Reflected Wave Field Research Articles

Separation of Lamb modes at a plate edge by using orthogonality relation

Lamb modes are widely used for non-destructive evaluation of plate-like structures and simple interpretation procedures for the analysis of the monitored structures are needed. In this study we apply the orthogonality relation based method for post-processing Finite Element (FE) predictions in order to separate Lamb modes at a plate edge. The reflected wave field from the free edge is a superposition of all the eigenmodes of an infinite plate. The eigenmode amplitudes of the reflected wave field are determined by applying the orthogonality-based method. Overlapping wavepackets of Lamb modes at a plate edge are simulated by using the FE model of the incident S0 mode in a plate with a crack. Time-domain signals of propagating and non-propagating modes are extracted.

Impulsive Radiation From a Horizontal Electric Dipole Above an Imperfectly Conducting Surface

Solutions for the impulsive wave fields generated by a horizontal electric dipole situated above an imperfectly conducting surface are derived. The space-time expressions for the reflected wave fields open the door to analysis of their properties in the far-, intermediate-, and near-field regions, and can serve as benchmark for numerical methods employed to wave simulation with applications in antenna design and radio communication. The EM properties of the conductive material are represented by a surface impedance and translated to the wave motion via employing the local plane wave relation as the boundary condition. At the core of tackling the impedance boundary value problem is the derivation of three space-time reflected-wave Green's functions. In contrast to the vertical electric dipole problem, a coupling term is present in the transform-domain wave solutions, and hinders direct application of the extended Cagniard-De Hoop method. A partial-fraction decomposition of this coupling term is the key to furnishing the transformation back to the time domain. Numerical results illustrate time traces and spectra of the measurable reflected electric field strength.

Impulsive Radiation From a Vertical Electric Dipole Above an Imperfectly Conducting Surface

Solutions for the impulsive wave fields generated by a horizontal electric dipole situated above an imperfectly conducting surface are derived. The space-time expressions for the reflected wave fields open the door to analysis of their properties in the far-, intermediate-, and near-field regions, and can serve as benchmark for numerical methods employed to wave simulation with applications in antenna design and radio communication. The EM properties of the conductive material are represented by a surface impedance and translated to the wave motion via employing the local plane wave relation as the boundary condition. At the core of tackling the impedance boundary value problem is the derivation of three space-time reflected-wave Green's functions. In contrast to the vertical electric dipole problem, a coupling term is present in the transform-domain wave solutions, and hinders direct application of the extended Cagniard-De Hoop method. A partial-fraction decomposition of this coupling term is the key to furnishing the transformation back to the time domain. Numerical results illustrate time traces and spectra of the measurable reflected electric field strength.

Investigation of the parameters of signals reflected from the ionosphere on the basis of regular radio-field measurements performed in the long-wave band

Diurnal and seasonal variations of the signal reflected from the ionosphere are investigated on the basis of regular measurements of the amplitude and phase of the radio field of a reference radio station operating at a frequency of 50 kHz. The reflected signal is extracted from the mixture of the ground-wavel and reflected-wave fields using a special procedure. Effective parameters of an exponential ionospheric model, which characterize the statistical parameters of the signals in the long-wave band at medium distances, are proposed.

Inverse Problem for Shape Reconstruction of Plate-Thinning by Guided SH-Waves

In this paper, a new method for shape reconstruction of local plate thinning from reflection coefficients of guided SH-waves, based on guided wave scattering theory, is presented. The Green’s function for the SH-wave problem is used to express the reflected wave field in an integral form in terms of the surface shape of flaw and the total wave displacement. By introducing the Born approximation and the far-field approximation into the integral form of the reflected wave, the depth of plate thinning is obtained as a function of the horizontal coordinate by performing the inverse Fourier transform of the reflection coefficients at various frequencies. Numerical examples are given and the accuracy of proposed inverse approach is discussed by means of parametric comparisons for different wave modes, frequency ranges and various thinning shapes. [doi:10.2320/matertrans.I-M2012823]

Crosswell Technologies: New Solutions for Enhanced Reservoir Surveillance

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 144271, ’Crosswell Technologies: New Solutions for Enhanced Reservoir Surveillance,’ by Bruce Marion, SPE, Muhammad Safdar, SPE, Michael Wilt, SPE, Ping Zhang, Fabian Loh, SPE, and Ajay Nalonnil, SPE, Schlumberger, prepared for the SPE Enhanced Oil Recovery Conference, Kuala Lumpur, 19-21 July 2011. The paper has not been peer reviewed. Resolution and measurement diversity help characterize the subsurface and help optimize reservoir management. Crosswell measurements image the interwell space at reservoir scale. Crosswell-seismic data provide high-resolution reflection images of reservoir architecture. Crosswell electromagnetics (EM) expands the scale investigated by traditional resistivity logging to deliver a more extensive understanding of fluid distribution and movement at reservoir scale, away from the wells. These techniques complement each other, but integrating the measured data with conventional logs and surface data into the modeling workflow gives new insight into reservoir structure and fluid movement in the formation. Introduction Crosswell measurements enable greater understanding of reservoir heterogeneity and improve fluid-front monitoring. Geologic heterogeneity and the complexity of reservoir behavior when subjected to improved-recovery processes make crosswell surveillance useful in constraining scaling-up techniques during static modeling and in providing better predictability of injection performance. The two case studies detailed in the full-length paper describe early applications of crosswell surveys in the USA in the Chevron-operated Cymric field in California’s San Joaquin Valley. Theory Crosswell seismic produces images of the interwell space with a vertical resolution five to 10 times higher than that of surface-seismic data. Both direct- and reflected-wave fields are processed to provide a detailed image of the reservoir. By use of higher-frequency sources deployed alongside the reservoir interval, crosswell-seismic surveying generates high-vertical-resolution reflection images with resolution on the order of 1 to 3 m. This is the result of high bandwidth of the transmitters used during acquisition, with upper frequencies ranging from 800 Hz to 2 kHz. Because seismic velocity is sensitive to pressure, temperature, and saturation changes caused by the injection of CO2, gas, and steam, crosswell seismic provides valuable information for reservoir characterization and for monitoring injection performance and efficiency. Crosswell seismic can detect compressional-wave velocity changes as small as 1 to 3% reliably. Also, because the migrated-reflection section provides a high-resolution image of the structure between wells, it helps determine the geologic causes of the observed performance and fluid flow. Crosswell EM is a natural extension of the single-well induction-logging method whereby the transmitter and receiver are placed in separate wells. This geometry provides high-resolution resistivity distribution of the subsurface between the wells. When obtained at different timesteps during injection and production, this resistivity distribution provides valuable information that can be integrated with other data to interpret changes in the reservoir rock and the fluid distribution between wells. These data are valuable in updating the reservoir model with reduced uncertainty and enhanced predictability. Resistivity is especially responsive to changes in fluid composition in the reservoir and is an excellent indicator of temperature-related changes in the reservoir.

Vibro-acoustic response of orthogonally stiffened panels: The effects of finite dimensions

This paper investigates the effects of finite dimensions on the vibro-acoustic response of orthogonally stiffened panels. Three types of excitations are considered: acoustical excitation, point force excitation and random excitation by a turbulent boundary layer. In each case, a spatially windowed periodic model is compared with a Rayleigh–Ritz model where the modes of the un-stiffened panel are used as the basis functions. The latter model accounts for the reflected wave field generated at the boundaries by assuming that the panel is simply supported. On the contrary, the windowed periodic model only accounts for finiteness on sound radiation (the assumption of an infinite periodic structure is used to calculate the panel response). Numerical studies show that when the bending wavelength becomes comparable or smaller than the stiffener spacing, the periodic model is able to reproduce the results obtained with the Rayleigh–Ritz model. To complement the study, the developed models are compared with numerical simulations (finite element method) and with experimental results.

Experimental and numerical study of the wave run-up along a vertical plate

Results from experiments on wave interaction with a rigid vertical plate are reported. The 5m long plate is set against the wall of a 30m wide basin, at 100m from the wavemaker. This set-up is equivalent to a 10m plate in the middle of a 60m wide basin. Regular waves are produced, with wavelengths of 1.6m, 1.8m and 2m, and steepnesses H/L (H being the double amplitude and L being the wavelength) ranging from 2% to 5%. Free-surface elevations along the plate are measured with a row of 20 gauges. The focus is on the time evolution of the free-surface profile along the plate. At all steepnesses, strong deviations from the predictions of linear theory gradually take place as the reflected wave field develops in the basin. This phenomenon is attributed to third-order interactions between the incoming and reflected wave systems, on the weather side of the plate. The measured profiles along the plate are compared with the predictions of two numerical models: an approximate model based on the tertiary interaction theory of Longuet-Higgins & Phillips (J. Fluid Mech., vol. 12, 1962, p. 333) for plane waves, which provides a steady-state solution, and a fully nonlinear numerical wavetank based on extended Boussinesq equations. In most of the experimental tests, despite the large distance from the wavemaker to the plate and the small amplitude of the incident wave, no steady state is attained by the end of the exploitable part of the records.

Nonlinear Time-Domain Simulation of a Land-Based Oscillating Water Column

A two-dimensional time domain, fully nonlinear numerical wave tank (NWT) based on potential theory, the mixed Eulerian-Lagrangian approach, and the boundary element method was developed and applied to land-based oscillating water columns (OWCs) with compressed air inside the chamber. The nonlinear free-surface condition inside the chamber was specially devised to represent both the viscous effect of the water column motion and the pneumatic effect of the time-varying pressure. The latter not only influenced the water column motions, but also generated radiated waves to interfere with incident and reflected wave fields. Both linear and quadratic models are used for the viscous and pneumatic effects. The regular-wave cases are also compared with irregular-wave cases. The developed NWT was verified through comparison with viscous-flow-based numerical and experimental results for both narrow-gap and wide-gap chambers at two different skirt depths, with and without air ducts. All of the NWT simulations correlated well with experimental values for a variety of wave and chamber conditions, so that the developed numerical tool can be practically used for the optimal design of land-based OWCs. The fully nonlinear simulations were also compared with linear simulations. In case that had the same skirt depth and air duct area, the efficiency of the wide-gap chamber was generally higher than that of the narrow-gap chamber over a wider range of wavelengths, due to the larger amount of compressed air and the corresponding higher flow velocities.

Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series

In the direct nonlinear inversion method and in algorithms for 1D elastic media, P-wave velocity, S-wave velocity, and density are depth dependent. “Direct nonlinear” means that the method uses explicit formulas that (1) input data and directly output changes in material properties without the need for indirect procedures such as model matching, searching, optimization, or other assumed aligned objectives or proxies and that (2) the algorithms recognize and directly invert the intrinsic nonlinear relationship between changes in material properties and the recorded reflection wavefields. To achieve full elastic inversion, all components of data (such as PP, SP, and SS data) are needed. The method assumes that only data and reference medium propertiesare input, and terms in the inverse series for moving mislocated reflectors resulting from the linear inverse term are separated from amplitude correction terms. Although in principle this direct inversion approach requires all components of elastic data, synthetic tests indicate that a consistent value-added result may be achieved given only PP data measurements, as long as the PP data are used to approximately synthesize the PS and SP components. Further value would be derived from measuring all components of the data as the method requires. If all components of data are available, one consistent method can solve for all of the second terms (the first terms beyond linear). The explicit nonlinear inversion formulas provide an unambiguous data requirement message as well as conceptual and practical added value beyond both linear approaches and all indirect methods.

Cross-polarization of light at a dielectric-biisotropic medium interface

The problem of reflection and refraction of TE- and TM-polarized electromagnetic waves at oblique incidence on a dielectric-biisotropic medium interface has been solved. Conditions for the Brewster angles, at which the reflected wave field contains only the cross-polarized component, are established and the influence of the chirality and nonreciprocity parameters on the reflection coefficients is analyzed. It is shown that the appearance of cross-polarization upon reflection from the biisotropic medium is caused by the presence of nonreciprocity in addition to chirality.

A two-way paraxial system for simulation of wave backscattering by a random medium

This paper presents a probabilistic analysis of an iterative two-way paraxial scheme for the simulation of wave propagation in anisotropic random media. This scheme has the computational cost of the standard one-way paraxial wave equation but has the accuracy of the full wave equation in a regime beyond the classical paraxial regime. More precisely, it accurately predicts the statistics of the reflected wave field. The accuracy depends on two parameters: the order of the iterative scheme and the ratio of the random backscattering intensity over the random forward-scattering intensity.

Underestimation of scale lengths in stochastic fields and their seismic response: a quantification exercise

The possibility that parts of the Earth's continental lower crust can be described with stochastic geological models has been suggested for some time. Recent studies of deeper well logs also indicate a possible stochastic structure at mid-crustal levels. This motivates a closer examination of the relation between the statistics of reflection wavefields and that of the lower crust. Such a relation can put important constraints on possible lower crustal models. This study follows up earlier efforts to quantify the statistics of both stochastic lower crustal models and the reflected wavefield. Since modelling of the seismic response of stochastic (von Karman) fields implies the usage of the impedance contrast field of the latter, we wish to compare the second-order statistics of both types of fields (velocity and impedance). This study concludes that the vertical derivative operator on a von Karman velocity field, implicitly present in the impedance contrast field, alters the second-order horizontal von Karman statistics of the velocity fields in a profound way. Wavefield effects, undoubtedly present in observed seismic data, which have earlier been proposed as possible causes for the aforementioned change, seem to play a secondary role. The vertical derivative operation, inherent in the impedance contrast field, reduces the estimated horizontal scale length and Hurst number by a factor of 2–22 and 1–3, respectively. Original vertical scale length and Hurst number of the velocity fields have a (quasi-)linear influence on this underestimation. Horizontal scale lengths and Hurst numbers were also estimated from the seismic response (Primary Reflectivity Section) of the von Karman fields. The values obtained are close to those obtained from the causative impedance contrast fields, and are similarly underestimated. This suggests a dominant role for the vertical derivative operator in the underestimation of horizontal scale length and Hurst number. This attempt to quantify the relation between the horizontal spatial statistics of von Karman fields and the estimates derived from their seismic response, may be useful in upscaling the latter.

Multi-component seismic wavefield separation via spectral matrix filtering

SUMMARY Spectral matrix filtering (SMF) is a vector-processing method that uses frequency, slowness and particlemotion information to distinguish between wave types. The algorithm operates in the f-x domain and exploits the eigenstructure of the frequency-domain covariance matrix of the multi-component seismic signal. SMF has previously been demonstrated on VSP data. A number of practical considerations for the application of SMF to surface-reflection data are considered. Practical application of SMF requires the user to specify a number of data-dependent parameters, including trace-width and time extent of the data-analysis window, and the frequency bandwidth of the filter. Synthetic and realdata examples illustrate that SMF can successfblly extract high-amplitude wavefields while preserving other wave types in a surface-seismic record. Thus, while extensive testing suggests that SMF is not viable for separating P and PS reflection wavefields, SMF has the potential to routinely suppress groundroll energy and other high-amplitude surface-related events that can mask desirable reflection energy.

Experimental Study Applying a Migration Technique in Structural Health Monitoring

This article presents the experimental results of adopting a geophysical migration technique to interpret the ultrasonic flexural wave signals for the purpose of realizing quantitative damage identification in structures. In this study, a homogeneous isotropic plate is examined with a surface-mounted linear array of piezoelectric ceramic (PZT) disk. The piezoelectric disks function as actuators to excite flexural waves and also as sensors to receive the waves scattered from the structural damage in the plate. A prestack reverse-time migration technique, which is an advanced technique in geophysics to reverse the reflection wavefield and to image the Earth’s interior, is then used to back-propagate the scattering waves and to image damage in the plate. The configuration of the experimental setup is presented and its capability of accurately generating and receiving flexural waves is validated by comparing the collected signals with an analytical solution of transient response of a narrowband signal in a piezoelectric sensor/actuator integrated plate using Mindlin plate theory. Finally, the migration results from the scattering waves of an artificial damage are presented. It is shown that the existence of the damage is correctly revealed through migration process in the experiment as it has been shown using synthetic data.

End reflections in a layered piezoelectric circular cylinder

End reflection phenomenon in a semi-infinitely long layered piezoelectric circular cylinder is constructed with modal data from a spectral decomposition of the differential operator governing its natural vibrations. These modal data consist of all propagating modes and edge vibrations and they constitute the basis for a wave function expansion of the reflection of waves arriving at the traction-free end of the cylinder. Without any other external stimulus, a passive reflection event occurs. This traction-free end condition is enforced at the Gaussian integration points over the end cross-section on the combination of incoming and reflected wave fields. Reflections due to monochromatic incoming axisymmetric ( m = 0) and flexural ( m = 1) waves are studied and two numerical examples are presented. For an incoming axisymmetric wave, there is a particular frequency that induces an end resonance, which is characterized by high (but finite) amplitudes of end displacements vis-a-vis those of neighboring (i.e., slightly different) frequencies. This phenomenon is illustrated in the two cylinder examples. It is possible to modify the passive reflection event by imposing some voltage distribution over the free end. For an oscillating end voltage that is out-of-phase with the incoming wave, it is possible to extract electrical energy from it, i.e., energy harvesting. Examples of such an oscillating voltage with a particular radial distribution are given, that illustrate the amount of extracted energy as a function of the frequency of the incident monochromatic wave.

The crustal structure under Sanjiang and its dynamic implications: Revealed by seismic reflection/refraction profile between Zhefang and Binchuan, Yunnan

The fault belts in Sanjiang mainly include Jinshajiang-Honghe fault, Lancangjiang fault and Nujiang fault (called Sanjiang faults) in western Yunnan Province, China. By interpreting the wide-angle seismic reflection/refraction profile between Zhefang and Binchuan, which crosses Tengchong and Baoshan blocks in Dianxi (western Yunnan) tectonic zone, we reconstruct the crustal structure with seismic traveltime tomography for crustal P-wave velocity and the seismic scattering image for crustal seismic reflection structure. In this paper, we firstly present the crustal structure images of P-wave velocity and seismic reflection under the wide-angle seismic profile. These results demonstrate that, the crustal velocity structure and seismic reflection structure along the profile can be divided into 3 segments, and there is an obvious difference of crustal structure among the eastern, the western and the middle segment. Generally, crustal P-wave velocities in the Baoshan segment are 0.1―0.2 km/s slower and seismic reflection amplitudes from Moho discontinuity are stronger than the other 2 segments. In the studied area, crustal thickness is about 40 km, and shows the thickening tendency from west to east along the profile. Additionally, it can be seen that there is one strong-amplitude seismic reflection event as bright points at the depths of 8―10 km, along the segment of 80―115 km of the profile (southward of Tengchong); and seismic reflection wave-field from Moho discontinuity varies obviously along the lateral direction. Finally, we make some discussions on the crustal thickening pattern in the Sanjiang fault belt, structural environment of earthquake development and the contact rela-tionship between the Tengchong block, Banshan block and Luxi trough.

The role of tertiary wave interactions in wave–body problems

Results from experiments on wave interaction with a rigid plate are reported. The plate is projected from one of the sidewalls of the basin. The sidewall acts as a plane of symmetry, thereby doubling the widths of the plate and of the basin. The tests are carried out in regular waves of varying periods and steepnesses. At wavelengths comparable with the width of the plate, strong run-ups are observed at the plate–wall intersection, increasing with the wave steepness. These run-ups take many wave cycles to develop, with no steady state being reached in some cases. It is advocated that these phenomena result from third-order interactions between the incident and reflected wave fields, over a wide area on the weather side of the plate. A theoretical model is proposed, based on tertiary wave interaction. A parabolic equation is derived that describes the transformation of the incoming waves through their interaction with the reflected wave field. A steady-state solution is obtained through iterations. Results from the theoretical model are compared with the experimental data, with good agreement.

Acoustic pulse in a wall-less waveguiding

The reflection of an acoustic wave from a concave cone-shaped surface leads to the formation of an intense wave propagating along the symmetry axis, with a flat front and a radial profile described by a zero-order (n=0) Bessel function of the first kind. The wave front profile retains the shape over an extended path, as if the wave would be propagating in an acoustic waveguide; the role of the waveguide walls is performed by the side energy supply. In the case of a cone-shaped reflecting surface with a spiral directrix, the radial profile of the reflected wave field corresponds to the first-kind Bessel function with n>0 and the wave propagates as if in a hollow waveguide.

Resolution enhancement algorithm utilizing multiple reflections for image reconstruction in the conduit

In the acoustical endscopy, due to the physical limitations, the transducer array is composed of a small number of elements and each interspacing is larger than the acoustical wave length that is called a sparse array system. In such case, the volumetric image reconstruction process becomes ill-posed caused by the interference of the reverberation in the tube. Consequently, the reconstructed image is interfered by widely spread strong spurious lobes. This paper proposes a novel volumetric image reconstruction algorithm for a 3D sparse aperture acoustical holography, which visualizes the forward-looking image in the conduit tube. The proposed algorithm utilizes prior knowledge about both field, object, and observed signal as (1) the support of the object is limited within the conduit, and (2) the multiple reflected wave field scattered by the object is statistically independent of the reverberation in the tube. The proposed sparse array acoustical imaging system utilizes, therefore, the multiple reflected wavefronts in order to enhance the resolution. By experiments, it is proven that the proposed algorithm has the following improvements: (1) Targets can be identified when multiple reflections exist in the tubes. (2) Artifacts caused by the spurious lobes can be reduced.