Nonhyperbolic normal moveout stretch correction with deep learning automation

Normal moveout (NMO) correction is a fundamental step in seismic data processing. It consists of mapping seismic data from recorded traveltimes to corresponding zero-offset times. This process produces wavelet stretching as an undesired byproduct. We address the NMO stretching problem with two methods: 1) an exact stretch-free NMO correction that prevents the stretching of primary reflections, and 2) an approximate post-NMO stretch correction. Our stretch-free NMO produces parallel moveout trajectories for primary reflections. Our post-NMO stretch correction calculates the moveout of stretched wavelets as a function of offset. Both methods are based on the generalized moveout approximation and are suitable for application in complex anisotropic or heterogeneous environments. We use new moveout equations and modify the original parameter functions to be constant over the primary reflections, and then interpolate the seismogram amplitudes at the calculated traveltimes. For fast and automatic modification of the parameter functions, we use deep learning. We design a deep neural network (DNN) using convolutional layers and residual blocks. To train the DNN, we generate a set of 40,000 synthetic NMO corrected common midpoint gathers and the corresponding desired outputs of the DNN. The data set is generated using different velocity profiles, wavelets, and offset vectors, and includes multiples, ground roll, and band-limited random noise. The simplicity of the DNN task –a 1D identification of primary reflections– improves the generalization in practice. We use the trained DNN and show successful applications of our stretch-correction method on synthetic and different real data sets.

Seismic anelastic attenuation estimation using prestack seismic gathers

The seismic quality factor [Formula: see text] quantifies the anelastic attenuation of seismic waves in the subsurface and can be used in assisting reservoir characterization and as an indicator of hydrocarbons. Usually, the [Formula: see text]-factor is estimated by comparing the spectrum changes of vertical seismic profiles and poststack seismic data. However, seismic processing such as the normal moveout (NMO) stretch would distort the spectrum of the seismic data. Hence, we have estimated [Formula: see text] using prestack time migration gathers. To mitigate the NMO stretch effect, we compensate the NMO stretch of prestack seismic gathers in the time-frequency domain. Similar to the log spectral method, our method obtains the [Formula: see text] by measuring the log spectral ratio (LSR) of seismic events of the top and base of the reservoir at a zero-offset seismic trace. The LSR has a linear relationship with a new parameter [Formula: see text] by assuming that the source wavelet is a constant-phase wavelet. The parameters [Formula: see text] and LSR vary with the offset value (traveltime). We use the values of [Formula: see text] and LSR obtained from nonzero-offset seismic traces to simulate the values of [Formula: see text] and LSR at a zero-offset seismic trace. Finally, we obtain [Formula: see text] by applying the classic LSR method to the simulated [Formula: see text] and LSR. To demonstrate the validity and effectiveness of our method, we first apply it to noise-free and noisy synthetic data examples and then to real seismic data acquired over the Sichuan Basin, China. The synthetic and real seismic applications demonstrate the effectiveness of our method in highlighting high anelastic-attenuation zones.

Horizon-based semiautomated nonhyperbolic velocity analysis

With higher capacity recording systems, long-offset surveys are becoming common in seismic exploration plays. Long offsets provide leverage against multiples, have greater sensitivity to anisotropy, and are key to accurate inversion for shear impedance and density. There are two main issues associated with preserving the data fidelity contained in the large offsets: (1) nonhyperbolic velocity analysis and (2) mitigating the migration/NMO stretch. Current nonhyperbolic velocity analysis workflows first estimate moveout velocity [Formula: see text] based on the offset-limited gathers, then pick an effective anellipticity [Formula: see text] using the full-offset gathers. Unfortunately, estimating [Formula: see text] at small aperture may be inaccurate, with picking errors in [Formula: see text] introducing errors in the subsequent analysis of effective anellipticity. We have developed an automated algorithm to simultaneously estimate the nonhyperbolic parameters. Instead of directly seeking an effective stacking model, the algorithm finds an interval model that gives the most powerful stack. The searching procedure for the best interval model was conducted using a direct, global optimization algorithm called differential evolutionary. Next, we applied an antistretch workflow to minimize stretch at a far offset after obtaining the optimal effective model. The automated velocity analysis and antistretch workflow were tested on the data volume acquired over the Fort Worth Basin, USA. The results provided noticeable improvement on the prestack gathers and on the stacked data volume.

Nonstretch normal moveout through iterative partial correction and deconvolution

Source to receiver distances used in seismic data acquisition have been steadily increasing and it is now common to work with data acquired with more than 10 km of offset. Subbasalt exploration and seismic undershooting are just two applications in which long-offset reflections are sought. However, such reflections are often subjected to muting to suppress normal moveout (NMO) stretch artifacts, thus causing a loss of valuable information. To retrieve these portions of the recorded wavefield, we developed a nonstretch NMO correction based on wavelet estimation and on an iterative procedure of partial NMO correction and deconvolution. We evaluated this methodology using fourth-order traveltime curve approximations to increase the offset of usable reflections, but it can be adapted to traveltime curves of any order. Time- and space-variant wavelets, estimated by means of singular value decomposition along the sought traveltimes, were used to build the desired output for the deconvolution that aims at retrieving the original shape of the partially stretched wavelets. We tested our method on a synthetic gather presenting time and offset varying wavelets, on a real-marine line simulating an undershooting pattern and on true undershooting land-marine data. These examples demonstrated that our new algorithm effectively limits the stretching associated with the NMO correction and enables the recovery of those portions of the stacked sections that are typically lost from muting in the standard NMO correction.

Nonstretching NMO correction of prestack time-migrated gathers using a matching-pursuit algorithm

Wide-azimuth, long-offset surveys are becoming increasingly common in unconventional exploration plays where one of the key routine processes is maintaining data fidelity at far offsets. The conventional NMO correction that processes the data sample-by-sample results in the well-known decrease of frequency content and amplitude distortion through stretch, which lowers the seismic resolution and hinders [Formula: see text] and amplitude variation with offset and azimuth (AVAz) analysis of the long-offset signal. To mitigate the stretch typically associated with large offsets, we use a matching-pursuit-based normal moveout correction (MPNMO) to reduce NMO-stretch effects in long-offset data. MPNMO corrects the data wavelet-by-wavelet rather than sample-by-sample, thereby avoiding stretch. We apply our technique (1) to a set of synthetic gathers and (2) as part of a residual velocity analysis workflow to a prestack time-migrated data volume acquired over the Northern Chicontepec Basin, Mexico. Test results show that MPNMO can produce relatively nonstretched events and generate higher temporal resolution prestack gathers.