Common Midpoint Gather Research Articles

Multiple-Reflection Noise Attenuation Using Adaptive Randomized-Order Empirical Mode Decomposition

We propose a novel approach for removing noise from multiple reflections based on an adaptive randomized-order empirical mode decomposition (EMD) framework. We first flatten the primary reflections in common midpoint gather using the automatically picked normal moveout velocities that correspond to the primary reflections and then randomly permutate all the traces. Next, we remove the spatially distributed random spikes that correspond to the multiple reflections using the EMD-based smoothing approach that is implemented in the $f-x$ domain. The trace randomization approach can make the spatially coherent multiple reflections random along the space direction and can decrease the coherency of near-offset multiple reflections. The EMD-based smoothing method is superior to median filter and prediction error filter in that it can help preserve the flattened signals better, without the need of exact flattening, and can preserve the amplitude variation much better. In addition, EMD is a fully adaptive algorithm and the parameterization for EMD-based smoothing can be very convenient.

Nonhyperbolic stretch-free normal moveout correction

Normal moveout (NMO) correction is routinely applied to traces of each common-midpoint (CMP) gather before forming a stack section. Conventional NMO correction has the drawback of producing stretching as a natural result of convergence of the NMO trajectories. Although this problem exists on completely hyperbolic reflections, the reflections will be further deviated from the desirable zero-offset equivalent if they indicate nonhyperbolic behavior. We have addressed this issue and developed a new method of stretch-free NMO correction in two steps: first, a novel way of rectifying NMO correction trajectories in a shifted hyperbolic NMO base, and second, a prioritized successive process of mapping data samples into an NMO-corrected gather. We have determined the advantage of the proposed method over two preceding methods: isomoveout and local stretch zeroing. The effectiveness of the new method in producing a stretch-free NMO gather was tested on synthetic data generated by ray tracing and a real data set of 200 CMP gathers of an Iranian oil field. The proposed method can be used in the presence of hyperbolic and nonhyperbolic events, and it recovers the amplitudes of interfering reflections to extend the usable offsets.

Velocity analysis using high-resolution semblance based on sparse hyperbolic Radon transform

Semblance measures the lateral coherency of the seismic events in a common mid-point gather, and it has been widely used for the normal-moveout-based velocity estimation. In this paper, we propose a new velocity analysis method by using high-resolution semblance based on sparse hyperbolic Radon transform (SHRT). Conventional semblance can be defined as the ratio of signal energy to total energy in the time gate. We replace the signal energy with the square of the sparse Radon panel and replace the total energy with the sparse Radon panel of the square data. Because of the sparsity-constrained inversion of SHRT, the new approach can produce higher resolution semblance spectra than the conventional semblance. We test this new semblance on synthetic and field data to demonstrate the improvements in velocity analysis.

Seismic random noise attenuation using artificial neural network and wavelet packet analysis

In this paper, we present a method for attenuating background random noise and enhancing resolution of seismic data, which takes advantage of semi-automatic training of feed forward back propagation (FFBP) artificial neural network (ANN) in a multiscale domain obtained from wavelet packet analysis (WPA). The images of approximations and details of the input seismic sections are calculated and utilized to train neural network to model coherent events by an automatic algorithm. After the modeling of coherent events, the remainder data are assumed to be related to background random noise. The proposed method is applied on both synthetic and real seismic data. The results are compared with that of the adaptive Wiener filter (AWF) in synthetic shot gather and real common midpoint gather and also with that of band-pass filtering on real common offset gather. The comparison indicates substantially higher efficiency of the proposed method in attenuating random noise and enhancing seismic signals.

Improving homomorphic wavelet estimation by compensating for residual NMO stretching on stack section

Wavelet estimation is a common step in seismic data processing and inversion. Homomorphic wavelet estimation has long utilized as a method that uses a seismic stack section with no phase presumption. Forming a stack section, normal move-out (NMO) correction must be applied on common midpoint (CMP) gathers, although it introduces NMO stretching. After stacking, residual of the NMO stretching may affect the stack section even after muting the highly stretched zone of the NMO corrected CMP gather. Presence of significant residual NMO stretching changes the spectral characteristics of data in time direction, by different degrees. Considering that in homomorphic process the wavelet is estimated based on the spectral characteristics of data, compensating for the residual NMO stretching, can improve the accuracy of the process. Here, we introduce a fast method of calculating the amount of residual NMO stretching and compensating for its effect on wavelet estimation. The proposed method needs limited prestack information like offsets and velocity function and include no prestack processing. We apply the proposed method on synthetic and real datasets and demonstrate the improvement of the estimated wavelet.

A layer-stripping method for 3D near-surface velocity model building using seismic first-arrival times

In order to improve the efficiency of 3D near-surface velocity model building, we develop a layer-stripping method using seismic first-arrival times. The velocity model within a Common Mid-Point (CMP) gather is assumed to be stratified into thin layers, and the velocity of each layer varies linearly with depth. The thickness and velocity of the top layer are estimated using minimum-offset first-arrival data in a CMP gather. Then the top layer is stripped and the second layer becomes a new top layer. After removing the effect of the top layer from the former first-arrival data, the new first-arrival data are obtained and then used to estimate the parameters of the second layer. In this manner, the velocity model, being regarded as that at a CMP location, is built layer-by-layer from the top to the bottom. A 3D near-surface velocity model is then formed using the velocity models at all CMP locations. The tests on synthetic and observed seismic data show that the layer-stripping method can be used to build good near-surface velocity models for static correction, and its computation speed is approximately hundred times faster than that of grid tomography.

Source wavelet estimation using common mid-point gathers

The source wavelet estimation is a crucial process for full waveform inversion because we can hardly know source information from observed data. In order to implement the full waveform inversion in the common mid-point (CMP) domain, source wavelet estimation may be performed using CMP gathers for efficiency and consistency. In this paper, we introduce the source wavelet estimation using CMP gather data. Since the CMP gather is the time–domain data, the source wavelet is transformed into the frequency domain to apply full Newton method. Finally, it is transformed back into the time domain. Through numerical examples, we show how sensitive the source wavelet inversion is to both the direct waves on CMP gathers and the uncertainty of initial velocity. We can succeed in accurately estimating source wavelet if we introduce time damping and the CMP data has direct waves in spite of an incorrect initial velocity. This is because direct waves, which are key elements for source estimation, propagate through water layer of which velocity information is precisely known. Therefore, we have to exploit direct wave for successful source wavelet estimation in full waveform inversion.

Deblending using a high-resolution radon transform in a common midpoint domain

The advantages of simultaneous sources acquisition are weakened by blended noise. Many conventional filtering methods are ineffective due to the existence of coherent blended noise in common shot gather (CSG). However, the coherent interference appears to be incoherent in a common midpoint (CMP) domain. In light of this characteristic, we propose a high-resolution radon transform based deblending approach. There are four steps for the implementation: (1) transform the original data from a CSG domain to a CMP domain; (2) apply the high-resolution radon transform to CMP gather to obtain the radon spectrum; (3) filter the radon spectrum with iterative threshold method; (4) transform the filtered data from the radon domain back to time spatial domain. The key step of the proposed method is to obtain the high-resolution radon spectrum to which the threshold filtering is applied. We give synthetic and field data examples to show the effectiveness of our approach.

Groundwater Level Monitoring for Hydraulic Characterization of an Unconfined Aquifer by Common Mid-point Measurements using GPR

Because of its limited bandwidth, ground penetrating radar (GPR) signal has an oscillating character that degrades the ability to distinguish reflection events and introduces an error in the velocity analysis. In this paper, we use the analytic signal to calculate the envelope velocity spectrum, which is void of the oscillating nature of a GPR wavelet. A comparison study on a synthetic common mid-point (CMP) gather demonstrates that the envelope velocity spectrum gives a more robust velocity estimation. We applied this technique to explore the potential of GPR for monitoring the pumping-induced groundwater level change, then estimating the hydraulic properties of an aquifer in Ulaanbaatar, the capital of Mongolia. A field survey was conducted along three different directions when a production well was under pumping and static conditions. In addition, a simple velocity picking scheme was suggested based on the maximum coherency curve. From the velocity picks, the vertical profiles of interval electromagnetic velocity and water content were estimated. The groundwater table was easily identified in these profiles. The groundwater level changes under the CMP sounding locations along the northeast and north survey lines were estimated to be 27 and 23 cm, respectively, whereas it failed to detect the groundwater level change on the northwest survey line because of the effect of strong scatterers near the groundwater table. The estimated groundwater level change was input into the unconfined aquifer model for estimating the hydraulic conductivity, which yields comparable results with a previous study. We conclude that the hydraulic parameter estimation using GPR is much easier and effective than the conventional hydraulic test methods.

Curvatures and inhomogeneities: An improved common-reflection-surface approach

Multiparameter stacking is an important tool to obtain a first reliable time image of the subsurface. In addition, it provides wavefield attributes, which form the basis for many important applications. The quality of the image and the attribute estimates relies heavily on the accuracy of the traveltime moveout description. The commonly used hyperbolic common-reflection-surface (CRS) operator reduces to the NMO hyperbola in the common-midpoint gather. Its accuracy, however, depends on the curvature of the reflector under consideration. The conventional multifocusing (MF) operator, a time-shifted double-square-root expression, leads to good results for high reflector curvatures and moderate inhomogeneities of the overburden. We used a new implicit CRS formulation that combines the robustness of CRS regarding heterogeneities with the high sensitivity to curvature of the MF approach. It assumes reflectors to be locally circular and can be applied in an iterative fashion. For simple but common acquisition and subsurface configurations, the new traveltime expression reduces to familiar formulas. Quantitative studies revealed that the new operator performs equally well over the full range of curvatures even in the presence of strong heterogeneities, while providing higher accuracy than the conventional CRS and MF methods. In addition, its application resulted in more reliable attribute estimates and an improved time-migrated section. Comparison of stacking and migration results for the complex synthetic Sigsbee 2a data set confirmed the potential of the suggested approach.

Deblending using normal moveout and median filtering in common-midpoint gathers

The benefits of simultaneous source acquisition are compromised by the challenges of dealing with intense blending noise. In this paper, we propose a processing workflow for blended data. The incoherent property of blending noise in the common-midpoint gathers is utilized for applying median filtering along the spatial direction after normal moveout (NMO) correction. The key step in the proposed workflow is that we need to obtain a precise velocity estimation which is required by the subsequent NMO correction. Because of the intense blending noise, the velocity scan cannot be obtained in one step. We can recursively polish both the deblended result and the velocity estimation by deblending using the updated velocity estimation and velocity scanning using the updated deblended result. We use synthetic and field data examples to demonstrate the performance of the proposed approach. The migrated image of deblended data is cleaner than that of blended data and is similar to that of unblended data.

Parameter estimation from non‐hyperbolic reflection traveltimes for large aperture common midpoint gathers

ABSTRACTAs far as superficial seismic reflection events are concerned, the classical normal moveout (NMO) process, which leads to the construction of seismic zero‐offset (or stacked) sections, encounters several difficulties due to the large data aperture. One of these difficulties is that the hyperbolic approximation of the reflection traveltime in common midpoint (CMP) gathers is no longer valid when offset largely exceeds the target depth. Recently, Fomel and Kazinnik proposed a novel, multi‐parameter, non‐hyperbolic formula for the traveltime of such reflection events. This formula, which will be referred to here as the FK traveltime after the authors, is exact for reflectors whose shape can be described by a hyperbola, and shows promising accuracy for long offsets and/or curved reflectors. It also depends on the same set of parameters as the common reflection surface (CRS) traveltime. In this paper, we propose strategies for estimating these CRS parameters based on the FK traveltime using large aperture data. However, in contrast to traditional CRS processing, and due to their widespread use, only common midpoint (CMP) gathers will be considered for the parameter searches. We will begin with a sensitivity analysis, showing the impact of each parameter on the traveltime. Based on this analysis, we will propose a two‐step estimation strategy, that could lead to improved seismic images, especially for very shallow, high aperture events. We will then highlight, through synthetic examples and discussions, the strengths and limitations of this strategy.

Generating starting models for seismic refraction tomography with common offset stacks

Common offset refraction (COR) traveltime attributes are derived from multi-fold data with novel adaptations of the generalised reciprocal method (GRM). COR GRM stacks are generated from a refraction equivalent of common midpoint (CMP) gathers, which are computed at each CMP with the COR GRM algorithms. The COR GRM stacks, which generate detailed spatially varying attributes for each layer detected in the near surface region, provide useful starting models for automatic refraction tomography.The spatial resolution of the depth models of the wavepath eikonal traveltime (WET) refraction tomograms obtained with starting models derived with the COR GRM is similar to the WET tomogram obtained with the standard GRM, whereas the COR GRM seismic velocity model is a smoothed version of the standard GRM model. In all cases, the GRM-derived WET tomograms avoid the generation of undetectable artefacts with common implementations of automatic refraction tomography, which can occur with the use of default starting models consisting of smooth vertical velocity gradients and with the need to minimise misfit errors through over-processing.The COR GRM attributes demonstrate that the traveltime data are consistent with minimal penetration within the sub-weathering, representative of uniform seismic velocities, and that the spatial variations in the time model and seismic velocities are more significant than any variations caused by vertical velocity gradients in the sub-weathered zone. However, the occurrence of vertical velocity gradients in the sub-weathering largely remains unresolved because minimal penetration of the first arrivals can occur even with large vertical velocity gradients, such as the hyperbolic velocity function.The WET tomograms generated with the COR GRM time model and seismic velocity attributes are generally very similar visually to the starting models, even though the misfit errors may differ. It is concluded that COR GRM starting models can frequently be a useful alternative to refraction tomography.

A physical model study of the travel times and reflection points of SH-waves reflected from transversely isotropic media with tilted symmetry axes

In reflection seismology, detailed knowledge of how seismic waves propagate in anisotropic media is important for locating reservoirs accurately. The SH-wave possesses a pure mode polarization which does not convert to P- and SV-waves when reflecting from a horizontal interface, and vice versa. The simplicity of the SH-wave thus provides an easy way to view the details of SH-wave propagation in anisotropic media. In this study, we attempt to inspect the theoretical reflection moveouts of SH-waves reflected from transversely isotropic (TI) layers with tilted symmetry axes and to verify the reflection point, which could be shifted away from the common midpoint (CMP), by numerical calculations and physical modelling.In travel time-offset analyses, the moveout curves of SH-waves reflected from horizontal TI media (TIM) with different tilted angles of symmetry axes are computed by the TI modified hyperbolic equation and Fermat’s principle, respectively. It turns out that both the computed moveout curves are similar and fit well to the observed physical data. The reflection points of SH-waves for a CMP gather computed by Fermat’s principle show that they are close to the CMP for TIM with the vertical and horizontal symmetry axes, but they shift away from the CMP for the other tilted angles of symmetry axes. The shifts of the reflection points of the SH-waves from the CMP were verified by physical modelling.

Georadar‐derived estimates of firn density in the percolation zone, western Greenland ice sheet

Greater understanding of variations in firn densification is needed to distinguish between dynamic and melt‐driven elevation changes on the Greenland ice sheet. This is especially true in Greenland's percolation zone, where firn density profiles are poorly documented because few ice cores are extracted in regions with surface melt. We used georadar to investigate firn density variations with depth along a ∼70 km transect through a portion of the accumulation area in western Greenland that partially melts. We estimated electromagnetic wave velocity by inverting reflection traveltimes picked from common midpoint gathers. We followed a procedure designed to find the simplest velocity versus depth model that describes the data within estimated uncertainty. On the basis of the velocities, we estimated 13 depth‐density profiles of the upper 80 m using a petrophysical model based on the complex refractive index method equation. At the highest elevation site, our density profile is consistent with nearby core data acquired in the same year. Our profiles at the six highest elevation sites match an empirically based densification model for dry firn, indicating relatively minor amounts of water infiltration and densification by melt and refreeze in this higher region of the percolation zone. At the four lowest elevation sites our profiles reach ice densities at substantially shallower depths, implying considerable meltwater infiltration and ice layer development in this lower region of the percolation zone. The separation between these two regions is 8 km and spans 60 m of elevation, which suggests that the balance between dry‐firn and melt‐induced densification processes is sensitive to minor changes in melt.

On standard and optimal designs of industrial-scale 2-D seismic surveys

SUMMARY The principal aim of performing a survey or experiment is to maximize the desired information within a data set by minimizing the post-survey uncertainty on the ranges of the model parameter values. Using Bayesian, non-linear, statistical experimental design (SED) methods we show how industrial scale amplitude variations with offset (AVO) surveys can be constructed to maximize the information content contained in AVO crossplots, the principal source of petrophysical information from seismic surveys. The design method allows offset dependent errors, previously not allowed in non-linear geoscientific SED methods. The method is applied to a single common-midpoint gather. The results show that the optimal design is highly dependent on the ranges of the model parameter values when a low number of receivers is being used, but that a single optimal design exists for the complete range of parameters once the number of receivers is increased above a threshold value. However, when acquisition and processing costs are considered we find that a design with constant spatial receiver separation survey becomes close to optimal. This explains why regularly-spaced, 2-D seismic surveys have performed so well historically, not only from the point of view of noise attenuation and imaging in which homogeneous data coverage confers distinct advantages, but also to provide data to constrain subsurface petrophysical information.

Seismic noise attenuation using nonstationary polynomial fitting

We propose a novel method for seismic noise attenuation by applying nonstationary polynomial fitting (NPF), which can estimate coherent components with amplitude variation along the event. The NPF with time-varying coefficients can adaptively estimate the coherent components. The smoothness of the polynomial coefficients is controlled by shaping regularization. The signal is coherent along the offset axis in a common midpoint (CMP) gather after normal moveout (NMO). We use NPF to estimate the effective signal and thereby to attenuate the random noise. For radial events-like noise such as ground roll, we first employ a radial trace (RT) transform to transform the data to the time-velocity domain. Then the NPF is used to estimate coherent noise in the RT domain. Finally, the coherent noise is adaptively subtracted from the noisy dataset. The proposed method can effectively estimate coherent noise with amplitude variations along the event and there is no need to propose that noise amplitude is constant. Results of synthetic and field data examples show that, compared with conventional methods such as stationary polynomial fitting and low cut filters, the proposed method can effectively suppress seismic noise and preserve the signals.

Inverse Common-Reflection-Surface

SUMMARY The Common-Reflection-Surface (CRS) stack method is a powerful tool to produce high-quality stacked images of multicoverage seismic data. As a result of the CRS stack, not only a stacked section, but also a number of attributes defined at each point of that section, are produced. In this way, one can think of the CRS stack method as a transformation from data space to attribute space. Being a purely kinematic method, the CRS stack lacks amplitude information that can be useful for many purposes. Here we propose to fill this gap by means of a combined use of a zero-offset section (that could be a short-offset or amplitude-corrected stacked section) and common midpoint gather. We present an algorithm for an inverse CRS transformation, namely one that (approximately) transforms the CRS attributes back to data space. First synthetic tests provide satisfying results for the two simple cases of single dipping-plane and single circular reflectors with a homogeneous overburden, and provide estimates of the range of applicability, in both midpoint and offset directions. We further present an application for interpolating missing traces in a near-surface, high-resolution seismic experiment, conducted in the alluvial plain of the river Gave de Pau, near Assat, southern France, showing its ability to build coherent signals, where recording was not available. A somewhat unexpected good feature of the algorithm, is that it seems capable to reconstruct signals even in muted parts of the section.

An overview of seismic azimuth for towed streamers

Conventional 3D streamer seismic processing generally ignores any azimuth component in the data. We are used to the convenience of acquiring overlapping shot gathers in straight lines, as we can sort the data into common midpoint gathers, and then exploit the power of stack in processing to attenuate random noise. The higher the fold, the more random noise we attenuate. Conventional 3D surveys are acquired using “swath”or “racetrack” vessel shooting, wherein the survey has a single line orientation (or “survey azimuth”), and a long, narrow spread of streamers are towed by a single vessel. Apart from the front of the streamers (short source-receiver offsets), most source-receiver combinations have a relatively common azimuth (the angle between their particular vector and the survey orientation, Figure 1). Thus, the subsurface geology is illuminated only from one particular shooting direction. We assume that most coherent noise types are well behaved and we can remove them in processing. We assume that the target illumination is acceptably uniform, and we can produce clean seismic images. Most of the time these assumptions are in the ballpark of truth and our resultant seismic data allow us to achieve our exploration and appraisal objectives.

3D velocity-independent elliptically anisotropic moveout correction

Azimuthal anisotropy or lateral velocity variations cause azimuthal variations in moveout velocity, which can degrade seismic images if handled improperly. In cases in which apparent azimuthally anisotropic moveout is present, a single picked velocity is inadequate to flatten an event on a 3D CMP gather. Conventional velocity-analysis techniques require a significant amount of time and effort, especially in areas where apparent anisotropy is observed. We propose a velocity-independent imaging approach to perform an elliptically anisotropic moveout correction in three dimensions. The velocity-independent approach relies on volumetric local traveltime slopes rather than aggregate velocities and therefore provides an azimuthally flexible description of traveltime geometries throughout the gather. We derive theoretical expressions for extracting the moveout slowness matrix and the angle between the symmetry and acquisition axes as volumetric local attributes. A practical inversion scheme to extract the same parameters is also developed. These parameters are used to solve for moveout slowness as a function of azimuth. Tests on a synthetic common-midpoint (CMP) gather show accurate results for the automatic moveout correction and the inversion scheme. A field data example from west Texas illustrates the application of the automatic moveout correction as a residual moveout.