Phase Of Wave Field Research Articles

Elastic wave pre-stack reverse-time migration based on the second-order P- and S-wave decoupling equation

Abstract The problems of large computation, large storage and low-frequency noises have been the key factors limiting the development of elastic wave pre-stack reverse-time migration (RTM). Most research has centered on the wave equation of first-order velocity stress and using Helmholtz separation to get pure primary and secondary waves. However, the cost is enormous and the amplitude and phase of wavefields will be changed. So, we use the second-order P- and S-wave decoupling equations to construct seismic wavefields that reduce the number of variables, and the storage space required for boundary wavefields is reduced by ∼78%. Then we bring the boundary-saving approach into our study during the wavefield extrapolation process so that we can reconstruct the source wavefields completely. Finally, for the wave equations of second-order displacement used in this study, the Poynting vector expressed by the traditional method was not applicable. Therefore, we derived the formula of the energy flux density vector represented by displacements and used it in directional traveling wave decomposition to suppress low-frequency noise in the imaging profile. Subsequently, based on the inner product imaging conditions, the RTM of the 2-D salt dome model was calculated. The results illustrate the effectiveness and practicability of the proposed solution.

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.

Phase-amplitude-based polarized direct envelope inversion in the time-frequency domain

Large-scale geologic structures with strong contrasts present difficulties for seismic imaging and inversion. Previously, direct envelope inversion (DEI) with ultralow frequency has been proposed to retrieve strong-contrast velocity models. However, the envelope signals lose the instantaneous phase of the original wavefield, resulting in erroneous seismic inversion results. To solve this problem, the instantaneous phase of the wavefield is encoded into envelopes for DEI. In this way, a polarized envelope is created to contain both abundant low frequencies and the instantaneous phase information of the original seismic waveform. Furthermore, to improve the resolution of deep regions underneath the strong reflections, we propose a phase-amplitude-based polarized direct envelope inversion (PA-PDEI) misfit in the time-frequency domain that uses an amplitude factor to emphasize the phase information. This makes it possible to adjust the amplitude influence and boost the low-amplitude seismic signals for deep targets. Tests on a model with a salt body and on field data show that combining the PA-PDEI with the phase-amplitude-based full-waveform inversion (PA-FWI) make it possible to reliably reconstruct velocity models, especially for deep regions, despite large and strong perturbations.

Wave field reconstruction and phase imaging by electron diffractive imaging.

In electron diffractive imaging, the phase image of a sample is reconstructed from its diffraction intensity through iterative calculations. The principle of this method is based on the Fourier transform relation between the real-space wave field transmitted by the sample and its Fraunhofer diffraction wave field. Since Gerchberg's experimental work in 1972, various advancements have been achieved, which have substantially improved the quality of the reconstructed phase images and extended the applicable range of the method. In this review article, the principle of diffractive imaging, various experimental processes using electron beams and application to specific samples are explained in detail.

Multidimensional manipulation of wave fields based on artificial microstructures

Artificial microstructures, which allow us to control and change the properties of wave fields through changing the geometrical parameters and the arrangements of microstructures, have attracted plenty of attentions in the past few decades. Some artificial microstructure based research areas, such as metamaterials, metasurfaces and phononic topological insulators, have seen numerous novel applications and phenomena. The manipulation of different dimensions (phase, amplitude, frequency or polarization) of wave fields, particularly, can be easily achieved at subwavelength scales by metasurfaces. In this review, we focus on the recent developments of wave field manipulations based on artificial microstructures and classify some important applications from the viewpoint of different dimensional manipulations of wave fields. The development tendency of wave field manipulation from single-dimension to multidimensions provides a useful guide for researchers to realize miniaturized and integrated optical and acoustic devices.

Damage imaging in a stiffened curved composite sandwich panel with wavenumber index via Riesz transform

Imaging a damage using the phase of wavefield “video” in the physical domain is developed and applied to a stiffened curved composite sandwich panel for visualization of a barely visible impact damage. The ultrasonic guided waves are generated by the thermoelastic effect induced by a Nd:YAG Q-switched pulse laser and then are captured point-by-point by a laser Doppler vibrometer. The wavefield “video” is reconstructed by measuring out-of-plane velocity on the smooth outside surface of the panel. Newly generated wavenumbers from the geometry/material discontinuities caused by either the stiffener or the impact damage can be detected by observing the change of wavenumber from the reconstructed wavefield “video.” The instantaneous wavenumber (i.e. the magnitude of instantaneous wavevector) derived via Riesz transform and its difference can be shown and highlighted using a proposed imaging condition, named as wavenumber index. The wavenumber index sums the wavenumber values followed by a wave energy threshold filter which is performed in the time domain. This is in contrast to other imaging conditions implemented in the frequency-wavenumber domain by the use of complex wavenumber filtering and wave mode decomposition. Since wavenumber index is the phase-based imaging technique instead of conventional intensity-based technique for the wavefield “video,” this technique is robust in that the impact damages located in the vicinity of geometry/material discontinuities can yield consistent damage image resolution with high sensitivity even for wave propagating from the direction across the stiffener. The barely visible impact damage of the composite structure becomes therefore “visible” with the proposed imaging technique.

Computationally Efficient Phase Shift Plus Interpolation Seismic Migration Method

In this letter, we propose a computationally efficient implementation of the phase shift plus interpolation (PSPI) seismic migration technique. The PSPI is among the well-known migration techniques in the frequency-wavenumber ( $\omega -k_{x}$ ) domain that accounts for lateral velocity variations in the earth subsurface. However, the large number of complex multiplications required to perform PSPI makes this method computationally expensive. The proposed method replaces the use of complex multiplications in the frequency-wavenumber ( $\omega -k_{x}$ ) domain with real additions, reducing the computational complexity greatly. It also replaces the real-by-complex multiplications with real multiplications. It does so by using the fact that the PSPI technique maintains the amplitude and shifts the phase of seismic wavefields in the passband region of the extrapolators while attenuating the amplitude and maintaining the phase of the wavefield in the evanescent region of the extrapolators. The proposed method was tested by performing 2-D poststack depth migration to the well-known SEG/EAGE Salt Model. The computational complexity in the $\omega -k_{x}$ domain was reduced by 76.9%, while producing an accurate migrated section of the salt model.

Geohydroacoustic Noise Monitoring of Under-Ice Water Areas of Northern Seas

The paper presents the results of theoretical and experimental research into the structure of geohydroacoustic wave fields generated in continuous ice-covered northern seas. A simplified mathematical model is constructed that takes into account experimental data demonstrating that the generation of different types of geohydroacoustic waves in the lithosphere–hydrosphere–ice cover system are primarily influenced by the water layer with the ice cover. The seafloor structure mainly affects the characteristics of propagating waves rather than the generation of new modes. Mathematical modeling results have laid the basis for new technologies to localize inhomogeneities in ice-covered water areas. The main distinguishing feature of this novel technology for monitoring a medium under ice-covered marine conditions is the possibility to measure noise signal parameters without active geohydroacoustic emission sources. Methods that measure the characteristics of surface-type waves are the most promising for use in northern sea conditions, in particular, microseismic sounding and noise tomography. Integration of these methods combines the recent achievements of passive geophysics and takes into account the particularities of underwater acoustics. To obtain information on the wave propagation medium, both the wave field amplitude and phase characteristics are used. To detect particular types of waves in records, spatiotemporal signal processing methods are used with the appropriate choice of frequency range. The authors describe their new-generation seismohydroacoustic information-measuring modules (embedded buoys), which are equipped with vector and molecular-electronic primary transducers. The information-measuring modules are designed for combined use with distributed ice-class arrays capable of monitoring continuous ice-covered northern seas year round. Studies of how ice-embedded information-measuring systems function, as well as verification of the obtained theoretical results, were carried out during field tests in February 2017. At each measurement point, the receiver system consisted of three reference devices that took measurements on the seafloor, in the water column, and on the ice surface. Mockups of the tested geohydroacoustic buoys were embedded at points offset by 1 km. Dropped 32 kg weights were used as the sources. Controlled perturbations in the ice experiments made it possible to obtain qualitative spectrograms of geohydroacoustic perturbations in layered structures and analyze the dispersion curves. When the fundamental bottom modes were studied, the signal source consisted of an underwater charge at a depth of 10 m. The embedded seismohydroaoustic information-measuring modules successfully passed the ice-based tests in field conditions at low temperatures, demonstrating the reliability of the obtained seismohydroacoustic information. The experimental data agree very well with theoretical estimates obtained with the created model of a layered geological medium. These studies demonstrated that natural sea noise contains useful information reflecting the internal structure of the seafloor and the water layer and led to development of the instrumental and methodological foundations of a noise technology for localizing inhomogeneities in the aquatic environment and layered bottom structures of northern seas by means of passive microseismic noise monitoring.

Resonance Interaction of Relativistic Electrons with Ion-Cyclotron Waves. I. Specific Features of the Nonlinear Interaction Regimes

We analyze the resonant interaction of relativistic electrons with ion-cyclotron waves in the Earth radiation belts. Finite-length wave packets with variable frequencies and different amplitude profiles are considered. Specific features of the nonlinear interaction regimes are analyzed on the basis of solving numerically a system of equations of the particle motion along with the efficiency of this interaction for a single pass of the particle through the wave packet. In the first part of this work, the peculiarities of the trajectories of individual particles are analyzed. The influence of the shape of the wave packet on the well-known regimes, such as particle trapping by the wave field and particle phase bunching, which leads to a non-zero average variation in the pitch angle in an inhomogeneous medium, are considered. It is shown that a long stay of a particle near the separatrix on the phase plane in the region far from the saddle leads to a strong decrease in the pitch angle of the particle in the absence of the trapping as well. This nonlinear regime (directed scattering) is possible for comparatively low initial pitch angles. In this case, the value of the pitch angle decrease depends on the initial phase of the particle. It is shown that the trajectories corresponding to the directed scattering can be regarded as a transitional type of trajectories, between the trajectories of the untrapped and trapped particles. Quantitative estimates of variations in the pitch angle are obtained, and it is confirmed that the directed scattering and trapping of particles by the wave field can lead to electron precipitation into the loss cone.

Diffraction separation by plane-wave prediction filtering

Seismic data processing typically deals with seismic wave reflections and neglects wave diffraction that affect the resolution. As a general rule, wave diffractions are treated as noise in seismic data processing. However, wave diffractions generally originate from geological structures, such as fractures, karst caves, and faults. The wave diffraction energy is much weaker than that of the reflections. Therefore, even if wave diffractions can be traced back to their origin, their energy is masked by that of the reflections. Separating and imaging diffractions and reflections can improve the imaging accuracy of diffractive targets. Based on the geometrical differences between reflections and diffractions on the plane-wave record; that is, reflections are quasi-linear and diffractions are quasi-hyperbolic, we use plane-wave prediction filtering to separate the wave diffractions. First, we estimate the local slope of the seismic event using planewave destruction filtering and, then, we predict and extract the wave reflections based on the local slope. Thus, we obtain the diffracted wavefield by directly subtracting the reflected wavefield from the entire wavefield. Finally, we image the diffracted wavefield and obtain high-resolution diffractive target results. 2D SEG salt model data suggest that the plane-wave prediction filtering eliminates the phase reversal in the plane-wave destruction filtering and maintains the original wavefield phase, improving the accuracy of imaging heterogeneous objects.

Kirchhoff migration without phases

We present a simple, frequency domain, preprocessing step to Kirchhoff migration that allows the method to image scatterers when the wave field phase information is lost at the receivers, and only intensities are measured. The resulting imaging method does not require knowing the phases of the probing field or manipulating the phase of the wave field at the receivers. In a regime where the scattered field is small compared to the probing field, the problem of recovering the full-waveform scattered field from intensity data can be formulated as an embarrassingly simple least-squares problem. Although this only recovers the projection (on a known subspace) of the full-waveform scattered field, we show that, for high frequencies, this projection gives Kirchhoff images asymptotically identical to the images obtained with full waveform data. Our method can also be used when the source is modulated by a Gaussian process and autocorrelations are measured at an array of receivers.

Extracting depth information of 3-dimensional structures from a single-view X-ray Fourier-transform hologram.

We demonstrate how information about the three-dimensional structure of an object can be extracted from a single Fourier-transform X-ray hologram. In contrast to lens-based 3D imaging approaches that provide depth information of a specimen utilizing several images from different angles or via adjusting the focus to different depths, our method capitalizes on the use of the holographically encoded phase and amplitude information of the object's wavefield. It enables single-shot measurements of 3D objects at coherent X-ray sources. As the ratio of longitudinal resolution over transverse resolution scales proportional to the diameter of the reference beam aperture over the X-ray wavelength, we expect the approach to be particularly useful in the extreme ultraviolet and soft-X-ray regime.

Simultaneous measurement of phase and local orientation of linearly polarized light: implementation and measurement results.

Optical components manipulating both polarization and phase of wave fields find many applications in today's optical systems. With modern lithography methods it is possible to fabricate optical elements with nanostructured surfaces from different materials capable of generating spatially varying, locally linearly polarized-light distributions, tailored to the application in question. Since such elements in general also affect the phase of the light field, the characterization of the function of such elements consists in measuring the phase and the polarization of the generated light, preferably at the same time. Here, we will present first results of an interferometric approach for a simultaneous and spatially resolved measurement of both phase and polarization, as long as the local polarization at any point is linear (e.g., for radially or azimuthally polarized light).

A New Optical Surface Measurement Method with Iterative Sparsity-Constrained Threshold Phase Retrieval Algorithm

Due to its low complexity and acceptable accuracy, phase retrieval technique has been proposed as an alternative to solve the classic optical surface measurement task. However, to capture the overall wave field, phase retrieval based optical surface measurement (PROSM) system has to moderate the CCD position during the multiple-sampling procedure. The mechanical modules of CCD movement may bring about unexpectable deviation to the final results. To overcome this drawback, we propose a new PROSM method based on spatial light modulator (SLM). The mechanical CCD movement can be replaced by an electrical moderation of SLM patterns; thus the deviation can be significantly suppressed in the new PROSM method. In addition, to further improve the performance, we propose a new iterative threshold phase retrieval algorithm with sparsity-constraint to effectively reconstruct the phase of wave field. Experimental results show that the new method provides a more simple and robust solution for the optical surface measurement than the traditional techniques and achieves higher accuracy.

Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

SUMMARY Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

Evaluation algorithms for multistep measurement of spatially varying linear polarization and phase

Optical components manipulating both polarization and phase of wave fields find more and more applications in today's optical systems. In particular, the polarization orientation may vary across the aperture. New measurement techniques and evaluation algorithms are needed to simultaneously characterize the properties of such elements. In this Letter, a general measurement algorithm for locally linear polarization distributions is presented, extending the methods of phase shifting interferometry to the simultaneous determination of polarization and phase. A class of evaluation algorithms is derived, and some example algorithms are described and tested for their resilience against systematic and stochastic stepping errors.

ГЕОДИНАМІКА

In the paper the implementation of energy wave field analysis approach for developed informational model of the geological medium is considered. The solutions of seismic inverse problem are presented, which involves geophysical parameters obtaining of geological medium with the use of field seismic data. In order to obtain geological and geophysical environmental parameters the number of wave field transformations are being carried out, conventionally divided into primary and final part (interpretation). Interpretational phase of wave fields’ transformation involves usage of the elaborated mathematical algorithms.

Raster method for recording optical wave fields

We propose a new method for recording the wave field. The method is based on that the angular spectrum of the field is modulated using an amplitude mask. It is shown that the new method ensures high spatial and angular resolutions. An optical scheme for implementing the method and an algorithm for reconstructing the wave-field phase from the measurement data are developed. Computer simulation of the experiment for recording the wave field on the basis of the proposed method is performed.

Relationships Between Smooth- and Small-Phase Conditions in X-Ray Phase-Contrast Imaging

We analyze some relationships between the small- and smooth-phase conditions in propagation-based X-ray phase-contrast imaging. Although these conditions are generally well-understood, our analysis yields the identification of physical conditions under which they are mathematically equivalent. We also demonstrate that the smooth-phase condition depends not only on the imaging system resolution and object-to-detector distance, but also on the topography of the wavefield phase function.

Phase mapping of domain kinetics in lithium niobate by digital holographic interferometry

The phase mapping of domain kinetics under the uniform steady-state electric field is achieved and investigated in the LiNbO3 crystals by digital holographic interferometry. We obtained the sequences of reconstructed three-dimensional and two-dimensional wave-field phase distributions during the electric poling in the congruent and near stoichiometric LiNbO3 crystals. The phase mapping of individual domain nucleation and growth in the two crystals are obtained. It is found that both longitudinal and lateral domain growths are not linear during the electric poling. The phase mapping of domain wall motions in the two crystals is also obtained. Both the phase relaxation and the pinning-depinning mechanism are observed during the domain wall motion. The residual phase distribution is observed after the high-speed domain wall motion. The corresponding analyses and discussions are proposed to explain the phenomena.