Short-wavelength Statics Research Articles

Low-rank-based residual statics estimation and correction

Surface consistency forms the basis for short-wavelength statics estimation. When raypaths in the near surface diverge from a normal incidence or when the normal moveout (NMO) velocity is inaccurate, surface-consistent methods may fail to estimate accurate statics. Existing nonsurface-consistent techniques can be prone to errors due to the need to construct pilot traces or pick horizons while imposing additional computational costs. To overcome these limitations and correct for the surface- and nonsurface-consistent statics, we have developed a low-rank-based residual statics (LR-ReS) estimation and correction framework. The method makes use of the redundant nature of seismic data by using its low-rank structure in the midpoint-offset-frequency domain. Due to the near-surface effect, the low-rank structure is destroyed. Therefore, we estimate the statics by means of low-rank approximation and crosscorrelation. To alleviate the need for accurate rank selection for low-rank approximation and improved statics estimation, we implement the method in an iterative and multiscale fashion. Because the low-rank approximation deteriorates at high frequencies, we use its better performance at low frequencies and exploit the common statics among the different frequency bands. The LR-ReS estimation and correction can be applied to data without an NMO correction, which makes statics estimation independent of the NMO velocity errors. Consequently, it can reduce the multiple iterations of the NMO velocity estimation and short-wavelength statics correction commonly needed for conventional methods to improve their performance. Moreover, the LR-ReS estimation does not require windowing of a noise-free area containing aligned primaries or mute to avoid the NMO stretch effect, which enables statics correction of the wavefield of all offsets. To evaluate the performance of our method, we apply it to simulated data and a challenging field data set affected by complex weathering layers and noise, which indicate a substantial improvement compared with conventional short-wavelength statics correction.

Derivation of refraction statics solution for 3D seismic data in an onshore prospect Niger Delta field

The near-surface imaging and characterization of an onshore prospect field in the Niger Delta was successfully carried out in a previous study (Adizua et al. 2019) using an integrated approach of combining inversion of refracted arrivals and uphole measurements. The output of that study which revealed the layer characteristics of the near-surface (0–500 m) over the prospect field is now being used as a starting model to derive a complete refraction statics solution to be adapted for processing the 3D seismic dataset from the prospect field. The complete statics solution derived included the field or datum statics, refraction statics, and the 1st and 2nd residual statics which addressed the unresolved and remnant spatial long and short wavelength statics effect on the traces across the investigated field. The comprehensive solution was then incorporated into a PROMAXTM routine and applied to the seismic datasets using appropriate flow commands to perform the statics correction procedure. The outcome of the derived and implemented statics correction was demonstrated on shot gathers from the field in FFID configuration. Results from the several shot gathers analyzed after the application of the statics correction across the field showed that traces were adjusted back to their appropriate positions. The reflectors became better aligned and assumed a near-hyperbolic pattern which is a positive indication that the derived and applied refraction statics solution was the most appropriate for the dataset.

Statics correction methods for 3D converted-wave (PS) seismic reflection

One of the most difficult steps in the PS processing sequence is estimation of the S-wave receiver statics. This process is particularly important at the coal scale, due to the need for higher frequency content (better resolution).We present an analysis of three approaches for estimating 3D PS statics. These include a surface-consistent inversion algorithm (analogous to the residual-statics method used in conventional P-wave processing), PPS refraction statics, and a so-called robust statistical method. This analysis is achieved through the use of synthetic models, and a coal-scale 3D-3C survey acquired in the Bowen Basin.The presented datasets demonstrate that the surface-consistent inversion method can become unstable in certain environments. This is likely due to parameter leakage between receiver and structural terms, caused by the highly asymmetric nature of the shallow PS reflection paths. The robust statistical method appears reliable for determination of short-wavelength receiver statics, and hence is useful for continuity enhancement. The PPS refraction approach can provide both short-wavelength and long-wavelength solutions, provided the PPS arrivals can be picked reliably. As with P-wave analysis, a combination of algorithms may provide the most effective production tool for determination of PS receiver statics.

Integrating long- and short-wavelength statics with the generalized reciprocal method and the refraction convolution section

Statics, the corrections for variations in the elevation of the ground surface and for the weathered layer, represent the major challenge to improving the resolution of land seismic reflection data. This study describes a simple approach to determining long- and short-wavelength refraction statics that are generally accurate to a few milliseconds with good quality data. The approach employs the generalized reciprocal method (GRM) and the refraction convolution section (RCS).The resolution achieved with the GRM and RCS is comparable to that achieved with the delay-time method (DTM) together with one application of residual statics. Furthermore, a comparison with a coincident set of data recorded with different acquisition parameters shows that there is a long-wavelength static error with the DTM but not the GRM.There is a limit in the lateral resolution of variations in the base of the weathering, which is demonstrated with triplications or ‘frowns’ in the shot records. However, the statics model also exhibits short-wavelength variations, which suggest a resolution considerably greater than that indicated to be possible by the ‘frowns’. This study proposes that the long-wavelength component represents the variations in the time model of the weathering, which are caused by gross variations in the thickness of the weathered layer, while the short-wavelength components represent the variations in the surface soil layers.With the data used in this study, variations of more than 10 ms in the time model of the weathering were observed over distances of 10 m. Such variations result in similar intra-array statics with receiver arrays over comparable distances. These intra-array statics are a major cause of reduced resolution of reflection data and poor signal-to-noise ratios with first-break refraction data, especially in arid regions. Poor quality refraction data are the major impediment to obtaining accurate refraction statics.

A simple approach to refraction statics with the Generalized Reciprocal Method and the Refraction Convolution Section

We derive refraction statics for seismic data recorded in a hard rock terrain, in which there are large and rapid variations in the depth of weathering. The statics corrections range from less than 10 ms to more than 70 ms, often over distances as short as 12 receiver intervals. This study is another demonstration of the importance in obtaining accurate initial refraction models of the weathering in hard rock terrains in which automatic residual statics may fail.We show that the statics values computed with a simple model of the weathering using the Generalized Reciprocal Method (GRM) and the Refraction Convolution Section (RCS) are comparable in accuracy to those computed with a more complex model of the weathering, using least-mean-squares inversion with the conjugate gradient algorithm (Taner et al., 1998). The differences in statics values between the GRM model and that of Taner et al. (1998) systematically vary from an average of 2 ms to 4 ms over a distance of 8.8 km. The differences between these two refraction models and the final statics model, which includes the automatic residual values, are generally less than 5 ms. The residuals for the GRM model are frequently less than those for the model of Taner et al. (1998). The RCS statics are picked approximately 10 ms later, but their relative accuracy is comparable to that of the GRM statics.The residual statics values show a general correlation with the refraction statics values, and they can be reduced in magnitude by using a lower average seismic velocity in the weathering. These results suggest that inaccurate average seismic velocities in the weathered layer may often be a source of short-wavelength statics, rather than any shortcomings with the inversion algorithms in determining averaged delay times from the traveltimes.

A simple approach to refraction statics with the Generalized Reciprocal Method and the Refraction Convolution Section

We derive refraction statics for seismic data recorded in a hard rock terrain, in which there are large and rapid variations in the depth of weathering. The statics corrections range from less than 10 ms to more than 70 ms, often over distances as short as 12 receiver intervals. This study is another demonstration of the importance in obtaining accurate initial refraction models of the weathering in hard rock terrains in which automatic residual statics may fail.We show that the statics values computed with a simple model of the weathering using the Generalized Reciprocal Method (GRM) and the Refraction Convolution Section (RCS) are comparable in accuracy to those computed with a more complex model of the weathering, using least-mean-squares inversion with the conjugate gradient algorithm (Taner et al., 1998). The differences in statics values between the GRM model and that of Taner et al. (1998) systematically vary from an average of 2 ms to 4 ms over a distance of 8.8 km. The differences between these two refraction models and the final statics model, which includes the automatic residual values, are generally less than 5 ms. The residuals for the GRM model are frequently less than those for the model of Taner et al. (1998). The RCS statics are picked approximately 10 ms later, but their relative accuracy is comparable to that of the GRM statics.The residual statics values show a general correlation with the refraction statics values, and they can be reduced in magnitude by using a lower average seismic velocity in the weathering. These results suggest that inaccurate average seismic velocities in the weathered layer may often be a source of short-wavelength statics, rather than any shortcomings with the inversion algorithms in determining averaged delay times from the traveltimes.

Detailed Refraction Statics with the GRM and the RCS

We derive refraction statics for seismic data recorded in a hard rock terrain, in which the statics corrections range from less than 10 ms to in excess of 70 ms, over distances as short as 12 receiver intervals or 480 m. We compare statics values computed with a simple model of the weathering using the generalized reciprocal method (GRM) and the refraction convolution section (RCS) with those computed with a more complex model of the weathering using least-mean-square inversion with the conjugate gradient algorithm (Taner et al, 1998). The differences between the GRM model and that of Taner et al (1998), systematically vary from an average of 2 ms to 4 ms over a distance of 8.8 km. The differences between these two refraction models and the final statics model which includes the automatic residual values, are generally less than 5 ms. The residuals for the GRM model are frequently less than those for the model of Taner et al (1998). The RCS statics are picked approximately 10 ms later, but their relative accuracy is comparable to that of the GRM statics. The residual statics values show a general correlation with the refraction statics values, and they can be reduced in magnitude by using a lower average seismic velocity in the weathering. These results suggest that inaccurate average seismic velocities in the weathered layer may often be a source of short wavelength statics, rather than any shortcomings with the inversion algorithms in determining averaged delay times from the traveltimes. The significance of these results is that the RCS achieves improved accuracy through stacking to improve signal-to-noise ratios prior to the measurement of any traveltimes. Therefore, the RCS offers a new approach to determining more accurate statics with second arrivals such as shear waves, for which signal-to-noise ratios on shot records can be much less than those of the first arrival compressional waves.

First-Arrival Alignment Static Corrections Applied to Shallow Seismic Reflection Data

The proper handling of static corrections is an issue that is of critical importance to shallow seismic reflection surveys because of the high frequencies used, and the significant velocity and thickness variations that frequently exist in the very-near surface. The application of standard conventional methods of determining static corrections must be very carefully considered, as these are sometimes inadequate for shallow seismic reflection data. This paper addresses the problem of static corrections for shallow reflection data in terms of long-, medium-, and short-wavelength statics related to topography and variations in the very-low-velocity, near-surface layer, and presents a first-arrival alignment method of static corrections which is an adaptation of refraction and common offset methods. First-break picking is completed on the entire data set, and a refraction analysis of first-arrival data at selected intervals along the survey line is used to estimate a laterally-interpolated, layered, near-surface velocity structure. The first arrivals on all shot gathers are then aligned to the determined velocity function. This process corrects for medium- (i.e., within spread length), and long-wavelength ([Formula: see text] length), near-surface velocity variations, as well as most of the static contributions related to individual geophone locations and elevations (i.e., short-wavelength corrections). Residual statics are used to correct any remaining short-wavelength errors. Finally, topographic variations (long-wavelength) are corrected post-stack. Both model results and application of this method to actual shallow seismic reflection data show this to be a robust and effective method of correcting for statics related to a very-low-velocity near-surface layer, though the method (based on refraction analyses) cannot account for near-surface velocity inversions, if these exist.

A unified method for 2-D and 3-D refraction statics

Most of the seismic data processing procedures are divided into 2-D, 2.5-D, crooked lines or 3-D versions dictated by the differences in the shot and receiver configurations. In this paper, we introduce a tomographic approach that overcomes these geometrical difficulties and provides stable statics solutions from picked first‐break times. We also show that the first‐break picks contain both the short and the long wavelength surface statics. The solutions are obtained by solving a set of generalized surface‐consistent delay‐time equations using the method of weighted least squares and conjugate gradient. While iterating, each first‐break pick is evaluated to ensure its consistency with the least‐squares solution. Based on consistency, we weight the traveltime picks and use them in the next iteration. These weights also serve as an indicator of anomalous picks to the user. We show that long wavelength solutions leave large residual errors in the least‐squares solutions. We also use the expected length of the Fresnel zone to differentiate between short and long wavelength static solutions. After removing the influence of long wavelength statics, we apply short wavelength statics to reduce the residual errors further. We demonstrate the validity of our unified method by applying it to actual data examples. The removal of both long and short wavelength statics improves the initial data set that produces a more consistent set of velocities and leaves only the short wavelength residual reflection statics, which are generally less than quarter wavelet period delays. This removes the most probable cause of the leg jump contamination and poor velocity estimates from the residual statics computations, especially from the 3-D data.

Turning‐ray tomography

Turning‐ray tomography is useful for estimating near‐surface velocity structure in areas where conventional refraction statics techniques fail because of poor data or lack of smooth refractor/velocity structure. This paper explores the accuracy and inherent smoothing of turning‐ray tomography in its capacity to estimate absolute near‐surface velocity and the statics times derived from these velocities, and the fidelity with which wavefields collapse to point diffractors when migrated through these estimated velocities. The method comprises nonlinear iterations of forward ray tracing through triangular cells linear in slowness squared, coupled with the LSQR linear inversion algorithm. It is applied to two synthetic finite‐ difference data sets of types that usually foil conventional refraction statics techniques. These models represent a complex hard‐rock overthrust structure with a low‐velocity zone and pinchouts, and a contemporaneous near‐shore marine trench filled with low‐ velocity unconsolidated deposits exhibiting no seismically apparent internal structure. In both cases velocities are estimated accurately to a depth of one‐ fifth the maximum offset, as are the associated statics times. Of equal importance, the velocities are sufficiently accurate to correctly focus synthetic wavefields back to their initial point sources, so migration/datuming applications can also use these velocities. The method is applied to a real data example from the Timbalier Trench in the Gulf of Mexico, which exhibits the same essential features as the marine trench synthetic model. The Timbalier velocity inversion is geologically reasonable and yields long and short wavelength statics that improve the CMP gathers and stack and that correctly align reflections to known well markers. Turning‐ray tomography estimates near‐surface velocities accurately enough for the three purposes of lithology interpretation, statics calculations, and wavefield focusing for shallow migration and datuming.