Input Wavefield Research Articles

Helmholtz decomposition with a scalar Poisson equation in elastic anisotropic media

P- and S-wave separation plays an important role in elastic reverse-time migration. It can reduce the artifacts caused by crosstalk between different modes and improve image quality. In addition, P- and S-wave separation can also be used to better understand and distinguish wave types in complex media. At present, the methods for separating wave modes in anisotropic media mainly include spatial non-stationary filtering, low-rank approximation, and vector Poisson equation. Most of these methods require multiple Fourier transforms or the calculation of large matrices, which require high computational costs for problems with large scale. In this paper, an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain. For 2D problems, the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation. Therefore, compared with existing methods based on pseudo-Helmholtz decomposition operators, this method can significantly reduce the computational cost. Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.

Separation and imaging of diffractions using a dilated convolutional neural network

Seismic diffractions provide high-resolution details of small-scale geologic discontinuities, and diffraction imaging can be an important contribution to the exploration of faults, fractures, and cavities. However, reflections with strong energy generally mask the existence of weak diffractions in seismic records, and separating diffractions is necessary to see the full benefit of diffraction imaging. Here, a modified convolutional neural network (CNN) is used for separating diffractions. The input wavefields are modeled as the summation of individual diffractions and reflections, the network parameters are learned from multiple input data instances by minimizing the distance between the output of the network and the diffractions, and reflections are implicitly removed. To enhance the diffraction separation performance, we have used dilated convolutions to aggregate diffraction information, then combined batch normalization and residual learning to speed up the training process. The modified CNN can realize adaptive diffraction separation and avoid setting parameters in the subsequent application process. The synthetic Sigsbee2A model demonstrates the performance of the proposed method in removing high-slope reflections and imaging small-scale scatterers. The application to the Nankai field data further illustrates the ability of the methods to extract weak diffractions beneath the interference of other waves, revealing potential reservoir-related geologic features.

A fast computational model for near- and far-field noise prediction due to offshore pile driving.

This paper presents a computationally efficient modeling approach for predicting underwater noise radiation from offshore pile driving. The complete noise prediction model comprises two modules. First, a sound generation module is adopted to capture the interaction between the pile, the fluid, and the seabed, aiming at modeling the sound generation and propagation in the vicinity of the pile. Second, a sound propagation module is developed to propagate the sound field at larger distances from the pile. To couple the input wavefield obtained from the sound generation module, the boundary integral equations (BIEs) are formulated based on the acousto-elastodynamic reciprocity theorem. To advance the mathematical formulation of the BIEs, the Green's tensor for an axisymmetric ring load is derived using the complex wavenumber integration technique. The model advances the computational efficiency and flexibility of the noise prediction in both near- and far-fields from the pile. Finally, model predictions are benchmarked against a theoretical scenario and validated using measurement data from a recent offshore pile-installation campaign.

3D Complete Nonlinear Methods for Soil–Building Interaction Based on an Input Wavefield

AbstractThree-dimensional (3D) complete nonlinear methods for examining soil–building interaction based on an input seismic wavefield were developed. A seismic wavefield means seismic waves propaga...

Self-Action of Nonparaxial Few-Cycle Optical Waves in Dielectric Media

A mathematical model of evolution of the space–time spectra of nonparaxial few-cycle optical waves in isotropic dielectric media with an arbitrary dispersion of the refractive index and the inertialess third-order nonlinearity has been discussed. It has been shown that, at the self-focusing of a wave single-cycle at the input to a nonlinear medium into an optical filament with transverse dimensions comparable with the central radiation wavelength, the strength of the increased longitudinal component of its electric field can become larger than the initial longitudinal component by a factor of 7 and can be 18% of the transverse component of the input wave field. Errors of the calculations of the self-action of radiation with superwide time and spatial spectra within simplified mathematical models have been estimated.

Soil–Building Interaction Analysis with Nearby Water Body, Based on an Input Wavefield

Soil–Building Interaction Analysis with Nearby Water Body, Based on an Input Wavefield

Relative Seismic Risk Evaluation of Various Buildings Based on an Input Wave Field

Relative Seismic Risk Evaluation of Various Buildings Based on an Input Wave Field

Exact local refinement using Fourier interpolation for nonuniform-grid modeling

Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited. Traditional interpolation methods would fail at high upsampling ratios (say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.

3D Methods for Examining Soil–Building Interaction for Nonlinear Soil Behavior Based on an Input Wave Field

AbstractThis paper proposes three-dimensional (3D) simplified nonlinear methods for examining the soil–building interaction for nonlinear behavior of soils based on an input seismic wave field. A seismic wave field is defined as seismic waves propagating in a 3D medium. The proposed 3D methods were developed on the basis of the 3D linear method, which was recently proposed to adequately treat seismic surface waves trapped by a several-kilometer-deep underground structure. To demonstrate the feasibility of the proposed methods, interaction analyses of a midrise RC building and a wood building were performed in the reclaimed zone of Tokyo Bay in the cases of soils with linear, nonlinear, and liquefaction behavior for the 1923 Kanto earthquake. These interaction analyses provide a reasonable evaluation of building performance. In particular, building responses became excessively large, following extremely large increases in the amplitudes of surface waves in liquefied soils. The building responses provide si...

Joint Deconvolution of Building and Downhole Strong‐Motion Recordings: Evidence for the Seismic Wavefield Being Radiated Back into the Shallow Geological Layers

In this study, the strong‐motion recordings collected by a vertical array of borehole sensors and a network of accelerometers installed in a nearby building (distance between borehole and building ∼10 m) are innovatively jointly analyzed through wavefield‐deconvolution analysis. The analysis shows complicated patterns in the deconvolved wavefield of the borehole sensors that are interpreted by taking advantage of synthetic seismograms generated considering vertically propagating plane waves in the soil and building. Using a constrained deconvolution approach, we show that it is possible to separate the different components of the wavefield and, in particular, to retrieve the input ground motion and the wavefield radiated back by the building at different levels in the borehole, without a priori information about the attenuation structure (and velocity) of the building and soil. This therefore allows the energy radiated back by the structure at different depth to be estimated, which, in the case of the bottom of the borehole (at −145 m), is of the order of 10% of the energy of the input wavefield in the 1–10 Hz frequency band.

Wavefield separation and polarity reversal correction in elastic reverse time migration

In elastic reverse time migration (RTM), one of the problems that are often encountered is the cross-talk between P- and S-wavefields. A useful processing technique to reduce the cross-talk is separating the P- and S-wavefields by using divergence and curl operators before applying an elastic imaging condition. However, the separated wavefields lose their physical meaning because their phase and amplitude are changed. In this paper, we modify the divergence and curl operators to give the separated wavefields a clear physical meaning: the separated wavefield is the first derivative of the input wavefield with respect to time. Another problem often encountered is polarity reversals in PS and SP images, which can cause destructive interference in the final stacked image and thus destroy the migrated events. In this paper we also develop a procedure for polarity reversal correction based on the polarization vectors of the P- and S-wavefields in the common-shot domain. The correction factor is first calculated at every imaging point during the wavefield reconstruction and is then multiplied by the PS and SP images at each time step when an elastic imaging condition is applied. Numerical examples with synthetic data have shown that the modified wavefield separation method is correct, and the procedure of polarity reversal correction is effective for a complex model.

Three-Dimensional Nonlinear Soil Response Methods Based on a Three-Component Input Wave Field

AbstractIn a previous study, three-dimensional (3D) linear and simplified nonlinear finite-element soil response methods based on a horizontal-component input seismic wave field were proposed. A seismic wave field means seismic waves propagating in a 3D medium. The method had been developed with the goal of adequately treating short-period (less than a few seconds) seismic surface waves trapped by a deep (several km) underground structure in a shallow soil model. In the present study, along with improvements of the methods, 3D linear and simplified nonlinear soil response methods based on a three-component input seismic wave field are developed, and are applied to estimate seismic soil responses in the three geotechnical zones (the reclaimed, alluvial, and hill zones) of Tokyo during two large earthquakes. The more reasonable soil responses revealed that, in a practical sense, vertical ground motions affected soil responses very little. They also clarified large effects of liquefaction in the reclaimed zo...

Seismic Responses of Two RC Buildings and One Wood Building Based on an Input Wave Field

AbstractA recently proposed three-dimensional (3D) linear method for examining soil-building interactions based on an input seismic wave field is, after some improvements, applied to estimate seismic building responses in the reclaimed zone of Tokyo Bay, where ground motions include a considerable amount of surface waves, thus reconfirming the effects of the method in a different situation. A seismic wave field involves seismic waves propagating in a 3D medium. The proposed method was developed with the goal of adequately treating seismic surface waves trapped by a (several-kilometers) deep underground structure in a soil-building interaction system. Two simulations were carried out. The first simulation successfully reproduced surface, downhole, and building accelerograms that were recorded at one borehole station during two medium-sized earthquakes. In the second simulation, seismic responses of a midrise RC model building and a wood model building were favorably calculated at the other borehole station...

Nonlinear seismic response for the 2011 Tohoku earthquake: borehole records versus one-directional three-component propagation models

The seismic response of surficial multilayered soils to strong earthquakes is analysed through a non-linear one-directional three-component (1D-3C) wave propagation model. The three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for dry soils under cyclic loading is implemented in a quadratic line finite element model. The soil rheology is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. Its major advantage is that the rheology is characterized by few non-linear parameters commonly available. Previous studies showed that, when comparing one to 3C unidirectional wave propagation simulations, the soil shear modulus decreases and the dissipation increases, for a given maximum strain amplitude. The 3-D loading path due to the 3C-polarization leads to multiaxial stress interaction that reduces soil strength and increases non-linear effects. Non-linearity and coupling effects between components are more obvious with decreasing seismic velocity ratio in the soil and increasing vertical to horizontal component ratio for the incident wave. This research aims at comparing computed ground motions at the surface of soil profiles in the Tohoku area (Japan) with 3C seismic signals recorded during the 2011 Tohoku earthquake. The 3C recorded downhole motion is imposed as boundary condition at the base of soil layer stack. Notable amplification phenomena are shown, comparing seismograms at the bottom and at the surface. The 1D-3C approach evidences the influence of the 3-D loading path and input wavefield polarization. 3C motion and 3-D stress and strain evolution are evaluated all over the soil profile. The triaxial mechanical coupling is pointed out by observing the variation of the propagating wave polarization all along the duration of seismograms. The variation of the maximum horizontal component of motion with time, as well as the influence of the vertical component, confirm the interest of taking into account the 3C non-linear coupling in 1D wave propagation models for such a large event.

Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging

In dynamic computer-generated holography that utilizes spatial light modulators, both hologram synthesis and hologram representation are essential in terms of fast computation and high reconstruction quality. For hologram synthesis, i.e. the computation step, Fresnel transform based or point-source based raytracing methods can be applied. In the encoding step, the complex wave-field has to be optimally represented by the SLM with its given modulation capability. For proper hologram reconstruction that implies a simultaneous and independent amplitude and phase modulation of the input wave-field by the SLM.In this paper, we discuss full complex hologram representation methods on SLMs by considering inherent SLM parameter such as modulation type and bit depth on their reconstruction performance such as diffraction efficiency and SNR. We review the three implementation schemes of Burckhardt amplitude-only representation, phase-only macro-pixel representation, and two-phase interference representation. Besides the optical performance we address their hardware complexity and required computational load. Finally, we experimentally demonstrate holographic reconstructions of different representation schemes as obtained by functional prototypes utilizing SeeReal's viewing-window holographic display technology. The proposed hardware implementations enable a fast encoding of complex-valued hologram data and thus will pave the way for commercial real-time holographic 3D imaging in the near future.

Three-Dimensional Finite-Element Method for Soil-Building Interaction Based on an Input Wave Field

AbstractA three-dimensional (3D) FEM for examining the soil-building interaction based on an input seismic wave field is proposed. A seismic wave field means seismic waves propagating in a 3D medium. An input seismic wave field is employed with the goal of adequately treating seismic surface waves trapped by a deep (several kilometers) underground structure in a soil-building interaction system. As the first stage of the proposed method, a simple linear method is constructed. The linear method was applied to estimate seismic responses of low- to high-rise RC model buildings during a large earthquake at a soft-soil site in Mexico City where surface waves are dominant. At the soft-soil site, all the buildings with and without piles vibrated together with the ground, probably suppressing the pile damage. The proposed method qualitatively provided us with more realistic building responses, compared with a conventional interaction analysis based on an input base motion. When a considerable amount of surface wa...

Full-range, complex spatial light modulator for real-time holography

We demonstrate a full-range complex and transmissive spatial light modulator (SLM) for simultaneous and independent amplitude and phase modulation of an input wave field. Arbitrary scalar complex optical fields are generated by stacking a pixelated liquid crystal display operating in phase-only (2π) modulation with passive polarization-sensitive components. The principle is based on optical combining the light fields of two neighboring phase-only modulating pixels, which were made orthogonally polarized by a structured half-wave plate, then passing through a birefringent plate to laterally shift one of the beams collinear to the other, and finally bringing to interference by a linear polarizer. Complex modulation by the proposed SLM is experimentally verified in monochrome green operation.

Multiarrival Kirchhoff beam migration

Kirchhoff-type prestack depth migration is the method most popular for outputting offset gathers for velocity-model updating because of its flexibility and efficiency. However, conventional implementations of Kirchhoff migration use only single arrivals. This limits its ability to image complex structures such as subsalt areas. We use the beam methodology to develop a multiarrival Kirchhoff beam migration. The theory and algorithm of our beam migration are analogs to Gaussian beam migration, but we focus on attaining kinematic accuracy and implementation efficiency. The input wavefield of every common offset panel is decomposed into local plane waves at beam centers on the acquisition surface by local slant stacking. Each plane wave contributes a potential single-arrival in Kirchhoff migration. In this way, our method is able to handle multiarrivals caused by model complexity and, therefore, to overcome the limitation of conventional single-arrival Kirchhoff migration. The choice of the width of the beam is critical to the implementation of beam migration. We provide a formula for optimal beam width that achieves both accuracy and efficiency when the velocity model is reasonably smooth. The resulting structural imaging in subsalt and other structurally complex areas is of better quality than that from single-arrival Kirchhoff migration.

2D and 3D elastic wavefield vector decomposition in the wavenumber domain for VTI media

A pragmatic decomposition of a vector wavefield into P- and S-waves is based on the Helmholtz theory and the Christoffel equation. It is applicable to VTI media when the plane-wave polarization is continuous in the vicinity of a given wavenumber and is uniquely defined by that wavenumber, except for the kiss singularities on the VTI symmetry axis. Unlike divergence and curl, which separate the wavefield into a scalar and a vector field, the decomposed P- and S-wavefields are both vector fields, with correct amplitude, phase, and physical units. If the vector components of decomposed wavefields are added, they reconstruct those of the original input wavefield. Wavefield propagation in any portions of a VTI medium that have the same polarization distribution (i.e., the same eigenvector) in the wavenumber domain have the same decomposition operators and can be recon-structed with a single 3D Fourier transform for each operator (e.g., one for P-waves and one for S-waves).This applies to isotropic wavefields and to VTI anisotropic wavefields, if the polarization distribution is constant, regardless of changes in the velocity. Because the anisotropic phase polarization is local, not global, the wavefield decomposition for inhomogeneous anisotropic media needs to be done separately for each region that has a different polarization distribution. The complete decomposed vector wavefield is constructed by combining the P-, SV-, and SH-wavefields in each region into the corresponding composite P-, SV-, and SH-wavefields that span the model. Potential practical applications include extraction of separate images for different wave types in prestack reverse time migration, inversion, or migration velocity analysis, and calculation of wave-propagation directions for common-angle gathers.

Amplitude and phase of nonlinear magnetospheric wave growth excited by the HAARP HF heater

The High Frequency Active Auroral Research Program (HAARP) HF ionospheric heater is used to inject ELF/VLF signals into the magnetosphere to study wave‐particle interactions that lead to nonlinear amplification. HAARP‐generated whistler mode “echoes” are observed after twice crossing the equatorial plane in magnetospheric ducts. The magnetospheric paths traversed by the signals are determined to be in the range 5.06 < L < 5.19 with associated cold plasma densities of 177 cm−3 < Neq < 185 cm−3. The amplitude and phase of the echoes are observed to exhibit exponential temporal increase. A decrease in input amplitude by 14 dB is observed to yield a delay in onset of nonlinear growth by ∼1 s. Nonlinear theory of cyclotron resonant currents formed by electrons phase trapped in the potential well of the input wave is used to analyze the simultaneous evolution of amplitude and phase of the observations. The average nonlinear resonant current vector is found to rotate in relation to the input wavefields during growth, and the magnetospheric linear growth rate is estimated to be 31–45 dB/s.