Wavefield Transformation Research Articles

Spectral whitening based seismic data preprocessing technique to improve the quality of surface wave's velocity spectra

A high-quality surface wave velocity spectrum, also known as a dispersion image, is paramount for any MASW survey to accurately predict subsurface earth properties. The presence of diversified noise during field acquisition and dissimilar attenuation due to mechanical and radial damping makes it challenging for any wavefield transformation technique to produce a detailed and precise velocity spectrum. Standard surface wave data preprocessing techniques, such as trace normalization and bandpass filtering, along with postprocessing techniques like frequency-wise amplitude normalization, fail to address all these issues appropriately. In this paper, we present a spectral whitening-based data preprocessing technique that can adequately eradicate most of the shortcomings associated with different wavefield transformation techniques. Instead of normalizing each trace, it normalizes the amplitude of every frequency present in the seismogram. The spectral whitening can regain the relative amplitude losses due to both radial and mechanical damping, thus improving the signal-to-noise ratio. Along with diversified field data including Love and Rayleigh wave surveys, a synthetic dataset is used to demonstrate the efficacy of the proposed technique. Furthermore, field noise is added to random traces to test the ability of the proposed technique to filter asymmetric noise. Overall, the spectral whitening procedure significantly improves the quality of the velocity spectrum and produces a sharper dispersion image with well-separated modes. The work presented here enhances our ability to interpret surface wave velocity spectra precisely and helps explore accurate properties of the subsurface earth. It can help avoid the need for repeated field tests in cases of extremely noisy data, thereby significantly reducing costs and saving time.

Goaf area detection using high-precision wavefield imaging method of ground-airborne transient electromagnetics

Abstract The coal goaf areas are the main cause of accidents involving water intrusion in coal mines. The ground collapse caused by water intrusion in goaf areas poses major threats to further coal mining as the conventional ground-based transient electromagnetic method is difficult to perform due to the hilly terrain in the Loess Plateau. In this study, a ground-airborne transient electromagnetic method for detecting coal goaf areas on the Loess Plateau was presented. First, a numerical model was built using the geological data of the study area. The transient electromagnetic method (TEM) responses of the coal goaf area were determined by forward modeling. Then, the high-precision wavefield transformation method was applied to image the forward model. It was found that compared with the apparent resistivity definition method, the results of the high-precision wavefield transformation method more accurately represented the subsurface structures and the volume effect was avoided. Finally, the high-precision time sweep wavefield imaging method was applied to process the field data. The results revealed that the high-precision wavefield imaging method was able to accurately determine the locations of the goaf areas. In addition, the upper and lower interfaces of the strata and the goaf areas were clearly identified.

Non-destructive testing of slab-like structures including pavements using Lamb and Rayleigh waves-based dispersion analysis

ABSTRACT Lamb and Rayleigh waves-based dispersion analysis has been carried out for non-destructive surface wave testing of different slab-like structures involving a concrete roof slab, a concrete floor, a concrete pavement, and an asphaltic pavement. An impact was generated by gently striking the slab’s free surface with a hammer. A method has also been given to generate the governing (predominant) dispersion mode in the case of Rayleigh wave propagation considering the complex nature of the dispersion function | D ( c , κ ) | ; c and κ refer to phase velocity and wavenumber, respectively. The theoretical dispersion plots generated from the inversion analysis by varying the values of different input parameters were subsequently closely matched with the corresponding obtained field dispersion images for different cases in order to back compute the elastic profile of the slab/pavement. For developing the dispersion images, the Park’s wavefield transformation method was employed. For checking the thicknesses of the different layers, cylindrical cores were also extracted. The study is expected to be useful for evaluating different slab-like structures, including pavements, by using surface wave-based non-destructive tests.

Investigations on the Complex Band Diagram of Flexural Wave through the Fluid-Loaded Phononic Plate

This paper investigates the complex band diagram of flexural waves in the phononic plate with semi-infinite heavy fluid loading. The system under examination is a square plate lattice with two-dimensional periodicity immersed in a fluid domain with infinite height. The numerical models based on the wave field transformation and the Galerkin method combined with the finite element discretization technique are developed to investigate the real and imaginary parts of the dispersion relation of flexural waves propagating through the phononic plate incorporating the fluid-loading effects. A perfect agreement is found between the location and width of stop bands from the real band diagram and the attenuation diagram, which supports the validity of the numerical models. Moreover, the complex band diagram is verified by the transverse vibration transmittance of the finite phononic plate. The results demonstrate that the external fluid loading is able to adjust the location, bandwidth, and decaying level as well as affect the degree of attenuation anisotropy of the complete and directional band gaps.

Phase-velocity and intercept-time scanning (PIS) technique for extracting experimental dispersion characteristics of surface waves

In active surface wave methods, the ability to extract the true dispersion trends from surface wave field data is critical for inferring accurate shear-wave velocity profiles. However, dispersion images such as those generated by the conventional wavefield transformation method are usually accompanied by numerical artifacts including side-lobes and aliasing, both of which decrease the dispersion image resolution and may lead to misinterpretation of dispersion modes. For example, the side lobes can be misinterpreted as higher or lower modes, which would introduce additional errors into the inverted stiffness profiles. A new experimental dispersion analysis method is presented to improve the resolution and sharpness of dispersion images and minimize the side lobes. The proposed method employs scanning of the phase-velocities and intercept-times of a series of harmonic signals obtained by Fourier transformation of raw multichannel data in the space-time (x-t) domain. Results obtained from synthetic and real field data demonstrate that the improved method can yield high-quality dispersion images compared to those of the conventional dispersion-imaging method. In addition, the improved method do not rely on the assumption that the impact point is the generation point of the Rayleigh waves, which is needed for the conventional method.

Wave beaming and diffraction in quasicrystalline elastic metamaterial plates

In this paper, we present evidence of directional wave behavior, i.e., beaming and diffraction, along high-order rotational symmetries of quasicrystalline elastic metamaterial plates. These structures are obtained by placing pillars on an elastic plate following a particular rotational symmetry arrangement, such as eightfold and tenfold rotational symmetries, as enforced by a design procedure in reciprocal space. We estimate the dispersion properties of the waves propagating in the plates through Fourier transformation of transient wave fields. The procedure identifies, both numerically and experimentally, the existence of anisotropic bands characterized by high-energy density at isolated zones in reciprocal space that follow their higher order rotational symmetry. Specific directional behavior is showcased at the identified frequency bands, such as wave beaming (predicted in simulations and confirmed experimentally) and diffraction (exemplified only with numerical results). This paper expands the wave directionality phenomena beyond the symmetries of periodic configurations (e.g., fourfold and sixfold), and opens possibilities for applications involving the unusual high-order wave features of the quasicrystals (e.g., eightfold and tenfold) such as superior guiding, focusing, sensing, and imaging.

A unified approach for relationships among Green's function, normal modes and dispersion spectrum in layered elastic half-space, with corrected misconceptions on surface wave dispersion and testing

SUMMARY In this paper, the global stiffness matrix [K] and the Fourier–Bessel series methods are proposed to derive the accurate Green's function and dynamic response in a form that is directly related to the dispersion curve and experimental dispersion spectrum. Detailed analyses are carried out for the two-layered half-space with different velocity profiles, including the homogeneous half-space as a special case. Our studies indicate that, in Rayleigh wave analysis, the original Rayleigh equation, instead of the rationalized Rayleigh equation as previously derived and used, should be used since the latter would contain extra non-physical roots. We further reveal and characterize three distinct types of leaky waves: the intrinsic surface leaky wave, the apparent Rayleigh mode with a frequency gap associated with a low-velocity half-space and the fast-guided P–SV wave in the layered medium with a high VS contrast between the upper layer and the lower half-space. All leaky modes can be captured by local minima of |det[K]| instead of tracing complex roots in other existing approaches. In the experimental estimation of dispersion curves for practical applications, we have observed that the truncation effect is the major source of uncertainty regardless of the wavefield transformation method utilized. Furthermore, the truncation effect is both location- and model-dependent, without a unique optimal near offset. As such, in order to reduce the uncertainty from the truncation effect, the receiver layout should be considered in the inversion of dynamic response, instead of relying on ensuring a minimum near offset. This becomes possible with the present fast and accurate complete dynamic Green's function by which all wave phenomena (including different types of leaky waves) and receiver locations can be considered in the wavefield transformation.

Virtual wave field characteristic extractions based on multi-window time-sweep wave field transformation

The extraction of multi-scale and multi-resolution wave field characteristics is the focus of transient electromagnetic wave field transformation. However, isuues have been encountered in deep electromagnetic detection and multi-window time-sweep wave field transformation has become an important method for resolving these problems. In this study, a multi-window time-sweep wave field transformation method was adopted to perform the wave field transformations of high and low-resistivity thin layer models with different buried depths, along with different-sized 3D models with various buried depths. By analyzing the wave field characteristics, it is proven that for geological bodies with different burial depths, there must be an optimal window which renders the wave field characteristics of the time-sweep wave field transformation most apparent. In this study,multiple windows of different sizes are used for time-sweep wave field transformations to analyze the wave field characteristics of geological bodies at different scales and depths. Finally, the results of time-sweep wave field transformations of each window are correlated and superimposed to realize multi-resolution characteristics extraction of wave field of multi-scale geological bodies.

Born approximation imaging technique for electrical source multi-component TEM

Abstract In this study, to obtain higher-resolution geoinformation in the electrical source transient electromagnetic method (TEM) interpretation, the pseudo-seismic Born approximation imaging method is applied to the vertical magnetic induction intensity ${B_z}$ and the horizontal electric field ${E_y}$, which is paralleled to the source. First, the differences between the two components are compared, and the results reveal that different components can reflect varied geological information. ${E_y}$ has a stronger signal and is more sensitive to the high-resistivity layer at a long offset, whereas ${B_z}$ has a greater relative difference in the low-resistivity layer at a short offset. The TEM field is then transformed into the pseudo-wavefield using the wavefield transformation method and the Born approximation pseudo-seismic imaging method is adopted to locate the electrical interface. After calculating the 3D model, the results indicate that the multi-component Born approximate imaging can intuitively and effectively locate the depth of the geological interface. Furthermore, the imaging results of a coal mine located in Gansu Province, China, proves that the proposed method can pinpoint the buried location of the coal goaf as well as the stratum trend. In general, the multi-component pseudo-seismic imaging technique plays a significant role in interpreting the electrical source TEM data.

Transient Electromagnetic Machine Learning Inversion Based on Pseudo Wave Field Data

Machine learning inversion (ML-inversion) has been widely used in the interpretation of geophysical data. However, because the transient electromagnetic (TEM) is not sensitive to the response of the small-size or large-depth abnormal body, there are some problems such as poor imaging accuracy and low-resolution when directly processing raw TEM data with ML method. To solve this problem, we propose to use the pseudo seismic wavelet (PSW) data obtained from TEM wave field transformation to perform TEM ML-inversion. Simulation and example application verify that compared with the TEM data, the PSW data has higher recognition sensitivity to the electrical changes of underground anomalies, and the ML-inversion based on the PSW data can significantly improve the TEM imaging accuracy. Our study demonstrates that the PSW data can be used to achieve TEM ML-inversion, which may provide a new way for the further combination of electromagnetic data processing and ML technology.

Multipole-phase division multiplexing.

The control of structured waves has recently opened innovative scenarios in the perspective of radiation propagation, advanced imaging, and light-matter interaction. In information and communication technology, the spatial degrees of freedom offer a wider state space to carry many channels on the same frequency or increase the dimensionality of quantum protocols. However, spatial decomposition is much more arduous than polarization or frequency multiplexing, and very few practical examples exist. Among all, beams carrying orbital angular momentum gained a preeminent role, igniting a variety of methods and techniques to generate, tailor, and measure that property. In a more general insight into structured-phase beams, we introduce here a new family of wave fields having a multipole phase. These beams are devoid of phase singularities and described by two continuous spatial parameters which can be controlled in a practical and compact way via conformal optics. The outlined framework encompasses multiplexing, propagation, and demultiplexing as a whole for the first time, describing the evolution and transformation of wave fields in terms of conformal mappings. With its potentialities, versatility, and ease of implementation, this new paradigm introduces a novel playground for space division multiplexing, suggesting unconventional solutions for light processing and free-space communications.

Specific features of SH-waves propagation in structures with prestressed inhomogeneous coating made of piezoceramics based on LiNbO3

Within the framework of the linearized theory of electroelastic wave propagation, a model of a piezoelectric structure with a prestressed functionally graded coating made of piezoceramics of a trigonal system with a symmetry class of 3m is considered. The ferroelectric LiNbO3 is used as the main material of the structure. The initial deformed state of the coating material is homogeneous, induced by the action of initial mechanical stresses and an external electrostatic field, the properties of the coating continuously change in thickness. By the example of the problem of the propagation of SH-waves from a remote source for structures with an inhomogeneous prestressed coating in the case of an electrically free and short-circuited surface, the influence of the nature and localization of the inhomogeneity of the coating on the features of SAW propagation is studied. The separate and combined effects of initial actions on changes in the physical properties of the structure, the transformation of the surface wave field, and the change in the SAW velocities in a wide frequency range is studied. The results obtained in this work are useful for understanding the dynamic processes in prestressed piezoelectric structures, in the optimization and design of new structures and devices on SAW with high performance characteristics.

Modelling of sound propagation in the ocean using the matrix propagator

The problem of sound propagation in an oceanic waveguide is considered. Attention is concentrated on properties of a wavefield propagator that governs transformation of an arbitrary wavefield in course of propagation. Using the basis of normal modes, we can represent the propagator in the matrix form. If horizontal inhomogeneity of a waveguide is weak, the propagator can be calculated by means of the first-order perturbation theory. In the case of random inhomogeneity, the apparatus of random matrix theory can be exploited. We demonstrate methods of propagator construction for realistic models of waveguides, including waveguides with adiabatic inhomogeneities and shallow-sea waveguides. A scheme of experimental measurement of a propagator in a shallow-sea waveguide is proposed.

Mapping water-abundant zones using transient electromagnetic and seismic methods when tunneling through fractured granite in the Qinling Mountains, China

Severe water inrush currently halts the excavation of the Qinling Water Transportation Tunnel and has even stopped tunneling. Based on the geologic conditions of the construction area, the source of water inrush is abundant groundwater in fractured granite. To accurately predict water inrush, we must know the location, geometry, and boundary information of water-abundant zones before excavation. We have developed a field study of integrated seismic and transient electromagnetic (TEM) applications to map the water-abundant zones ahead of the tunnel face. Before the in-tunnel survey, numerical experiments based on excavation and drilling records verified the feasibility of our scheme. To reveal the fractured zones that may be filled with groundwater, an equitraveltime plane algorithm was used in the seismic data processing. Then, the TEM apparent resistivity was calculated to investigate the water-bearing condition of the fractured zones. To detect the water-abundant zone boundaries, we conducted migration imaging of the TEM pseudowavefield that was extracted from the measured TEM signals. A correlation stacking process to extract the TEM pseudowavefield was used to mitigate the ill-posed effect in the inverse wavefield transformation and obtain boundary information of the water-abundant zones. As expected, the results revealed the depth and geometry of the front and rear boundaries of two water-abundant zones 30 m ahead of the tunnel face, which is consistent with drilling and excavation records after the survey. The results of our case study indicate that the integration of seismic imaging, apparent resistivity imaging, and TEM pseudowavefield migration is an efficient and cost-effective method to provide the location, geometry, and boundary information of water-abundant zones.

Transformation of first mode breather of internal waves above the bottom step in a three-layer fluid

In the present study we consider propagation of a localized internal perturbation in the form of an oscillating wave packet (breather) of the first mode in a three-layer fluid with an uneven bottom shaped as a smoothed step. The study is carried out by methods of numerical simulation within a fully nonlinear two-dimensional (vertical plane) set of NavierStokes equations. A set of calculations was carried out for different widths and heights of the bottom step. Inhomogeneity of the medium leads to transformation of the internal wave field with the formation of weak reflected waves and one or two first-mode breathers passed to the shallow zone. By analyzing linear stability in terms of Richardson and Froude numbers, it was revealed that potentially unstable regions arise at the smallest values of the step width. An amplitude and energy analysis of secondary reflected nonlinear waves was performed. The vertical mode composition of the fully nonlinear wave field is analyzed. It is shown that the first mode makes the largest contribution to the vertical structure of the full-nonlinear packet, though the fourth, second and the third modes also contribute noticeably.

Efficient holographic video generation based on rotational transformation of wavefields.

High-quality holographic video generation requires both high computational resources and time; therefore, algorithms that can generate holographic videos efficiently will be soon in demand for dynamic holographic 3D displays. In this work, we present two algorithms that use a motion compensation scheme - based on the rotational transformation of wavefields [Appl. Opt.47, D110 (2008)], to generate efficiently holographic frames. The effects of motions to the wavefield are analyzed, while video generation examples are provided to support our theory. We report that with the proposed motion compensation scheme combined with the Phong multiple wavefront recording plane CGH method, a 10 times acceleration was achieved with regard to the ray tracing method, with a trade-off of energy loss of 10%. This speedup can be further improved by parallelization of the computations.

Transformation of the First Mode Breather of Internal Waves above a Bottom Step in a Three-Layer Fluid

We consider the problem of the propagation of a localized internal perturbation in the form of an oscillating wave packet (breather) of the first mode in a three-layer fluid with an uneven bottom in the form of a smooth step. The study is carried out using a method of numerical simulation within a fully nonlinear two-dimensional (in the vertical plane) set of Navier–Stokes equations. A set of calculations has been performed for different widths and heights of the bottom step. Inhomogeneity of the medium leads to the transformation of the internal wave field with the formation of weak reflected waves of the lowest modes and one or two first-mode breathers that propagate to the region of shallower depths. It is found from the analysis of linear stability in the terms of Richardson and Froude numbers that potentially unstable regions appear at the smallest values of the step width. An amplitude and energy analysis of secondary reflected nonlinear waves has been performed. The vertical mode composition of the fully nonlinear wave field has been analyzed. It is shown that the first mode makes the largest contribution to the vertical structure of the full-nonlinear packet, though the fourth, second, and third modes also make a noticeable contribution.

A Resolution Enhancement of Rayleigh Wave Dispersive Imaging using Modified Phase-Shift Method

Multi-channel analysis of surface wave (MASW) method is an efficient tool for obtaining vertical shear wave profile. One of the key in the steps in the MASW method is generate a dispersion curves. To generate dispersion energy, the acquired shot gathers data have been transformed from the time-space (t-x) domain to the frequency-phase velocity (f-v) domain using 2D wavefield transformation so that the dispersion curve can be determined by picking the peak of dispersion energy. In this paper, we proposed a modified phase-shift method to increase the resolution of Rayleigh wave dispersive imaging so that the accuracy of the dispersion curve determination becomes higher. This method added processing step on the conventional phase-shift method. The algorithm is written in Matlab environment. We compared this method with the conventional phase-shift and frequency-wavenumber (F-K) method and applied to synthetic and real data. We used DISECA program in Matlab to generate synthetic waveforms. Our results from the synthetic and real data show that modified phase-shift method can improve the dispersion energy imaging resolution better than the conventional phase-shift and F-K method.

ПРИМЕНЕНИЕ ПСЕВДОВОЛНОВЫХ ТРАНСФОРМАНТ В ИМПУЛЬСНОЙ ЭЛЕКТРОРАЗВЕДКЕ ДЛЯ ВЫДЕЛЕНИЯ НАКЛОННЫХ ГЕОЛОГИЧЕСКИХ ГРАНИЦ

Актуальность. Метод нестационарных электромагнитных зондирований или зондирований становлением поля является востребованным инструментом при поиске и разведке месторождений различного типа полезных ископаемых. Современные задачи электроразведки требуют использования установок с большим числом источников и приёмников. Для подобного типа установок задача интерпретации полученных данных является весьма ресурсоемкой. Отсюда вытекает острая необходимость развития методов обработки и интерпретации данных, полученных в результате импульсных электромагнитных зондирований. Одним из возможных путей такого развития могут послужить трансформации данных зондирований становлением в пространство решений волнового уравнения. Цель: применить метод волновой трансформации к данным зондирований становлением, зарегистрированным над проводящими средами с наклонной границей в многоразносных установках, для получения новых качественных оценок исследуемого геоэлектрического разреза. Методика исследования базируется на новых численных алгоритмах для устойчивого преобразования данных зондирований становлением в волновую область. Исходные данные для отладки процедур трансформации (расчётные кривые становления поля) были получены с использованием программного комплекса MODEM3D, который предназначен для прямого моделирования переходных процессов диффузии электромагнитных полей. Результаты. Были получены псевдоволновые трансформанты сигналов нестационарных электромагнитных зондирований в средах с наклонной границей, и построены их годографы. Полученные наборы трасформаций позволяют выделить линию выхода наклонного контакта на дневную поверхность. Установлено, что перекрывающие наносы ослабляют максимумы псевдоволновых трансформаций и снижают возможность точной локализации линии выхода наклонной границы. Рассмотрено поведение тороидальных вихревых токов в зависимости от времени для модели геологической среды с наклонной границей.

Review of Geophysical Exploration on Mined-out Areas and Water Abundance

With the increase in mining depth, the presence of goafs has become increasingly severe in mine safety. The accurate and effective detection of underground goafs and their water abundance is the key to ensure the safety of mine production. On the basis of the relevant research, this paper defines different goaf types from the perspective of geophysical exploration and discusses the geophysical prerequisites for goaf detection. DC methods, electromagnetic methods, seismic methods, and other geophysical methods on the ground and in the subsurface are reviewed and summarized using the method's principle, research status, and technical features. Research progress on the geophysical methods in goafs and their water abundance detection are introduced, including the electrical source short-offset transient electromagnetic method (SOTEM), the wave-field transformation and synthetic aperture of the transient electromagnetic method, and comprehensive detection. At the end of the paper, a direction for the development of coal mined-out areas and their water abundance detection is put forward, including information fusion technology, ground-airborne electromagnetic methods, magnetic resonance sounding (MRS), surface-borehole transient electromagnetic method, surface-borehole seismic methods, and seismic while tunneling technology. The application prospects of these methods are discussed, and the results of this study are expected to considerably improve the location precision and resolution of the goaf detection on the basis of the implications of these techniques.