Normal Moveout Correction Research Articles

Thin-bed prestack spectral inversion

Prestack seismic data has been used in a new method to fully determine thin-bed properties, including the estimation of its thickness, P- and S-wave velocities, and density. The approach requires neither phase information nor normal-moveout (NMO) corrections, and assumes that the prestack seismic response of the thin layer can be isolated using an offset-dependent time window. We obtained the amplitude-versus-angle (AVA) response of the thin bed considering converted P-waves, S-waves, and all the associated multiples. We carried out the estimation of the thin-bed parameters in the frequency (amplitude spectrum) domain using simulated annealing. In contrast to using zero-offset data, the use of AVA data contributes to increase the robustness of this inverse problem under noisy conditions, as well as to significantly reduce its inherent nonuniqueness. To further reduce the nonuniqueness, and as a means to incorporate a priori geologic or geophysical information (e.g., well-log data), we imposed appropriate bounding constraints to the parameters of the media lying above and below the thin bed, which need not be known accurately. We tested the method by inverting noisy synthetic gathers corresponding to simple wedge models. In addition, we stochastically estimated the uncertainty of the solutions by inverting different data sets that share the same model parameters but are contaminated with different noise realizations. The results suggest that thin beds can be characterized fully with a moderate to high degree of confidence below tuning, even when using an approximate wavelet spectrum.

Ground‐roll attenuation using a 2D time‐derivative filter

ABSTRACTWe present a new filtering method for the attenuation of ground‐roll. The method is based on the application of a bi‐dimensional filter for obtaining the time‐derivative of the seismograms. Before convolving the filter with the input data matrix, the normal moveout correction is applied to the seismograms with the purpose of flattening the reflections. The method can locally attenuate the amplitude of data of low frequency (in the ground‐roll and stretch normal moveout region) and enhance flat events (reflections). The filtered seismograms can reveal horizontal or sub‐horizontal reflections while vertical or sub‐vertical events, associated with ground‐roll, are attenuated. A regular set of samples around each neighbourhood data sample of the seismogram is used to estimate the time‐derivative. A numerical approximation of the derivative is computed by taking the difference between the interpolated values calculated in both the positive and the negative neighbourhood of the desired position. The coefficients of the 2D time‐derivative filter are obtained by taking the difference between two filters that interpolate at positive and negative times. Numerical results that use real seismic data show that the proposed method is effective and can reveal reflections masked by the ground‐roll. Another benefit of the method is that the stretch mute, normally applied after the normal moveout correction, is unnecessary. The new filtering approach provides results of outstanding quality when compared to results obtained from the conventional FK filtering method.

Ultra‐shallow imaging using 3D seismic‐reflection methods

ABSTRACTThree‐dimensional ultra‐shallow seismic reflection methods were used to image multiple reflectors less than 20 m deep, including the top of saturated zone, a paleo‐channel feature and the top of bedrock at a field site located near Lawrence, Kansas. A small 3D demonstration survey was designed and acquired using source and receiver intervals of 0.5 m and source line and receiver line intervals of 2 m. The survey had a nominal fold of 48 and covered an area of ~15.5 m × 35.5 m. Large variations in velocity were present, ranging from ~300–600 m/s laterally in the shallowest layer and ~300–1600 m/s vertically, a degree of variability that is not uncommon in the ultra‐shallow subsurface. Normal moveout corrections cannot account for intersecting reflection hyperbolae such as those caused by large vertical velocity gradients, so a novel processing scheme was applied by extracting offset‐dependent subsets based on the optimum window for each reflection. The subsets were normal moveout corrected independently and then stacked together using conventional 3D processing techniques. Despite the large lateral and vertical velocity variations, we were successful in imaging the top of the saturated zone, paleo‐channel features and the overburden‐bedrock interface located at depths of ~5 m, 8 m and 14 m, respectively. Results of the 3D survey are in agreement with previous studies conducted at the site. The methods presented here could be applied to situations where 3D imaging of the ultra‐shallow subsurface is necessary and may help to identify possible contaminant sinks or flowpaths.

An Equivalent Offset time migration for anisotropic data

The Equivalent Offset (EO) method of migration is a Kirchhoff prestack method that forms prestack migrated gathers suitable for RMS velocity analysis. All input data, within the migration aperture, is summed into each EO gather. After normal moveout (NMO) correction, stacking completes the prestack migration. The migration can be in time or depth, however the time migration is much faster than a conventional Kirchhoff time migration as no time shifting is required when gathering. Antialiasing filtering, scaling, and NMO are only performed after the gathering has been completed. The EO gathers contain hyperbolic shaped reflection energy with the moveout shaped with RMS velocities. The fold in each bin of the EO gathers is very high, while the noise is very low proving accurate velocity analysis. Anisotropic parameters may be included when forming the EO gathers. A shifted hyperbola technique was used to map the input data to an appropriate offset bin of the EO gather. The moveout in these anisotropic EO gathers is still hyperbolic and conventional velocity analysis will produce the vertical RMS velocity.

Azimuthal τ-panalysis in anisotropic media

SUMMARY For the purpose of transversely isotropic (TI) normal moveout (NMO) correction, we propose analysis of plane wave transformed azimuthal gathers, interactively using a single azimuth data at a time and a new delay time equation (developed in this paper), which is a function of two parameters at each azimuth. Results from independently estimated multi-azimuth gathers, then, can be combined to estimate stiffness or Thomsen coefficients. Azimuthal τ–p analysis also avoids numerical ray tracing, resulting in a rapid algorithm. We demonstrate the applicability of our method using a set of P-wave synthetic seismograms from a multilayered medium, consisting of isotropic and HTI layers. Azimuth-dependent anisotropy parameters are derived by delay time fitting and NMO correction. The reflections from the bottom interface of an isotropic layer with an anisotropic overburden show apparent anisotropic traveltime behaviour, which is easily accounted for by our layer-stripping based azimuthal NMO analysis. Unlike the previous approximate HTI NMO correction equation, this equation performs better NMO correction for the HTI medium and is also applicable to the VTI medium. Presence of only two reduced parameters in the equation helps the anisotropic parameter estimation become less ambiguous.

Interval velocity estimation via NMO-based differential semblance

The differential semblance method of velocity analysis flattens image gathers automatically by updating interval velocity to minimize the mean square difference of neighboring traces. We detail an implementation using hyperbolic normal moveout correction as the imaging method. The algorithm is fully automatic, accommodates arbitrary acquisition geometry, and outputs 1D, 2D, or 3D interval velocity models. This variant of differential semblance velocity analysis is effective within the limits of its imaging methodology: mild lateral heterogeneity and data dominated by primary events. Coherent noise events such as multiple reflections tend to degrade the quality of the velocity model estimated by differential semblance. We show how to combine differential semblance velocity analysis with dip filtering to suppress multiple reflections and thus improve considerably the accuracy of the velocity estimate. We illustrate this possibility using multiple-rich data from a 2D marine survey.

Seismic reflection image of the crust structure along the KCRT-2002 profile in the southern Korean peninsula

In order to reveal the perspective of velocity structure in the southern part of the Korean peninsula, a seismic experiment was carried out along a WNW-ESE profile of 294-km length in December, 2002. In 100-m deep drill-holes, seismic explosives of 1000 and 500 kg were detonated on the west coast and near the center of the profile, respectively. The seismic signals were detected by 198 portable seismometers spaced approximately at an 1.5 km interval and digitally recorded for 115 s at an 120-Hz sampling rate. Normal moveout corrections were applied to yield reflection images for P, S, and PS converted waves followed by time-to-depth conversion through forward modeling of travel times using the fourth-order equation for wide angle reflections. Three distinct reflection events are identified at average two-way travel times of 4.90, 8.02, and 10.99 s on the NMO corrected P-wave sections. Their converted depths are 13.71, 23.37, and 33.67 km, respectively, and the P-wave interval velocities between the depth boundaries including the free surface are 5.60, 6.19, and 6.96 km/s from top to bottom. The reflection Moho is imaged as a sharp boundary in the middle of the profile while multi-layers are featured near both ends of the profile.

Data stacking beyond CMP

Stacking has been used in seismic data processing for a long time. In fact, stacked sections (or volumes in 3D) are standard deliverables in the industry, and the concepts of common-midpoint (CMP) gathers and normal moveout (NMO) correction are mentioned in almost every textbook on seismic processing. Although the general trend is toward prestack imaging (either in time or in depth), the construction of stacked sections remains an important step within the seismic processing flow, since they are almost always the first available interpretable images of the subsurface.

Prestack and poststack migration of crooked-line seismic reflection data: A case study from the South Portuguese Zone fold belt, southwestern Iberia

Crooked-line 2D seismic reflection survey geometries violate underlying assumptions of 2D imaging routines, affecting our ability to resolve the subsurface reliably. We compare three crooked-line imaging schemes involving prestack and poststack time migration using the 2D IBERSEIS deep seismic reflection profile running over the South Portuguese Zone thrust-and-fold belt to obtain crisp high-resolution images of the shallow crust. The crust is characterized by a complex subsurface geometry with conflicting dips of up to [Formula: see text]. In summary, the three schemes are (1) normal-moveout (NMO) corrections, dip-moveout (DMO) corrections, common-midpoint (CMP) stacking, CMP projection, and poststack time migration; (2) NMO corrections, DMO corrections, CMP projection, zero-offset time migration of the common-offset gathers, and CMP stacking; (3) CMP projection, prestack time migration in the common-offset domain, and CMP stacking. An essential element of all three schemes is a CMP projection routine, projecting the CMPs first binned along individual segments for preprocessing onto one straight line, which is parallel to the general dip direction of the subsurface structures. After CMP projection, the data satisfy the straight-line assumption of 2D imaging routines more closely. We observe that the prestack time-migration scheme yields comparable or more coherent synthetic and field-data images than the other two DMO-based schemes along the parts of the profile where the acquisition overall follows a straight line. However, the schemes involving DMO corrections are less plagued by migration artifacts than the prestack time-migration scheme along profile parts where the acquisition line is crooked. In particular, prominent migration artifacts on the prestack migrated synthetic data can be related to significant variations in source-receiver azimuths for which 2D prestack migration cannot account. Thus, the processing scheme including DMO corrections, CMP projection, and zero-offset migration of common-offset gathers offers a reliable and effective alternative to prestack migration for crooked-line 2D seismic reflection processing.

Diffraction enhancement in prestack seismic data

Seismic diffractions are often considered noise and are intentionally or implicitly suppressed during processing. Diffraction-like events include true diffractions, wave conversions, or fracture waves which may contain valuable information about the subsurface and could be used for interpretation or imaging. Using synthetic and field data, we examine workflows to separate diffractions from reflections that allow enhancement of diffraction-like signals and suppression of reflections. The workflows consist of combinations of standard processing modules. Most workflows apply normal moveout corrections to flatten reflection hyperbolas, which eases their removal. We observe that the most effective techniques are the decomposition of seismic gathers into eigensections and flows based on Radon transformations.

Accurate elevation and normal moveout corrections of seismic reflection data on rugged topography

The application of the seismic reflection method is often limited in areas of complex terrain. The problem is the incorrect correction of time shifts caused by topography. To apply normal moveout (NMO) correction to reflection data correctly, static corrections are necessary to be applied in advance for the compensation of the time distortions of topography and the time delays from near‐surface weathered layers. For environment and engineering investigation, weathered layers are our targets, so that the static correction mainly serves the adjustment of time shifts due to an undulating surface. In practice, seismic reflected raypaths are assumed to be almost vertical through the near‐surface layers because they have much lower velocities than layers below. This assumption is acceptable in most cases since it results in little residual error for small elevation changes and small offsets in reflection events. Although static algorithms based on choosing a floating datum related to common midpoint gathers or residual surface‐consistent functions are available and effective, errors caused by the assumption of vertical raypaths often generate pseudo‐indications of structures. This paper presents the comparison of applying corrections based on the vertical raypaths and bias (non‐vertical) raypaths. It also provides an approach of combining elevation and NMO corrections. The advantages of the approach are demonstrated by synthetic and real‐world examples of multi‐coverage seismic reflection surveys on rough topography.

Study and practice of wide-angle seismic data processing

This paper presents the special processing methods used for wide-angle land seismic data through both theoretical study and model testing. They are different from conventional ones in the following aspects: separation of reflection and refraction waves, long offset NMO and stacking and forward modeling and inversion. These processing techniques have been applied for the first time to land seismic data from Liaohe areas, resulting in greatly improved quality of the deep formation and better imaging of the shallow layer obtained in the volcanic-shielded area. Wide-angle reflection and refraction seismic surveys were carried out in the Liaohe area using the maximum offset of 6500m and with the target around 2000ms. In the processing, we adopted the τ ∼p transform and the high-order normal moveout correction.

Time‐migration velocity analysis by velocity continuation

Time‐migration velocity analysis can be performed by velocity continuation, an incremental process that transforms migrated seismic sections according to changes in the migration velocity. Velocity continuation enhances residual normal moveout correction by properly taking into account both vertical and lateral movements of events on seismic images. Finite‐difference and spectral algorithms provide efficient practical implementations for velocity continuation. Synthetic and field data examples demonstrate the performance of the method and confirm theoretical expectations.

Velocity analysis after migration

The double‐square‐root (DSR) equation used in pre‐stack migration is formulated in terms of velocity‐dependent and velocity‐independent terms. The velocity‐dependent term is shown to be the hyperbolic normal moveout (NMO) correction, whereas the velocity‐independent term is related to the recording geometry only. This separation of the velocity‐dependent term offers a means of applying vertical corrections to an initial migration velocity field. Using this concept, procedures are described both for velocity determination and for achieving improved structural imaging.This decoupling is accurate both for constant‐velocity media and for media whose velocity varies as a function of depth. In media whose velocity varies as a function of both space and depth, a procedure is described for building velocity models through common‐image gather (CIG) stacking following prestack depth migration (PSDM) and time conversion (TC). This so‐called PSDM‐TC stack procedure provides a means of (a) incorporating both vertical and lateral velocity updates into an initial velocity model, (b) obtaining improved structural imaging by using a non‐optimal velocity model for the prestack depth migration, and (c) updating velocity by flattening CIGs and maximizing stack energy. The procedure can be applied to both P‐P wave and P‐SV wave migration.

Low‐cost geophysical investigations of a paleochannel aquifer in the Eastern Goldfields, Western Australia

Compressional (P) wave and shear (S) wave seismic reflection techniques were used to delineate the sand and gravel aquifer within a highly saline clay‐filled paleochannel in the Eastern Goldfields of Western Australia. The seismic refraction and gravity methods were also used to investigate the paleochannel. The unsaturated loose fine‐grained sand up to 10 m in depth at the surface is a major factor in degrading subsurface imaging. The seismic processing needed to be precise, with accurate static corrections and normal moveout corrections. Deconvolution enhanced the aquifer and other paleochannel reflectors. P‐wave reflection and refraction layer depths had good correlation and showed a total of six boundaries: (1) water table, (2) change in velocity (compaction) in the paleochannel sediments, (3) sand and gravel aquifer, (4) red‐brown saprolite and green saprolite boundary, (5) weathered bedrock, and (6) unweathered bedrock. P‐wave explosive and hammer sources were found to have similar signal characteristics, and the aquifer and bedrock were both imaged using the hammer source. The deep shots below the water table have the most broadband frequency response for reflections, but stacking clear reflections was difficult. The S‐wave reflection results showed high lateral and vertical resolution of the basal saprolite clay, the sand and gravel aquifer, and very shallow clays above the aquifer. The S‐wave reflection stacking velocities were 10–20% of the P‐waves, increasing the resolution of the S‐wave section. The gravity data were modelled to fit the known drilling and P‐wave seismic reflection depths. The refraction results did not identify the top of bedrock, so refraction depths were not used for the gravity modeling in this highly weathered environment. The final gravity model mapped the bedrock topography beyond the lateral extent of the seismic and drilling data.

The use of shallow seismic reflection technique in near surface exploration of urban sites: an evaluation in the city of São Paulo, Brazil

In order to evaluate the use of shallow seismic technique to delineate geological and geotechnical features up to 40 meters depth in noisy urban areas covered with asphalt pavement, five survey lines were conducted in the metropolitan area of Sao Paulo City. The data were acquired using a 24-bit, 24-channel seismograph, 30 and 100 Hz geophones and a sledgehammer-plate system as seismic source. Seismic reflection data were recorded using a CMP (common mid point) acquisition method. The processing routine consisted of: prestack band-pass filtering (90-250 Hz); automatic gain control (AGC); muting (digital zeroin) of dead/noisy traces, ground roll, air-wave and refracted-wave; CMP sorting; velocity analyses; normal move-out corrections; residual static corrections; f-k filtering; CMP stacking. The near surface is geologically characterized by unconsolidated fill materials and Quaternary sediments with organic material overlying Tertiary sediments with the water table 2 to 5 m below the surface. The basement is composed of granite and gneiss. Reflections were observed from 40 milliseconds to 65 ms two-way traveltime and were related to the silt clay layer and fine sand layer contact of the Tertiary sediments and to the weathered basement. The CMP seismic-reflection technique has been shown to be useful for mapping the sedimentary layers and the bedrock of the Sao Paulo sedimentary basin for the purposes of shallow investigations related to engineering problems. In spite of the strong cultural noise observed in these urban areas and problems with planting geophones we verified that, with the proper equipment, field parameters and particularly great care in data collection and processing, we can overcome the adverse field conditions and to image reflections from layers as shallow as 20 meters.

Estimating residual statics using prestack migration

A method is presented for estimating residual statics that are computed prior to normal moveout correction. No velocity information is required, and the offset and structure terms are eliminated from the decomposition. Model source (shot) records are formed using the EOM method of prestack migration to provide a one-to-one trace for cross-correlation. After cross-correlation, the estimated time shifts are decomposed directly into source and receiver statics. The method is stable for ling time windows that are input to the cross-correlation, and provides solutions for structured data where other methods fail.

Estimation of groundwater level by GPR in an area with multiple ambiguous reflections

Ground-penetrating radar (GPR) was applied to estimate the groundwater level in Ulaanbaatar City, Mongolia. Multiple reflectors occur at different levels. Any one of these was a possible water table reflector. In order to identify the groundwater reflection amongst a set of ambiguous reflectors and to increase the signal-to-noise ratio, the common-midpoint (CMP) method was used. The operation frequency of the radar system was 100 MHz. The start position of a survey line was 10 m away from a building that influenced GPR data. However, a reflection from the building can be suppressed significantly by two-dimensional f– k filtering. By noise reduction, velocity analysis, normal moveout correction, stacking and migration using estimated velocities, the subsurface images are obtained. The signal-to-noise ratio of the stacked CMP profile is much higher than that of the common-offset profile. The usual detectable range of GPR is several meters, however, we can measure more than 10 m in depth because of the improvement of the signal-to-noise ratio by CMP and due to the very dry soil. Also, we can estimate the vertical dielectric constant distribution from the interval velocities obtained from the CMP. Then we can locate a groundwater reflection within a multitude of ambiguous reflectors, and find that the depth of the groundwater level is approximately 8.0 m. The experiment results show that GPR data collected by the CMP method not only improves the quality of the radar profile but also enables us to estimate the subsurface vertical profile of the dielectric constant.

Applications of seismic pattern recognition and gravity inversion techniques to obtain enhanced subsurface images of the Earth's crust under the Central Metasedimentary Belt, Grenville Province, Ontario

SUMMARY Project Lithoprobe's Abitibi–Grenville transect seismic reflection lines 32 and 33 traverse the exposed Central Metasedimentary Belt (CMB) located in the Grenville province of the Precambrian Shield of Canada in southern Ontario. These seismic lines image a zone with a protracted deformational history spanning more than 300 Myr. Detailed examination of the commercially processed stacked sections reveals a number of significant deficiencies in some important areas. The image quality in these zones of reduced coherency needs to be enhanced to examine specific features and their relation to the surface geology. Examination of near-vertical seismic data from Lines 32 and 33 revealed that the signal-to-noise ratio was not improved by stacking, due to misalignment of signals even after static, normal moveout corrections and residual static corrections. The presumed reason is that reflected seismic energy following long ray paths in heterogeneous media suffers from relative advances and delays in its propagation, and hence arrives at slightly different times at the receivers, tending to be poorly aligned relative to its theoretical traveltime curves. A pattern recognition (PR) method for signal enhancement followed by energy stacking in moving time windows was used in this study to improve the images in spite of misalignments. Reprocessing has refined the geometry of the reflection profiles. The objective of this paper is to use enhanced images of the seismic reflection data obtained by using a PR approach together with gravity data, using 2.5-D forward and 3-D inversion routines, to give an improved model of subsurface structure in the vicinity of lines 32 and 33. Line 32 is dominated by southeast-dipping reflectors soling into the lower crust. The listric geometry of the strong reflection packages of the CMB boundary thrust zone is interpreted to represent a crustal-scale ramp–flat geometry that accommodated northwest-directed tectonic transport of the CMB. This interpretation is also supported by the gravity data.

Receiver function arrays: a reflection seismic approach

The receiver function method (RFM) is a commonly used technique to study the crustal and upper mantle velocity structure. Early receiver function (RF) investigations were performed mostly at individual permanent stations. They were focused on crustal structures, and later on upper mantle velocity discontinuities (410 km and 660 km discontinuities). Only recently has research been directed towards the study of the lateral (2- and 3-D) variability of major velocity boundaries in the crust and upper mantle by receiver function arrays using temporary and permanent, three-component, short-period and broad-band seismic stations. To improve the signal-to-noise ratio, receiver functions are calculated for individual earthquakes and are then binned, moveout corrected and stacked. We show that this processing sequence is similar to that applied routinely in exploration seismology. Therefore, existing tools from the nearvertical data processing can be adopted for receiver functions: velocity analysis tools, solutions for static and residual static problems, coherence enhancement of seismic phases, migration, etc. The high spatial density of seismic stations of recent and future receiver function experiments provides the opportunity (and obligation) to use the more sophisticated migration methods (full wavefield migration) commonly and successfully used in exploration seismics. paraSynthetics calculated by the finite difference method for simple 2-D crustal models are employed here to test our processing approach and to show the potentials and limitations of stacking and migrating RF data. We show that binning, normal moveout (NMO) corrections, stacking and post-stack migration of the synthetic data can reconstruct the models reliably with a high spatial resolution.