Common-offset Gathers Research Articles

Extraction of reflected waves from acoustic logging data using variation mode decomposition and curvelet transform

Remote reflection waves, essential for acquiring high-resolution images of geological structures beyond boreholes, often suffer contamination from strong direct mode waves propagating along the borehole. Consequently, the extraction of weak reflected waves becomes pivotal for optimizing migration image quality. This paper introduces a novel approach to extracting reflected waves by sequentially operating in the spatial frequency and curvelet domains. Using variation mode decomposition (VMD), single-channel spatial domain signals within the common offset gather are iteratively decomposed into high-wavenumber and low-wavenumber intrinsic mode functions (IMFs). The low-wavenumber IMF is then subtracted from the overall waveform to attenuate direct mode waves. Subsequently, the curvelet transform is employed to segregate upgoing and downgoing reflected waves within the filtered curvelet domain. As a result, direct mode waves are substantially suppressed, while the integrity of reflected waves is fully preserved. The efficacy of this approach is validated through processing synthetic and field data, underscoring its potential as a robust extraction technique.

Non-Parametric Simultaneous Reconstruction and Denoising via Sparse and Low-Rank Regularization

Spatial irregular sampling and random noise are two important factors that restrict the accuracy of seismic imaging. Seismic wavefield reconstruction and denoising based on sparse representation are two popular antidotes to these two inevitable issues, respectively. This article presents a non-parametric simultaneous reconstruction and denoising via sparse and low-rank regularization that dealt with the prestack gathers efficiently and automatically. The proposed method makes no additional prior assumptions on original data other than that the seismic signal is compressible. The key parameters estimation adopts a data-driven framework without person-dependent intervention. The basic idea of the approach is to combine the two related algorithms. Thus, the sparse decomposition needs to be performed only once. We first extract the solution matrix via Fourier dictionary and then perform the reconstruction and denoising successively in the sparse domain. Obtaining a perfect interpolation result requires that the seismic data satisfy the Shannon–Nyquist sampling theorem. However, data with steep-dip events or gaps, which cannot be adequate for the procedure, are a challenge that must be faced. This work proposes to deal with the common-offset gathers, which is characterized by flat, even approximate horizontal events, to handle the under-sampling obstacle. Another excellent property of the common-offset gathers is the simple and periodic repetitive texture structure, which can be represented sparsely and accurately by the Fourier dictionary. Thus, the computational complexity of the sparse representation is reduced. Both synthetic and practical applications indicate that our algorithm is efficient and effective.

Iterative Deblending of Simultaneous-Source Seismic Data via a Robust Singular Spectrum Analysis Filter

We solve the simultaneous source separation problem by adopting the projected gradient descent (PGD) method to iteratively estimate the data one would acquire via a conventional seismic acquisition. The projection operator is a windowed robust singular spectrum analysis (SSA) filter that suppresses source interferences in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f-x$ </tex-math></inline-formula> (frequency-space) domain. We reformulate the SSA filter as a robust optimization problem solved via a bifactored gradient descent (BFGD) algorithm. Robustness becomes achievable by adopting Tukey’s biweight loss function for the design of the robust SSA filter. The SSA filter requires breaking down common-receiver gathers or common offset gathers into small overlapping windows. The traditional SSA method needs the filter rank as an input parameter, which can vary from window to window. The latter has been a shortcoming for the application of classical SSA filtering to complex seismic data processing. The proposed robust SSA filter is less sensitive to rank-selection, making it appealing for deblending applications that require windowing. Additionally, the robust SSA projection provides an effective attenuation of random source interferences during the initial iterations of the PGD method. Comparing classical and robust SSA filters, we also report an acceleration of the PGD method convergence when we adopt the robust SSA filter. Finally, we provide synthetic and real data examples, and discuss heuristic strategies for parameter selection.

Observations of Internal Structure Changes in Shoaling Internal Solitary Waves Based on Seismic Oceanography Method

High spatial resolution and deep detection depths of seismic reflection surveying are conducive to studying the fine structure of the internal solitary wave. However, seismic images are instantaneous, which are not conducive to observing kinematic processes of the internal solitary waves. We improved the scheme of seismic data processing and used common-offset gathers to continuously image the same location. In this way, we can observe internal fine structure changes during the movement of the internal solitary waves, especially the part in contact with the seafloor. We observed a first-mode depression internal solitary wave on the continental slope near the Dongsha Atoll of the South China Sea and short-term shoaling processes of the internal solitary wave by using our improved method. We found that the change in shape of waveform varies at different depths. We separately analyzed the evolution of the six waveforms at different depths. The results showed that the waveform in deep water deforms before that in shallow water and the waveform in shallow water deforms to a greater degree. We measured four parameters of the six waveforms during the shoaling including phase velocity, amplitude, wavelength, and slopes of leading and trailing edge. The phase velocity and amplitudes of waveforms in shallow water increase, the wavelengths decrease, and the slopes of trailing edge gradually become larger than that of the leading edge, while the amplitudes of the deep water waveforms do not change significantly and the phase velocities decrease. Our results are consistent with previous studies made by numerical simulations, which suggest the effectiveness of the new processing scheme. This improved scheme cannot only study the internal solitary waves shoaling, but also has great potential in the study of other ocean dynamics.

Viscoacoustic diffraction imaging to delineate karst features in a carbonate reservoir

We demonstrate an attenuation-compensated diffraction imaging workflow to image complex carbonate reservoirs with overburden challenges including shallow gas accumulations. Diffraction separation is performed on pre-migration regularized common-offset gathers compatible with Kirchhoff migration, which allowed us to migrate the diffractions using our preferred viscoacoustic algorithm for the field. When carried out in parallel with conventional seismic data processing, diffraction analysis can help to constrain process parameters and decisions, ultimately leading to better results for both. We show that seismic attributes derived from such a workflow can help to better delineate karsts, fractures, and collapse features, which can be incorporated into the reservoir model and improve our confidence in well placement.

Estimating infiltration front depth using time-lapse multioffset gathers obtained from ground-penetrating-radar antenna array

Nondestructive and noninvasive visualization and quantification of dynamic subsurface hydrologic processes are needed. Using a ground-penetrating-radar (GPR) antenna array, time-lapse common-offset gather and common midpoint (CMP) data can be collected by fixing the antenna at a given location when scanning the subsurface. We have determined wetting front depths continuously during a field infiltration experiment by estimating electromagnetic (EM) wave velocities at given elapsed times using GPR antenna array data. A surface GPR antenna array system, consisting of 10 transmitters (Tx) and 11 receivers (Rx), that can scan each Tx-Rx combination in 10 s at a millisecond scale has been used to acquire all 110 Rx-Tx combinations in approximately 1.5 s. The field infiltration experiment has been conducted at an experimental field near the Tottori Sand Dunes in Japan. Using the estimated EM wave velocity from the CMP data, the depth to the wetting front is computed every minute. The estimated wetting front arrival time agrees with the time at which a sudden increase in the moisture sensor output is observed at a depth from 20 cm and below. We determine that time-lapsed CMP data collected with the GPR antenna array system could be used to estimate EM wave velocities continuously during the infiltration. The GPR antenna array is capable of accurate and quantitative tracking of the wetting front.

First-arrival traveltime inversion of seismic diving waves observed on undulant surface

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

The shoaling mode-2 internal solitary waves in the Pacific coast of Central America investigated by marine seismic survey data

In this paper, the shoaling mode-2 internal solitary waves (ISWs) in the Pacific coast of Central America are studied for the first time using seismic oceanography method. It is found that there is an asymmetry in the vertical amplitude variation of the mode-2 ISWs front and rear during the shoaling process. The amplitude may weaken the effect of the pycnocline deviation on the stability of the mode-2 ISWs. For large amplitudes, the pycnocline needs to deviate greatly, so that the mode-2 ISWs become unstable; for small amplitude, the pycnocline deviates very little, and the mode-2 ISWs become unstable. The pre-stack migration sections of the common offset gathers are used to calculate the apparent phase velocities of the mode-2 ISWs. It is found that in deep water, the seafloor depths and amplitudes simultaneously control the magnitude of the apparent phase velocities of the mode-2 ISWs; in shallow water, the amplitudes mainly control the magnitude of the apparent phase velocities of the mode-2 ISWs. For the mode-2 ISWs with small amplitudes (2a/h2≤2) in shallow water, the apparent phase velocities increase with the amplitudes, and increase rapidly; for the mode-2 ISWs with large amplitudes (2a/h2>2) in shallow water, the apparent phase velocities increase with the amplitudes, but increase slowly. By calculating the relative seismic spectrum energy, it is found that the seismic spectrum energy in the submesoscale wavenumber range corresponds well to the mode-2 ISWs waveform. The mode-2 ISWs in the shoaling process have submesoscale characteristics.

Random Noise Attenuation of Common Offset Gathers Using Iteratively Reweighted $\ell_{2,1}$ Norm Minimization

Sparse representation (SR)-based denoising method attenuates random seismic noise trace-by-trace, which may not be able to employ the coherency between neighboring traces. To address this, we propose a multiple measurement vector (MMV)-based algorithm for robust denoising of multichannel seismic gathers. Seismic reflectors in common offset gather (COG) is characterized by horizontal events, which satisfy the common sparsity assumption, making it ideal for the MMV approach. $\ell _{2,1}$ -norm regularization, which enforces two constraints on source matrix, i.e., temporal sparsity and the horizontal continuity, is then adopted in the MMV model to stabilize the lateral variation between channels. Besides, $\ell _{2,1}$ -norm regularization provides a reasonable intrinsic structure to reduce the multisolution of the algorithm. Celebrating the strengths of iteratively reweighted (IR), we present a novel MMV algorithm, IR $\ell _{2,1}$ norm minimization (IR- $\ell _{2,1}$ ), that further improves the performance. The formulated IR- $\ell _{2,1}$ can be minimized by the alternating direction method of multipliers. Both synthetic and field data applications confirm the effectiveness of the proposed denoising method.

Deep structures seismic enhancement using singular spectral analysis in time and frequency domain: Application in the regional transect of Parnaíba basin - Brazil

The Parnaíba basin is located in the Northeast of Brazil and it started in the Archaean. In a project involving Global Geophysical Services Incorporated and BP Energy do Brasil, a 2D seismic data, 1400 km long and 20 s of two-way travel time was acquired. Because of the acquisition characteristics and large volume of data it was necessary to develop a powerful filtering flow, in order to enhance the signal-to-noise ratio, particularly for deep structures, such as the Moho Discontinuity. For that matter, we have used a two-step recursive-adaptive singular spectral analysis (RA-SSA) to enhance the signal-to-noise ratio. First, we applied the RA-SSA in the t-x domain, along the time variable, for every seismic trace, to attenuate uncorrelated noise, and to enhance the low frequency content of the data. Second, the data was moved to the f-x domain, by means of the Fourier Transform of every single trace, and the RI-SSA method was applied for every frequency, along the x variable, to enhance the correlation of the reflectors between neighboring seismic traces. The filtered results, shown on common offset and CMP gather and on stacked data, show how successful the method was in enhancing the reflectors. We introduce a processing flow capable of enhancing the final stacked image quality, in order to map the Moho Discontinuity and interpret the transect to obtain a better understanding of the Parnaíba basin formation.

Pre‐stack Kirchhoff depth migration local space‐shift imaging condition: synthetic and data examples

ABSTRACTExtracting accurate common image angle gathers from pre‐stack depth migrations is important in the generation of any incremental uplift to the amplitude versus angle attributes and seismic inversions that can lead to significant impacts in exploration and development success. The commonly used Kirchhoff migration outputs surface common offset image gathers that require a transformation to angle gathers for amplitude versus angle analysis. The accuracy of this transformation is one of the factors that determine the robustness of the amplitude versus angle measurements. Here, we investigate the possibility of implementing an extended imaging condition, focusing on the space‐lag condition, for generating subsurface reflection angle gathers within a Kirchhoff migration. The objective is to determine if exploiting the spatial local shift imaging condition can provide any increase in angle gather fidelity relative to the common offset image gathers. The same restrictions with a ray‐based approach will apply using the extended imaging condition as both the offset and extended imaging condition method use travel times derived from solutions to an Eikonal equation. The aims are to offer an alternative ray‐based method to generate subsurface angle gathers and to understand the impact on the amplitude versus angle response. To this end, the implementation of the space‐shift imaging condition is discussed and results of three different data sets are presented. A layered three‐dimensional model and a complex two‐dimensional model are used to assess the space shift image gathers output from such a migration scheme and to evaluate the seismic attributes relative to the traditional surface offset common image gathers. The synthetic results show that the extended imaging condition clearly provides an uplift in the measured amplitude versus angle over the surface offset migration. The noise profile post‐migration is also improved for the space‐lag migration due to the double summation inside the migration. Finally, we show an example of a space‐lag gather from deep marine data and compare the resultant angle gathers with those generated from an offset migration and a time‐shift imaging condition Kirchhoff migration. The comparison of the real data with a well log shows that the space‐lag result is a better match to the well compared to the time‐lag extended imaging condition and the common offset Kirchhoff migration. Overall, the results from the synthetics and real data show that a Kirchhoff migration with an extended imaging condition is capable of generating subsurface angle gathers with an incremental improvement in amplitude versus angle fidelity and lower noise but comes at a higher computational cost.

Modeling and assessing the effects of the sea surface, from being flat to being rough and dynamic

The sea surface acts as a very strong reflector because of the large impedance contrast between water and air. The reflection coefficient is [Formula: see text] in a very good approximation. Apart from the surface multiples, the sea surface is also responsible for generating the source and receiver ghost wavefields. These cause the well-known ghost notches in the spectrum: areas where the signal-to-noise ratio is very low. To model the ghost wavefields, ghost operators can be computed and applied to ghost-free data. Modeling experiments indicate that in the case of a flat sea surface, the character of the notches in various gather types, e.g., receiver gather, common-offset gather, shot record, is largely determined by the complexity of the earth. In a simple earth, e.g., horizontally layered, the notches are always well-defined and deep, but in a complex earth, they become blurry in some of the gather types. Therefore, in the case of a complex subsurface, source deghosting is best carried out in the common-receiver domain and receiver deghosting is best carried out in the common-shot domain. In the case of a simple subsurface, deghosting can be carried out in all domains. An additional factor is that the sea surface may be rough and dynamic. This causes blurry ghost notches in all gather types, even in the case of a simple earth. To model the source ghost for this situation, an effective static rough sea surface suffices. This keeps the computations simple. The condition is that the source has an impulsive character. However, to model the receiver ghost (and the source ghost for a nonimpulsive source), the dynamics of the sea surface must be included. This can be done by composing the final result from the results computed for several “frozen” snapshots of the dynamic sea surface.

Tracking Infiltration Front Depth Using Time-lapse Multi-offset Gathers Collected with Array Antenna Ground Penetrating Radar.

A Ground Penetrating Radar (GPR) system based on a ground-coupled, densely populated antenna array was used to collect data during an infiltration experiment conducted at a test site near the Tottori Sand Dune, Japan. The antenna array used in this study consists of 10 transmitting antennas (Tx) and 11 receiving antennas (Rx). For this experiment, the system was configured to use all possible Tx-Rx pairings, resulting in a Multi-Offset Gather (MOG) consisting of 110 Tx-Rx combinations. The array was left stationary at a position directly above the infiltration area and data were collected every 1.5 seconds using a time-based trigger. Common-Offset Gather (COG) and Common Mid-Point (CMP) data cubes were reconstructed from the MOG data during post-processing. There have been few studies that used time-lapse CMP data to estimate changes in velocity of propagation. In this study, electromagnetic (EM) wave velocity was estimated heuristically at 1-minute intervals from the reconstructed CMP data through curve fitting, using the hyperbola equation. We then proceeded to calculate the depth of the wetting front. The evolution of the wetting front over time obtain through this method is consistent with the observations from a soil moisture sensor which was placed at a depth below 20 cm. The results obtained in this study demonstrate the ability of such array GPR system to monitor a subsurface dynamic process like water infiltration accurately and quantitatively.

Tracking Infiltration Front Depth Using Time-lapse Multi-offset Gathers Collected with Array Antenna Ground Penetrating Radar

A Ground Penetrating Radar (GPR) system based on a ground-coupled, densely populated antenna array was used to collect data during an infiltration experiment conducted at a test site near the Tottori Sand Dune, Japan. The antenna array used in this study consists of 10 transmitting antennas (Tx) and 11 receiving antennas (Rx). For this experiment, the system was configured to use all possible Tx-Rx pairings, resulting in a Multi-Offset Gather (MOG) consisting of 110 Tx-Rx combinations. The array was left stationary at a position directly above the infiltration area and data were collected every 1.5 seconds using a time-based trigger. Common-Offset Gather (COG) and Common Mid-Point (CMP) data cubes were reconstructed from the MOG data during post-processing. There have been few studies that used time-lapse CMP data to estimate changes in velocity of propagation. In this study, electromagnetic (EM) wave velocity was estimated heuristically at 1-minute intervals from the reconstructed CMP data through curve fitting, using the hyperbola equation. We then proceeded to calculate the depth of the wetting front. The evolution of the wetting front over time obtain through this method is consistent with the observations from a soil moisture sensor which was placed at a depth below 20 cm. The results obtained in this study demonstrate the ability of such array GPR system to monitor a subsurface dynamic process like water infiltration accurately and quantitatively.

Extraction of amplitude-preserving angle gathers based on vector wavefield reverse-time migration

Angle-domain common-image gathers (ADCIGs) transformed from the shotdomain common-offset gathers are input to migration velocity analysis (MVA) and prestack inversion. ADCIGs are non-illusion prestack inversion gathers, and thus, accurate. We studied the extraction of elastic-wave ADCIGs based on amplitude-preserving elastic-wave reversetime migration for calculating the incidence angle of P-and S-waves at each image point and for different source locations. The P-and S-waves share the same incident angle, namely the incident angle of the source P-waves. The angle of incidence of the source P-wavefield was the difference between the source P-wave propagation angle and the reflector dips. The propagation angle of the source P-waves was obtained from the polarization vector of the decomposed P-waves. The reflectors’ normal direction angle was obtained using the complex wavenumber of the stacked reverse-time migration (RTM) images. The ADCIGs of P-and S-waves were obtained by rearranging the common-shot migration gathers based on the incident angle. We used a horizontally layered model, the graben medium model, and part of the Marmousi-II elastic model and field data to test the proposed algorithm. The results suggested that the proposed method can efficiently extract the P-and S-wave ADCIGs of the elastic-wave reverse-time migration, the P-and S-wave incident angle, and the angle-gather amplitude fidelity, and improve the MVA and prestack inversion.

L1-norm regularization and wavelet transform: An improved plane-wave destruction method

Seismic diffractions are the specific responses of small-scale inhomogeneities or discontinuous structures in the subsurface, such as faults and cracks, and can be used for locating reservoirs of oil and gas. However, because diffraction energy is much weaker than reflection energy, separating diffractions against the background of strong reflections from seismic data is difficult. In this paper, we propose a regularization method based on the l1-norm constraint to extract seismic diffractions from seismic records in the common-offset gathers. Regularization is a practical method for ill-posed nonlinear problems. The proposed method considers wavelet transform and l1-norm regularization in the plane-wave destruction method, which enhances the stability and accuracy of reflection local slopes. Wavelet transform has multi-level and multi-scale analysis properties and thus it is an effective method for sparse transform. Further, the l1-norm can effectively constrain sparsity properties. Through a synthetic example, the stability of this regularization method is demonstrated to be stronger than that of the conventional plane-wave destruction (PWD) method. Both the numerical simulation and field data application indicate that the proposed regularization method for diffraction extraction is promising and feasible in removing specular reflections and strengthening diffractions.

Opportunities and pitfalls in surface-wave interpretation

Many explorationists think of surface waves as the most damaging noise in land seismic data. Thus, much effort is spent in designing geophone arrays and filtering methods that attenuate these noisy events. It is now becoming apparent that surface waves can be a valuable ally in characterizing the near-surface geology. This review aims to find out how the interpreter can exploit some of the many opportunities available in surface waves recorded in land seismic data. For example, the dispersion curves associated with surface waves can be inverted to give the S-wave velocity tomogram, the common-offset gathers can reveal the presence of near-surface faults or velocity anomalies, and back-scattered surface waves can be migrated to detect the location of near-surface faults. However, the main limitation of surface waves is that they are typically sensitive to S-wave velocity variations no deeper than approximately half to one-third the dominant wavelength. For many exploration surveys, this limits the depth of investigation to be no deeper than approximately 0.5–1.0 km.

Simultaneous Sources Separation via an Iterative Rank-Increasing Method

Simultaneous sources acquisition attracts intensive attention from both academia and industry due to its greatly improved efficiency in acquiring high-density seismic data. Unfortunately, its merits are compromised by the strong interference noise between adjacent shots. In this letter, we propose a stepwise rank-increasing (RI) method to estimate the crosstalk noise in simultaneous sources acquisition. The proposed algorithm assumes that an ideal common offset gather (COG) can be represented via a low-rank matrix in the time-space domain. The coherent signals are estimated from low-rank decomposition and transformed to the crosstalk noise by employing a priori information about random dithering code, and then the blending noise is subtracted from the blended data. By increasing the rank of coherent signals step-by-step, the crosstalk noise can be gradually estimated with high accuracy. In this letter, singular value decomposition is utilized to increase the rank of COG data. Applications on synthetic and field data sets demonstrate the better performance of the proposed RI method not only by more effectively suppressing noise but also by accelerating the convergence rate.

Earthquake-faulting-related deformation in soil evidenced in S-wave shallow reflection data: Field results from Portugal

Expressions of ductile, soft-sediment deformations induced by ground movements due to past earthquakes are difficult to recognize in near-surface soils. We have carried out shallow S-wave reflection studies in a seismically active area located northeast of metropolitan Lisbon, Portugal. Identifying shallow disturbed zones and hidden fault segments in this area is important but quite difficult because of small vertical slips due to earthquakes, the Holocene alluvial cover hiding the fault segments, and a high rate of surficial sedimentation. We have performed S-wave reflection profiling at two sites — Vila Franca Xira and Castanheira de Ribatejo. We detected different but interrelated evidence of soft-sediment deformation in the seismic data. This evidence includes sharp lateral changes in the S-wave velocity field; changes in the reflection horizons in stacked sections; aligned diffractions in unmigrated sections; discontinuities in common-offset gathers; and discontinuities, backscattered, and diffracted arrivals in common-source gathers. Though not equally clear everywhere, this evidence is recognizable at many locations where earthquake-motion-induced disturbed zones are interpreted. To confirm these interpretations, we have performed synthetic modeling of a seismic wavefield using the same acquisition geometry as in the field experiments, and with multiple disturbed zones present as vertical emplacements through horizontally lying soil layers. The modeling results resemble the observations in field data. It is possible to confirm the signatures of soft-sediment deformation in the shallow S-wave reflection data. The approach that we used will be useful in many seismically active, soil-covered areas in the world.

High‐resolution Radon transforms for improved dipole acoustic imaging

ABSTRACTImaging using dipole acoustic logging reflections has become a research topic of increasing interest in recent years. Extracting reflections from the whole waveform is both important and extremely difficult because the reflections are obscured by large‐amplitude direct waves. A method of wavefield separation based on high‐resolution Radon transforms has been applied to separate the reflected waves. First, an analysis of the common offset gathers shows that the linear Radon transform can be used to separate the direct and reflected wave fields. However, traditional linear Radon transforms cannot focus the wave event using the least squares method. An improved high‐resolution linear Radon transform is achieved using the principles of maximum entropy and Bayesian methods based on previous studies. The separation method is tested using synthetic data for hard and soft formations, a void model, and a fault model. The high‐resolution Radon transform method is used to process a field dataset and exhibits improved results compared with those of the standard method.