Screen Propagator Research Articles

Viscoacoustic generalized screen propagator in constant-Q model

When seismic waves propagate through the geological formation, there is a significant loss of energy and a decrease in imaging resolution, because of the viscoacoustic properties of subsurface medium. This profoundly impacts seismic wavefield propagation, imaging and interpretation. To accurately image the true structure of subsurface medium, the consensus among geophysicists is to no longer treat subsurface medium as ideal homogeneous medium, but rather to incorporate the viscoacoustic properties of subsurface medium. Based on the generalized screen propagator using conventional acoustic wave equation (acoustic GSP), our developed method introduces viscoacoustic compensation strategy, and derives a one-way wave generalized screen propagator based on time-fractional viscoacoustic wave equation (viscoacoustic GSP). In numerical experiments, we conducted tests on two-dimensional multi-layer model and the Marmousi model. When comparing with the acoustic GSP using the acoustic data, we found that the imaging results of the viscoacoustic GSP using the viscoacoustic data showed a significant attenuation compensation effect, and achieved imaging results for both algorithms were essentially consistent. However, the imaging results of acoustic GSP using viscoacoustic data showed significant attenuation effects, especially for deep subsurface imaging. This indicates that we have proposed an effective method to compensate the attenuated seismic wavefield. Our application on a set of real seismic data demonstrated that the imaging performance of our proposed method in local areas surpassed that of the conventional acoustic GSP. This suggests that our proposed method holds practical value and can more accurately image real subsurface structures while enhancing imaging resolution compared with the conventional acoustic GSP. Finally, with respect to computational efficiency, we gathered statistics on running time to compare our proposed method with conventional Q-RTM, and it is evident that our method exhibits higher computational efficiency. In summary, our proposed viscoacoustic GSP method takes into account the true properties of the medium, still achieves migration results comparable to conventional acoustic GSP.

Enhancing one-way wave equation-based migration with deep learning

One advantage of one-way wave equation-based migration is its low computational cost. However, due to the limited wavefield propagation angle, it is difficult to use one-way wave equation-based migration for high-precision imaging of structures with large inclinations due to issues such as inaccurate amplitudes and migration image artifacts. In addition, when the model has large horizontal velocity differences, it is difficult for the one-way wave propagator to calculate an accurate wavefield phase. Reverse time migration (RTM) based on the two-way wave propagator has a high resolution and avoids the issues associated with one-way wave propagators; however, it has a high computational cost in practical applications. We develop a convolutional neural network (CNN) application mode that improves one migration method by learning from another one and design a CNN with a structure similar to U-net that combines the advantages of both migration methods. The CNN label is the RTM result, and the corresponding input is the result of one-way wave migration with a generalized screen propagator (GSP). The trained CNN model improves the amplitude in the one-way wave migration image and removes the errors caused by large lateral velocity perturbations. Moreover, by maintaining the high migration calculation efficiency, our CNN model allows for a high resolution, few artifacts, and accurate images of steep structures in the one-way wave migration result. With our method, the accuracy of the one-way wave migration result is close to that of the RTM result. The use of GSP-based migration in our CNN model rather than conventional RTM to generate prospecting images can considerably reduce the calculation costs.

An optimised one-way wave migration method for complex media with arbitrarily varying velocity based on eigen-decomposition

Abstract The classical one-way generalised screen propagator (GSP) and Fourier finite-difference (FFD) schemes have limitations in imaging large angles in complex media with substantial lateral variations in wave velocity. Some improvements to the classical one-way wave scheme have been proposed with optimised methods. However, the performance of these methods in imaging complex media remains unsatisfying. To overcome this issue, a new strategy for wavefield extrapolation based on the eigenvalue and eigenvector decomposition of the Helmholtz operator is presented herein. In this method, the square root operator is calculated after the decomposition of the Helmholtz operator at the product of the eigenvalues and eigenvectors. Then, Euler transformation is applied using the best polynomial approximation of the trigonometric function based on the infinite norm, and the propagator for one-way wave migration is calculated. According to this scheme, a one-way operator can be computed more accurately with a lower-order expansion. The imaging performance of this scheme was compared with that of the classical GSP, FFD and the recently developed full-wave-equation depth migration (FWDM) schemes. The impulse responses in media with arbitrary velocity inhomogeneity demonstrate that the proposed migration scheme performs better at large angles than the classical GSP scheme. The wavefronts calculated in the dipping and salt dome models illustrate that this scheme can provide a precise wavefield calculation. The applications of the Marmousi model further demonstrate that the proposed approach can achieve better-migrated results in imaging small-scale and complex structures, especially in media with steep-dipping faults.

Two-way wave equation depth migration using one-way propagator extrapolation

Two-way wave depth migration (TWDM) can achieve a wider imaging angle in media with significant lateral velocity changes and better imaging results for complex structures with high dip angles than in conventional one-way wave depth migration. Conventional one-way wave migration uses a boundary condition to approximately solve the second-order wave equation, leading to limited propagating angles and inaccurate imaging results, especially for complicated structures. Theoretically, a full-wave equation is of second order and requires two boundary conditions to solve it. The dual-sensor acquisition system can provide sufficient boundary conditions; however, it is challenging to acquire ideal, cost-effective, and factual seismic data, particularly in 3D seismic exploration. Overcoming these shortcomings, we propose a solution that uses conventional surface data to accurately estimate the wavefield at the second layer as another boundary condition. Based on the eigen-decomposition theory, a one-way propagator to suit arbitrary variant velocity on the surface is introduced.The conventional Fourier finite-difference (FFD) and generalised screen propagator (GSP) are utilised to perform the proposed TWDM schemes. The impulse responses proved that the proposed scheme using FFD and GSP operators had no limitation on the propagation angle. The single-shot migrated results in the flat model confirmed that the proposed schemes could achieve better amplitude-preserving performance than the conventional one-way schemes. The dip model showed that the proposed scheme was consistent with the characteristics of one-way wave propagators in imaging steep dippings. Imaging results of the Marmousi model further confirmed that the proposed scheme could obtain more accurate imaging sections for complex structures, especially for steep flanks and deep-seated anticlines. The application of actual dual-sensor seismic data demonstrated that the proposed scheme could achieve a higher imaging quality than the dual-sensor method.

Evaluation of Ionospheric Scintillation in GNSS Radio Occultation Measurements and Simulations

AbstractLike any other system relying on transionospheric propagation, Global Navigation Satellite System (GNSS) Radio Occultation (GNSS‐RO) is affected by ionospheric conditions during measurements. Regions of plasma irregularities in F region create abrupt gradients in the distribution of ionized particles. Radio signals propagated through such regions suffer from constructive and destructive contributions in phase and amplitude, known as scintillations. Different approaches have been proposed in order to model and reproduce the wave propagation through ionospheric irregularities. We present simulations considering single‐slope power law model of irregularities integrated with Multiple Phase Screen (MPS) propagation. In this work, the capability of the scintillation model to reproduce features in low‐latitude MetOp measurements in the early hours of DOY 76, 2015 is evaluated. Power spectral density (PSD) analysis, scintillation index, decorrelation time, and standard deviation of neutral bending angle are considered in the comparison between the simulations and RO measurements. The results demonstrate the capability of the simulator to replicate an equivalent error contribution to the neutral bending angle measurement in cases of moderate to strong scintillation.

Three-dimensional laser writing inside silicon using THz-repetition-rate trains of ultrashort pulses

Three-dimensional laser writing inside silicon remains today inaccessible with the shortest infrared light pulses unless complex schemes are used to circumvent screening propagation nonlinearities. Here, we explore a new approach irradiating silicon with trains of femtosecond laser pulses at repetition rates up to 5.6 THz. This extremely high repetition rate is faster than laser energy dissipation from microvolume inside silicon, thus enabling unique capabilities for pulse-to-pulse accumulation of free carriers generated by nonlinear ionization, as well as progressive thermal bandgap closure before any diffusion process comes into play. By space-resolved measurements of energy delivery inside silicon, we evidence a net increase on the level of space-time energy localization. The improvement is also supported by experiments demonstrating an apparent decrease of the energy threshold for modification and drastic improvements on the repeatability, uniformity, and symmetricity of the produced features. The unique benefits of THz bursts can provide a new route to meet the challenge of 3D inscription inside narrow bandgap materials.

Ultrafast Laser Writing Deep inside Silicon with THz-Repetition-Rate Trains of Pulses.

Three-dimensional laser writing inside silicon remains today inaccessible with the shortest infrared light pulses unless complex schemes are used to circumvent screening propagation nonlinearities. Here, we explore a new approach irradiating silicon with trains of femtosecond laser pulses at repetition rates up to 5.6 THz that is order of magnitude higher than any source used for laser processing so far. This extremely high repetition rate is faster than laser energy dissipation from microvolume inside silicon, thus enabling unique capabilities for pulse-to-pulse accumulation of free carriers generated by nonlinear ionization, as well as progressive thermal bandgap closure before any diffusion process comes into play. By space-resolved measurements of energy delivery inside silicon, we evidence changes in the interplay between detrimental nonlinearities and accumulation-based effects. This leads to a net increase on the level of space-time energy localization. The improvement is also supported by experiments demonstrating high performance for 3D laser writing inside silicon. In comparison to repeated single pulses, irradiation with trains of only four-picosecond pulses with the same total energy leads to an apparent decrease of the energy threshold for modification and drastic improvements on the repeatability, uniformity, and symmetricity of the produced features. The unique benefits of THz bursts can provide a new route to meet the challenge of 3D inscription inside narrow bandgap materials.

Two-way wave equation-based depth migration using one-way propagators on a bilayer sensor seismic acquisition system

Conventional migration uses the seismic data set recorded at a given depth as one initial condition from which to implement wavefield extrapolation in the depth domain. In using only one initial condition to solve the second-order acoustic wave equation, some approximations are used, resulting in the limitation of imaging angles and inaccurate imaging amplitudes. We use an over/under bilayer sensor seismic data acquisition system that can provide the two initial conditions required to make the second-order acoustic wave equation solvable in the depth domain, and we develop a two-way wave equation depth migration algorithm by adopting concepts from one-way propagators, called bilayer sensor migration. In this new migration method, two-way wave depth extrapolation can be achieved with two one-way propagators by combining the wavefields at two different depths. It makes it possible to integrate the advantages of one-way migration methods into the bilayer sensor system. More detailed bilayer sensor migration methods are proposed to demonstrate the feasibility. In the impulse response tests, the propagating angle of the bilayer sensor migration method can reach up to 90°, which is superior to those of the corresponding one-way propagators. To test the performance, several migration methods are used to image the salt model, including the one-way generalized screen propagator, reverse time migration (RTM), and our bilayer sensor migration methods. Bilayer sensor migration methods are capable of imaging steeply dipping structures, unlike one-way propagators; meanwhile, bilayer sensor migration methods can greatly reduce the numbers of artifacts generated by salt multiples in RTM.

Wavefield interpolation in 3D large‐step Fourier wavefield extrapolation

ABSTRACTExtrapolating wavefields and imaging at each depth during three‐dimensional recursive wave‐equation migration is a time‐consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier‐transform‐related wavefield extrapolation method. First, we formulate a three‐dimensional first‐order separation‐of‐variables screen propagator for large‐step wavefield extrapolation, which allows for wide‐angle propagations in highly contrasting media. This propagator significantly improves the performance of the split‐step Fourier method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform in each thick slab. We then extend the two‐dimensional Kirchhoff and Born–Kirchhoff local wavefield interpolators to three‐dimensional cases for each slab. The three‐dimensional Kirchhoff interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, whereas the three‐dimensional Born–Kirchhoff interpolator is derived from the Lippmann–Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the three‐dimensional salt model of the Society of Exploration Geophysicists/European Association of Geoscientists demonstrate that three‐dimensional first‐order separation‐of‐variables screen propagator Born–Kirchhoff depth migration using thick‐slab wavefield extrapolation plus thin‐slab interpolation tolerates a considerable depth‐step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed three‐dimensional interpolators are presented with one‐way Fourier extrapolation methods, they can be extended for applications to general migration methods.

High-order generalized screen propagator migration based on particle swarm optimization

Various migration methods have been proposed to image high-angle geological structures and media with strong lateral velocity variations; however, the problems of low precision and high computational cost remain unresolved. To describe the seismic wave propagation in media with lateral velocity variations and to image high-angle structures, we propose the generalized screen propagator based on particle swarm optimization (PSO-GSP), for the precise fitting of the single-square-root operator. We use the 2D SEG/EAGE salt model to test the proposed PSO-GSP migration method to image the faults beneath the salt dome and compare the results to those of the conventional high-order generalized screen propagator (GSP) migration and split-step Fourier (SSF) migration. Moreover, we use 2D marine data from the South China Sea to show that the PSO-GSP migration can better image strong reflectors than conventional imaging methods.

Comparative detection of a large population of grapevine viruses by TaqMan® RT-qPCR and ELISA

Grapevine (Vitis spp.) can be infected by numerous viruses that are often widespread and of great economic importance. Reliable detection methods are necessary for sanitary selection which is the only way to partly control grapevine virus diseases. Biological indexing and ELISA are currently the standard methods for screening propagation material, and PCR-methods are becoming increasingly popular. Due to the diversity of virus isolates, it is essential to verify that the tests allow the detection of the largest possible virus populations. We developed three quadruplex TaqMan® RT-qPCR assays for detecting nine different viruses that cause considerable damage in many vineyards world-wide. Each assay is designed to detect three viruses and the grapevine Actin as an internal control.A large population of grapevines from diverse cultivars and geographic location was tested for the presence of nine viruses: Arabis mosaic virus (ArMV), Grapevine fleck virus (GFkV), Grapevine fanleaf virus (GFLV), Grapevine leafroll-associated viruses (GLRaV-1, -2, -3), Grapevine rupestris stem pitting-associated virus (GRSPaV), Grapevine virus A (GVA), and Grapevine virus B (GVB). In general, identical results were obtained with multiplex TaqMan® RT-qPCR and ELISA although, in some cases, viruses could be detected by only one of the two techniques.

Three‐dimensional modeling of high‐latitude scintillation observations

AbstractGlobal Navigation Satellite System signals exhibit rapid fluctuations at high and low latitudes as a consequence of propagation through drifting ionospheric irregularities. We focus on the high‐latitude scintillation problem, taking advantage of a conjunction of European Incoherent Scatter Radar (EISCAT) observations and a GPS scintillation monitor viewing the same line of sight. Just after 20:00 UT on 17 October 2013, an auroral E region ionization enhancement occurred with associated phase scintillations. This investigation uses the scintillation observations to estimate the ionospheric electron density distribution beyond the spatial resolution of EISCAT (5–15 km along the line of sight in this case). Following the approach of Deshpande et al. (2014), signal propagation is modeled through a specified density distribution. A multiple phase screen propagation algorithm is applied to irregularities conforming to the description of Costa and Kelley (1977) and constrained to match the macroscopic conditions observed by EISCAT. A 50‐member ensemble of modeled outputs is approximately consistent with the observations according to the standard deviation of the phase (σp). The observations have σp = 0.23 rad, while the ensemble of modeled realizations has σp = 0.23 + 0.04–0.04. By comparison of the model output with the scintillation observations, we show that the density fluctuations cannot be a constant fraction of the mean density. The model indicates that E region density fluctuations whose standard deviation varies temporally between 5 and 25% of the mean (EISCAT‐observed) density are required to explain the observed phase scintillations.

Numerical modeling of seismic waves using frequency-adaptive meshes

An improved modeling algorithm using frequency-adaptive meshes is applied to meet the computational requirements of all seismic frequency components. It automatically adopts coarse meshes for low-frequency computations and fine meshes for high-frequency computations. The grid intervals are adaptively calculated based on a smooth inversely proportional function of grid size with respect to the frequency. In regular grid-based methods, the uniform mesh or non-uniform mesh is used for frequency-domain wave propagators and it is fixed for all frequencies. A too coarse mesh results in inaccurate high-frequency wavefields and unacceptable numerical dispersion; on the other hand, an overly fine mesh may cause storage and computational overburdens as well as invalid propagation angles of low-frequency wavefields. Experiments on the Padé generalized screen propagator indicate that the Adaptive mesh effectively solves these drawbacks of regular fixed-mesh methods, thus accurately computing the wavefield and its propagation angle in a wide frequency band. Several synthetic examples also demonstrate its feasibility for seismic modeling and migration.

Prestack elastic generalized-screen migration for multicomponent data

An efficient prestack depth migration method based on the elastic one-way wave equation was developed using an improved elastic generalized-screen propagator, which effectively describes the behavior of elastic waves with mode conversion at the interfaces and efficiently computes wave propagation in media with lateral velocity variations. The elastic propagator presented in this study was improved from the elastic generalized-screen propagator. Several terms of the vertical slowness right symbol with orders are corrected from the original formulation, and the vertical slowness operator in the propagator was expanded up to the 2nd order which yields a more accurate approximation. In each screen propagation step, the multicomponent wavefields are automatically separated into the P and S wavefields by the P–S decomposition operator included in the elastic generalized-screen propagator. This process facilitates the imaging of the P and S waves separately without any additional P and S separation process after the wavefield extrapolation. Impulse response tests of the improved elastic generalized-screen propagator in a uniform-property medium proved that propagation accuracy increases with order, even when large medium perturbations are assigned. Migration tests using the developed algorithm on a simple layered model and two complex models (the SEG/EAGE salt and elastic Marmousi-2 model) demonstrated the functional advantages and capabilities of the algorithm compared with elastic migration using the scalar wave equation.

Imaging tilted transversely isotropic media with a generalised screen propagator

One-way wave equation migration is computationally efficient compared with reverse time migration, and it provides a better subsurface image than ray-based migration algorithms when imaging complex structures. Among many one-way wave-based migration algorithms, we adopted the generalised screen propagator (GSP) to build the migration algorithm. When the wavefield propagates through the large velocity variation in lateral or steeply dipping structures, GSP increases the accuracy of the wavefield in wide angle by adopting higher-order terms induced from expansion of the vertical slowness in Taylor series with each perturbation term. To apply the migration algorithm to a more realistic geological structure, we considered tilted transversely isotropic (TTI) media. The new GSP, which contains the tilting angle as a symmetric axis of the anisotropic media, was derived by modifying the GSP designed for vertical transversely isotropic (VTI) media. To verify the developed TTI-GSP, we analysed the accuracy of wave propagation, especially for the new perturbation parameters and the tilting angle; the results clearly showed that the perturbation term of the tilting angle in TTI media has considerable effects on proper propagation. In addition, through numerical tests, we demonstrated that the developed TTI-GS migration algorithm could successfully image a steeply dipping salt flank with high velocity variation around anisotropic layers.

One‐Way Propagators Coupled with Reflection/Transmission Coefficients for Seismogram Synthesis in Complex Media

AbstractThe one‐way and one‐return approximation is a multiple‐forescattering‐single‐backscattering (MFSB) approximation. Compared with full‐waveform numerical methods, the one‐way approximation can save greatly computing time and memory, which makes it possible to simulate wave propagation over long distances. In this article, we combine both the one‐return and separation‐of‐variables approximations to develop a new one‐way propagator coupled with reflection/transmission (R/T) coefficients for seismogram synthesis in complex media. This method is derived from establishing simultaneous generalized Lippmann‐Schwinger equations in two adjoining heterogeneous layers followed by the separation‐of‐variables and one‐return approximations. The resulting one‐way propagator consists of two parts: the separation‐of‐variables screen propagator and the R/T operators that account for amplitude variations with incident angles across interfaces. The separation‐of‐variables screen propagator for one‐way wave propagation accounts for wide angles in large‐contrast media. The R/T coefficients are the implicit function of the dip angles of geological interfaces in subsurface, for which the calculation is coupled with one‐way propagation simulation in a natural manner. We compare the presented method with the full‐waveform BE method for two numerical examples and a real geology structure. The result shows that the presented method simulates reflected waves well in travel time, amplitude, and waveform for various velocity contrasts across interfaces.

Imaging salt bodies using explicit migration operators offshore Norway

We have tested the performance of 3D shot-profile depth migration using explicit migration operators on a real 3D marine data set. The data were acquired offshore Norway in an area with a complex subsurface containing large salt bodies. We compared shot-profile migration using explicit migration operators with conventional Kirchhoff migration, split-step Fourier migration, and common-azimuth by generalized screen propagator (GSP) migration in terms of quality and computational cost. Image quality produced by the explicit migration operator approach is slightly better than with split-step Fourier migration and clearly better than in common-azimuth by GSP and Kirchhoff migrations. The main differences are fewer artifacts and better-suppressed noise within the salt bodies. Kirchhoff migration shows considerable artifacts (migration smiles) within and close to the salt bodies, which are not present in images produced by the other three wave-equation methods. Expressions for computational cost were developed for all four migration algorithms in terms of frequency content and acquisition parameters. For comparable frequency content, migration cost using explicit operators is four times the cost of the split-step Fourier method, up to 260 times the cost of common-azimuth by GSP migration, and 25 times the cost of Kirchhoff migration. Our results show that in terms of image quality, shot-profile migration using explicit migration operators is well suited for imaging in areas with complex geology and significant velocity changes. However, computational cost of the method is high and makes it less attractive in terms of efficiency.

2.5D SH Wave Propagation in Heterogeneous Crustal Wave Guides Using the Phase Screen Method

Abstract One-way approximations for regional phases slice the half-space crustal wave guide into a number of slabs perpendicular to the propagation direction; the Moho discontinuity can be easily treated as a perturbation from the crustal background. The advantage of one-way propagation methods is their great saving of computing time and memory compared to full-waveform numerical methods, especially for 3D simulations. In this article, we present general 2.5D SH formulas for the thin-slab method and a generalized screen propagator (GSP) for simulating SH wave propagation in the heterogeneous half-space crustal wave guide. Comparisons of numerical results with a finite-difference (FD) algorithm for a standard flat crustal model show excellent agreement, demonstrating the validity and accuracy of the 2.5DGSP for the half-space problem. We then compare the curves of energy attenuation calculated by the 2D and 2.5D formulas. The comparison shows that the energy attenuation of the 2.5D case is about 1.5–3 times greater than that of the 2D case when the trapped mode is formed. The SH screen propagator is also used to simulate two laterally unvarying (in the y direction) crustal models, showing the path effects on regional wave propagation.

Beamlet migration using local cosine basis

We have developed the theoretical foundation and technical details of a migration method using a local-cosine-bases (LCB) beamlet propagator. A beamlet propagator for heterogeneous media based on local perturbation theory is derived, and a fast implementation method is constructed. The use of local background velocities and local perturbations results in a two-scale decomposition of beamlet propagators: a background propagator for large-scale structures and a local phase-screen correction for small-scale local perturbations. Because of its locally adaptive nature, the beamlet propagator can handle strong lateral velocity variations with improved accuracy. For high-efficiency migration, we use a table-driven method and apply some techniques of sparse matrix operations. Compared with the Fourier finite-dif-ference and generalized screen propagator methods, the image quality and computational efficiency are similar. In some cases, we see fewer migration artifacts around and inside salt bodies with our method. We attribute this to the better high-angle accuracy of beamlet propagators in strong-contrast media. Numerical tests using synthetic data sets of the SEG-EAGE 2D salt model, Marmousi model, and Sigsbee 2A model demonstrate its high accuracy and reasonable efficiency. Another special feature of LCB beamlet migration is the availability of information in the local wavenumber domain during migration, which can be used to correct acquisition aperture effect and for other processing. Compared to beamlet migration using the Gabor-Daubechies frame (GDF) propagator, LCB migration is much more efficient because LCB is an orthonormal basis, whereas GDF has redundancy (usually greater than two) in the decomposition.

Propagation dynamics of off-axis phase singularities

An analytical expression for the half-plane diffraction of off-axis phase singularity beams based on Gaussian intensity profile is derived, which enables us to study the propagation dynamics of off-axis phase singularities in detail. It is shown that the half-plane screen diffraction, off-axis displacement and propagation distance affect the propagation behavior and spatial distribution of phase singularities. By varying the off-axis displacement and propagation distance, the creation, shift and annihilation of phase singularities in the diffraction field may appear.