performs very well on regularly or irregularly sampled datasets. High frequencies are maintained by Radon DMO and amplitude relationships are preserved. Fourier and integral 3D DMO programs often require conditioning (trace interpolation and/or superbinning) prior to DMO in order to perform adequately on surveys with irregular geometry. These processes tend to make the output look smoother, but precision is sacrificed. Radon DMO does not require trace interpolation nor superbinning to perform well on such surveys. In both regularly and irregularly sampled data sets, it can be demonstrated that precursor and aliasing noises are reduced greatly by using Radon DMO.
Many 3D datasets are irregularly sampled with respect to fold, azimuth, and offset. Population deficiencies are exaggerated in the common offset domain such that the usually superior Fourier methods often produce questionable results. Integral (Kirchoff) DMO methods are implemented for 3D datasets largely for practical reasons, but these methods can be adversely affected by irregularly sampled data as well. To compensate, the integral methods should be nonaliased, which means that no precursor noise is introduced. However, even using the best nonaliased integral DMO methods for irregularly sampled data, the difficulties of obtaining good results are well-known. In order to succeed, the 3D DMO operator must be dealiasing. This means that no precursor noise is generated when data are irregularly sampled.
Conventional Integral (Kirchoff) DMO Methods
Conventional Integral DMO methods yield impulse responses that have an elliptical shape. Traces typically are sorted to common offset groups then mapped along elliptical trajectories in the space-time domain. After DMO correction, constructive and destructive interference yield the zero-offset reflections. In cases where data are poorly sampled, processing noise is caused by some remaining points that are not fully cancelled. Therefore, to accomplish all necessary destructive interference, conventional integral DMO must be implemented in the offset domain and requires regularly-sampled data.
Radon DMO Method
The Radon map of the DMO ellipse is a hyperbola. For a reflection in a zero-offset wavefield, the DMO ellipse mapping operator for a singular offset should introduce destructive interference to cancel all points of the ellipses except those along the reflection, such as that in Figure 1a. For the Radon DMO method, corresponding traces are directly mapped along hyperbolas in the Radon domain; all hyperbolas correspond to the ellipses and intersect at one point, producing a strong amplitude at this location. Figure 1b shows this phenomenon.
The Radon DMO method accepts input traces from singular or multiple offsets and yields correct results. If we supply traces from multiple offsets for conventional integral DMO methods, the destructive interference is incomplete. Figure 2a suggests this situation. In the Radon domain, however, the impulse response from the varying-offset traces only changes the shape of the hyperbolas, which still intersect at the point (t0,p0), such as that in Figure 2b. In the Radon domain, noises are cancelled more effectively and signal is preserved.
Figure 3 compares conventional Integral DMO with Radon DMO. The input data has gaps in the offset domain before DMO. Figure 3a is the result after applying conventional DMO; Figure 3b is the result after Radon DMO. In Figure 3b, precursor noise is insignificant while the phases and amplitude are well preserved.
Applications
Figure 4 compares DMO results on an irregularly-sampled 3D land dataset. For simplicity, one stacked crossline is shown. Note the improved signal to noise, frequency preservation, and superior steep-dip imaging in the Radon DMO result.
Conclusions
Radon DMO offers several advantages for processing surveys with less-than-ideal acquisition characteristics. First, missing traces do not cause serious spatial aliasing, precursor noise, or unbearable distortions of phase and amplitude. Second, Radon DMO does not require that input traces have the same offset. Third, the DMO corrected output can be either stacked or unstacked which enables the full range of post-DMO processing, including AVO and post-DMO velocity analysis. Fourth, Radon DMO does not require trace interpolation nor superbinning to perform well on surveys with irregular geometry; this makes it ideal for bin fractionation processing and steep-dip imaging objectives (e.g. salt dome flanks). Fifth, most integral methods include the application of a 45-degree phase shift as well as offset-, time-, and frequency-dependent gain factors when spreading the traces along ellipses. Such compensations are generally unnecessary with Radon DMO which greatly simplifies program development. Radon DMO not only provides high quality DMO-correction imaging but is also excellent for amplitude and frequency preservation. Radon DMO was developed by Vector Seismic Data Processing, Inc. The paper "DMO in Radon Domain" was presented at the SEG annual meeting (Houston, 1995), "Radon DMO Amplitude and Frequency Preservation" was presented at the SEG meeting (Denver, 1996) and "Dip-Moveout in Radon Domain" is published in Geophysics, 1999.