Multiple Wavefield Research Articles

Joint inversion of direct waves, primaries, and multiples for vertical cable seismic data

By anchoring vertical cable in seawater and receiving the data excited by the towing cable seismic source, the reflection data from subsurface structures with a high signal-to-noise ratio, wide frequency band, and wide azimuth angle can be obtained, thereby achieving high-quality imaging of the target area. However, due to drifting receivers driven by ocean currents and the nonuniform coverage caused by the vertical orientation of the receivers, the traditional imaging method cannot be directly used in the vertical cable seismic data. Furthermore, crosstalk between the primaries and multiples commonly contaminates the final imaging. A new inversion method, based on the Bayesian inference and the assumption that all errors are Gaussian distributed, is presented to address these problems. The direct waves are used to invert the source/receiver locations. The primary and multiple wavefields are accurately reconstructed based on the reconstructed direct wavefield, and the corresponding reflectivity updates are obtained. The model-domain Hessian matrices consisting of different data are approximated by their diagonal elements to mitigate the nonuniform coverage issue, and the related covariance matrices and data-domain Hessian matrices are defined and approximated, respectively, to alleviate the calculation problem. In addition, the zero-lag correlated wavefields in the gradient are consistent with the actual wavefield propagation process, e.g., a primary wave is generated when the direct wavefield encounters reflectivity, avoiding the crosstalk. Numerical examples for synthetic models and field data illustrate that our method can accurately recover the source/receiver locations and provide high-resolution balanced-amplitude imaging results without evident crosstalk.

Multiple hyperbolic waves.

This study presents a conceptual design for a hyperbolic material utilizing transformation optics. This material is designed to produce multiple hyperbolic wave fields or polaritons excited by a point source. The design dictates key parameters including branch number, propagation range, and overall propagation direction of deflection. Through this approach, the hyperbolic material demonstrates new effects compared to traditional hyperbolic materials. These advancements offer possibilities for the design and applications of photonic devices in other degrees of freedom.

Multiple Wavefield Solutions in Physics-Informed Neural Networks Using Latent Representation

Multiple Wavefield Solutions in Physics-Informed Neural Networks Using Latent Representation

Simulating Multicomponent Elastic Seismic Wavefield Using Deep Learning

Simulating seismic wave propagation by solving the wave equation is one of the most fundamental topics in applied geophysics. Considering the elastic nature of the Earth, it is important to simulate the elastic behavior of seismic waves. Compared to solving the acoustic wave equation, it often requires a larger computational cost to solve the elastic wave equation. For the finite-difference method, the computational cost for simulating elastic wavefields increases greatly to include multiple wavefield components. We propose to solve the scattered form of the frequency-domain elastic wave equation using a deep learning framework, called physics-informed neural networks (PINNs). PINNs use the physics principles (scattered elastic wave equations in our case) as the loss function. By inputting the spatial model coordinates and source locations into the network, we can evaluate the wavefield solutions of vertical and horizontal displacements in the domain of interest for arbitrary source locations. We demonstrate that this newly developed deep-learning based method can simulate multi-component elastic wavefields with reasonable accuracy.

Addressing the crosstalk issue in imaging using seismic multiple wavefields

Surface-related-multiple wavefields constitute redundant information in conventional migration and can often be difficult to attenuate. However, when used for migration, multiple wavefields can improve subsurface illumination. Unfortunately, the process of imaging using multiples involves the management of crosstalk, which largely restricts its application. Crosstalk causes phantom images formed by spurious correlation of unrelated events in a migration process. These events can be unrelated orders of multiples in the source and receiver wavefields; they can also be one event associated with a reflector in the source wavefield and another event generated by a different reflector in the receiver wavefield. We have first examined crosstalk by explicitly investigating its generation mechanisms in a migration process and classifying it into different categories based on causality. Following this analysis, crosstalk can be predicted in a migration process and subtracted in the image domain; however, this method is usually difficult to apply due to the complexity of wavefield separation and adaptive subtraction. Furthermore, we develop different algorithms to attenuate the crosstalk, including a deconvolution imaging condition, a least-squares migration (LSM) method, and an advanced algorithm combining LSM with a deconvolution imaging condition. We evaluate these different strategies with synthetic examples. A deconvolution imaging condition can attenuate some crosstalk, but it is less effective at suppressing strong coherent crosstalk events. However, the LSM method can fundamentally address the crosstalk issue, and this approach is further optimized when combined with a deconvolution imaging condition.

Order‐controlled closed‐loop focal beams and resolution comparison of primary and multiple reflections for seismic acquisition geometries

ABSTRACTFocal beam analysis has built a bridge between the acquisition parameters on the surface and the image quality of underground targets. However, as a practical matter, it is still difficult to answer how to choose a proper acquisition geometry according to the complexity of medium, especially considering the contradictory effects of multiple reflections on spatial resolution as they can be considered to be either potential signal or additional noise, depending on the envisioned imaging technology. We introduce an order‐controlled, closed‐loop focal beam method in which the migration operator and the resolution function can be analysed in the process of the closed‐loop migration with full control over the order of the surface and internal multiples considered. This method highlights the effects of primary and different‐order multiple wavefields on the imaging resolution for different acquisition geometries and various overburden strata. We apply the method to analyse the predicted resolution of seismic acquisition geometries considering multiples as either noise or signal. Results show, in the acquisition geometry design, that when the primaries cannot provide a complete spatial illumination for the subsurface target, e.g. because of the limited‐aperture acquisition geometries or the complicated overburden, we should use the closed‐loop focal beam analysis to assess the contradictory effects of multiples as both signal and noise, in which the maximum order of multiples ought to be chosen according to the core aim of the acquisition analysis. We can apply the second‐order closed‐loop focal beam analysis to quantify the effects of acquisition geometries on multiple‐wave suppression and can also perform the high‐order closed‐loop focal beam analysis to quantify the effects of acquisition geometries on high‐resolution imaging (migration). This method can also be used to choose the optimal order of multiples in the closed‐loop migration.

Multiple joint wavefield inversions: Theory and field data implementations

Accurate velocity models for the near surface and overburden are needed for seismic processing and reliable depth imaging. Seismic with multiphysics data, well logs, and geology information need to be quantitatively integrated to obtain high-resolution velocity models. We detail our development and application of the joint wavefield inversion software platform, which enables flexible algorithmic schemes for the integration of multiparameter data and constraints. Inversion is performed in cascade or simultaneously using a variety of input data to constrain the velocity field reconstruction at multiple scales. Coupling mechanisms based on structure similarity together with rock-physics relations are optimally combined to boost resolution and enhance accuracy of the inverted velocity models. Ill-posed inversion problems are then solved using extensive geologic and rock-physics regularization instead of relying on smoothness constraints alone. We detail workflows and algorithms to guide the application of multiparameter joint inversion for velocity model building whether the input data are seismic traveltimes, electromagnetics (time/frequency domains), gravity, and/or surface waves. Extensive applications of multiparameter joint inversion are presented for a variety of complex geologic scenarios in which various multiparameter coupling strategies are illustrated. Robust velocity modeling and enhanced seismic imaging in time and depth domains are obtained as a result, proving the importance of multiphysics integration for reliable earth model parameter estimation.

Inverse gaussian beam stack imaging in 3D crosswell seismic exploration of deviated wells and Its application

In crosswell seismic, imaging section produced by migration employed with wave equation has a serious arc phenomenon at its edge and small effective range due to the restriction of geometry. Another imaging section produced by VSP-CDP stack imaging employed with ray-tracing theory is amplitude-preserved but has difficulty in imaging 3D complex lithological structure accurately. Therefore, the paper proposes inverse Gaussian beam stack imaging in 3D crosswell seismic of deviated well based on the Gaussian beam ray-tracing theory. Through employing Gaussian beam ray-tracing theory into 3D crosswell seismic, the energy relationship between the seismic wave field and its effective rays is analyzed. Then the author converts the single channel seismic wave field data in the common shot point (CSP) gather into multiple effective wave fields in common reflection point (CRP) gather by inverse Gaussian beam when imaging and thus produces more intensive reflection points fold number. Finally, the wave fields of the effective reflection points in the same stack bin, selected from horizontal and vertical direction of the 2D measuring line, are projected onto the 2D measuring line, chosen according to the distribution characteristics of the reflection points, and stacked into an imaging section. The method is applied in X oilfield to identify the internal structure of offshore gas cloud area. The result provides positive support for inverse Gaussian beam stack imaging in producing accurate imaging in 3D complex lithological structure and make it a powerful imaging tool for 3D crosswell seismic data processing.

Improving Scholte-Wave Vibration Signal Recognition Based on Polarization Characteristics in Coastal Waters

Zhao, S.; Zhang, J.; Wang, Z.; Huang, H.; Hu, J., and Guo, C., 2020. Improving Scholte-wave vibration signal recognition based on polarization characteristics in coastal waters. Journal of Coastal Research, 36(2), 382–392. Coconut Creek (Florida), ISSN 0749-0208.Scholte waves on the underwater interface provide a lot of information, which can be employed to identify the target in coastal water and speculate the coastal underwater medium. However, as the practical acquired signals are the superposition of multiple wave fields, it is necessary to separate the Scholte wave and to improve its signal-to-noise ratio. The LS-DYNA software was used to simulate the underwater acoustic field to analyze the excitation mechanism and particle trajectory law of Scholte waves and to obtain the propagation characteristic of Scholte waves. The results showed that Scholte waves attenuate according to r–0.5 on the underwater interface and according to exponent in the depth direction. The amplitude of Scholte waves mainly concentrates below 25 Hz, and the corresponding particle trajectory makes a counterclockwise elliptical shape by filtering the acquired signals of particle vibration velocity below 25 Hz on and below the underwater interface. This method was applied to separate Scholte waves from the acquired complex signals of the wave field in the lake experiment to obtain the pure signals of the Scholte wave. This research can provide significant knowledge to better take advantage of resourceful information provided by Scholte waves in the coastal environment.

Free Surface Multiple Removal Using 3D Surface Related Multiple Elimination Technique on 3D Seismic Data from Offshore Niger Delta

In addition to de-spiking, gun delay correction, correction for spherical spreading and earth’s absorption, gun and cable correction, zero-phasing, noise attenuation and correction for time shifts between sail lines due to changes in velocity of the water column, multiple elimination is the other important true relative amplitude processing routine desired to produce seismic gathers consistent with DHI and AVO analysis to de-risk the presence of hydrocarbon interpreted from seismic data. Multiple problems associated with seismic data acquired in the Niger Delta offshore are those due mainly to the free air-water interface and the seabed, and their presence constitute noise in the seismic dataset. In this study, we employed an approach in which we convolved all possible source and receiver peglegs for every multiple event that strikes the free surface irrespective of its path in the subsurface to model the multiple wave field in a 3D sense, in a partially processed pre-migration seismic data acquired in the Niger Delta deep offshore. The method of adaptive subtraction was then used to eliminate the modeled multiples from the dataset. Un-like other demultiple techniques such as tau-p deconvolution and radon, our multiple modeling and subtraction techniques do not require prior knowledge of the subsurface geology in terms of the velocity and reflectivity of the multiple wave field. The aim of the study was to improve the overall quality of the seismic data and signal-to-noise ratio, in addition to the DHI and AVO compliant gathers output from the process. The approach was successful and effective in removal of the free, air-water surface multiples from the dataset.

Reverberant shear wave fields and estimation of tissue properties

The determination of shear wave speed is an important subject in the field of elastography, since elevated shear wave speeds can be directly linked to increased stiffness of tissues. MRI and ultrasound scanners are frequently used to detect shear waves and a variety of estimators are applied to calculate the underlying shear wave speed. The estimators can be relatively simple if plane wave behavior is assumed with a known direction of propagation. However, multiple reflections from organ boundaries and internal inhomogeneities and mode conversions can create a complicated field in time and space. Thus, we explore the mathematics of multiple component shear wave fields and derive the basic properties, from which efficient estimators can be obtained. We approach this problem from the historic perspective of reverberant fields, a conceptual framework used in architectural acoustics and related fields. The framework can be recast for the alternative case of shear waves in a bounded elastic media, and the expected value of displacement patterns in shear reverberant fields are derived, along with some practical estimators of shear wave speed. These are applied to finite element models and phantoms to illustrate the characteristics of reverberant fields and provide preliminary confirmation of the overall framework.

Reverse time migration of multiples: Applications and challenges

Marine seismic acquisitions record both primary and multiple wavefields. In a typical processing sequence, multiple energy is removed from the data before migration. However, valuable information might be contained in the multiple wavefield. A modification is proposed to the standard reverse time migration (RTM) algorithm to enable correct imaging between the primary wavefield and the first-order multiple wavefield. The advantages of this modification, reverse time migration of multiples (RTMM), are evaluated through three real data-processing projects and identified three key advantages. First, RTMM can recover small-angle reflections critical for shallow-water imaging that are missing in the primary wavefield. Second, RTMM has a wider illumination coverage, which significantly extends the image for an ocean-bottom node (OBN) project. Third, RTMM produces an image complementary to the primary image in a complex geologic setting, possibly assisting with interpretation. In addition, a synthetic study is presented of two types of cross-talk noise that hinder the full potential of RTMM, and corresponding practical strategies are proposed to handle them.

Application of laser ultrasound imaging technology in the frequency domain based on Wigner–Ville algorithm for detecting defect

Abstract According to the thermoelastic and heat conduction equations of laser ultrasonic, ultrasonic propagation images are obtained by solving finite element solution equations. Based on thermoelastic mechanism, a Wigner–Ville transform ultrasonic propagation imaging method of stronger frequency selectivity was proposed. An aluminum plate with defects was scanned by a pulsed laser, the ultrasonic waves produced by a pulsed laser were received by an ultrasonic sensor, and then ultrasonic propagation imaging on the aluminum plate was analyzed in detail. In order to isolate a damage-related ultrasonic wave, a Wigner–Ville algorithm as a frequency selectivity method was proposed to convert a complex time domain multiple wavefield into a simple frequency domain single wavefield. At last, we compared the conventional ultrasonic propagation imaging method with the Wigner–Ville transform ultrasonic propagation imaging method, which demonstrated that the Wigner–Ville transform ultrasonic propagation imaging method can effectively and intuitively evaluate the sizes of damages or flaws without any reference data, which should promote the application of the technique in the industry.

VSP imaging using free-surface multiples: A case study from the Gulf of Mexico

Vertical seismic profile surveys (VSP) provide a unique opportunity to obtain high-quality seismic images of the subsurface. Placing receivers downhole mitigates many near-surface and overburden challenges associated with surface seismic imaging and results in improved image quality. Unfortunately, these benefits are restricted by the limited area illuminated by the primary P-wave reflection wavefield (typically a relatively narrow cone that underlies the geophone array). The free-surface multiple wavefield recorded in a VSP survey illuminates a significantly larger area, both vertically and laterally, and so can provide an expanded imaging capability (Jiang et al, 2005; Jiang et al, 2007; Lou et al 2007). Subsurface imaging using the multiple wavefield has been demonstrated and is commonly used for imaging deep-water 3D node surveys, which are typically acquired using a sparse distribution of receivers. However, no case studies have been published yet, which present a critical analysis of the images provided by this technology when applied to VSP surveys.

Broadband extended images by joint inversion of multiple blended wavefields

Estimation of seismic velocities and subsurface reservoir properties in deep, complex, geologic environments calls for the coordination of new acquisition technology with novel depth-domain inversion methods. Here, we propose a method for inversion of subsurface reflectivity image gathers that jointly relies on broadband data acquired by multimeasurement methods (vector-acoustic data; pressure and its gradients) from monopole (pressure) and dipole (e.g., gradient) sources. Our inversion retrieves depth-domain extended images (EIs), which represent the full nonlinear reflectivity operators with pseudosources and pseudoreceivers within the subsurface, as a function of time or frequency. Based on recent advances in interferometry by multidimensional deconvolution (MDD), we present two MDD-based imaging conditions for an EI inversion. One imaging condition consists of deconvolving correlation-based EIs with the so-called joint point-spread function (JPSF). These methods can, in principle, account for imaging primaries as well as internal and free-surface multiples. Because it is based on MDD, our JPSF approach can fully account for blended/simultaneous-source data in imaging with no need to deblend/separate the simultaneous-source data prior to imaging. Using dual-source vector-acoustic data, we describe how the EI JPSF system is constructed by separating source and receiver wavefields from receiver-side upgoing and ghost data, from pressure and gradient sources. With numerical examples, we demonstrate how the method successfully inverts for EIs representing subsurface reflectivity, while benefiting from the increase in temporal and spatial bandwidth brought on by the joint use of dual-source vector-acoustic data. Although here we focus on broadband streamer seismic applications, our joint wavefield inversion approach provides a framework for jointly imaging data from multiple experiments of any kind (e.g., surface and borehole, active and passive) with acoustic, elastic, and electromagnetic fields.

Laser ultrasonic propagation imaging method in the frequency domain based on wavelet transformation

A wavelet-transformed ultrasonic propagation imaging method capable of ultrasonic propagation imaging in the frequency domain was developed and applied as a new structural damage or flaw visualization algorithm. Since the wavelet-transformed ultrasonic propagation imaging method has strong frequency selectivity, it can visualize the propagation of ultrasonic waves of a specific frequency (for example, to isolate ultrasonic mode of interest and a damage-related ultrasonic wave). The strong frequency selectivity of the wavelet-transformed ultrasonic propagation imaging method was demonstrated, isolating only the zeroth-order asymmetrical mode of the fundamental Lamb wave modes in an anisotropic carbon fiber-reinforced plastic plate with a thickness of 5 mm. The wavelet-transformed ultrasonic propagation imaging method can also convert a complex time domain multiple wavefield into a simple frequency domain single wavefield. This feature enables easy interpretation of the results, and facilitates the precise evaluation of the location and size of structural damage or flaws. We demonstrated this capability by detecting a disbond in a sandwich structure made of Al-alloy skins and a foam core. A disbond with a diameter of 20 mm, which is representative of a common manufacturing flaw, was successfully detected, localized, and evaluated. Since a method to determine the allowable maximum pulse repetition frequency depending on target materials and structures was found by investigating the residual wave caused from the previous laser impinging, our laser ultrasonic system can scan rapidly the target with an optimal pulse repetition rate. In addition, the proposed wavelet-transformed ultrasonic propagation imaging method can visualize damage or flaw without the need for reference data from the intact state of the structure. Hence, we propose the wavelet-transformed ultrasonic propagation imaging approach for automatic inspection of in-service engineering structures, or in-process quality inspection in manufacturing.

Seismic Velocity and Polarization Estimation for Wavefield Separation

We address the problem of estimating the shape parameters of seismic wavefields using linear arrays of three-component (3C) vector sensors with uncertain acquisition geometry. The goal is to separate the different seismic waves, which is of practical need for oil exploration and geophysics. We present a parametric model for multiple wideband polarized signals received by an array of three-component sensors with positional and rotational calibration errors, and derive the Cramer-Rao lower bounds on the performance of the model parameters for both the exact physical model and the model with uncertain acquisition geometry. We propose a method for jointly estimating the velocity and polarization parameters based on the shift-invariance properties of multiple wavefields impinging on the linear array. We then remove the interfering surface waves by using a beamforming filter designed to exploit the velocity and polarization diversity of the different seismic waves, after clustering of the shape-parameter estimates. Examples using simulated and experimental data illustrate the applicability of the proposed methodology.

Stereographic imaging condition for wave-equation migration

Imaging under the single-scattering approximation consists of two steps: wavefield reconstruction of source and receiver wavefields from simulated and recorded data, respectively, and imaging from the extrapolated wavefields of locations where reflectors occur. Conventionally, the imaging condition indicates the presence of reflectors when propagation times of reflections in the source and receiver wavefields match. The main drawback of a conventional crosscorrelation imaging condition is that it ignores the local spatial coherence of reflection events and relies only on their propagation time. This leads to interference between unrelated events that occur at the same time. Sources of crosstalk include seismic events corresponding to different seismic experiments, propagation paths, types of reflections (primary or multiple), or wave modes (P or S). An alternative imaging condition operates on the same extrapolated wavefields, but crosscorrelation takes place in a higher-dimension domain where seismic events are separated based on their local space-time slope. Events are matched based on two parameters (time and local slope), thus justifying the name “stereographic” for this imaging condition. Stereographic imaging attenuates wavefield crosstalk and reduces imaging artifacts compared with conventional imaging. Applications of the stereographic imaging condition include simultaneous imaging of multiple seismic experiments, multiple attenuation in the imaging condition, and attenuation of crosstalk between multiple wavefield branches or multiple wave modes.

A new estimation of direction of arrival algorithm with a special antenna shape

This paper presents a new subspace-based 2D direction of arrival (DOA) estimationalgorithm for narrow-band sources with high-resolution localization capabilities. DOAestimation is achieved by using the noise-subspace eigenvectors of a new extendedcorrelation matrix (ECM). A 2-L-shape antenna array is proposed. Unlike common planarand circular arrays, the novel antenna array with this special geometry requires no pairmatching between the azimuth and elevation angle estimation. The performance of theproposed approach is examined by a simulation study in the presence of multiple wavefields. The simulation results show a good estimated performance of the proposedmethod.

Multiple prediction through inversion: Theoretical advancements and real data application

Wave-equation-based multiple attenuation seismic methods may be divided into the two distinct phases of multiple modeling and multiple subtraction. These two are interrelated and must be optimized in order to produce an optimal final result. The multiple prediction through inversion (MPI) scheme updates the multiple model iteratively, as we usually do in a linearized inverse problem. The scheme models the multiple wavefield without an explicit knowledge of surface and subsurface structures or of the source signature; both are generally unknown in seismic surveys. However, compared to a conventional surface-related multiple attenuation method, the accuracy of the multiple model is improved both kinematically and dynamically. It is because the MPI scheme implicitly takes account of the spatial variation of the surface reflectivity, the source signature, the detector patterns and receiver ghosts, and other effects included in the so-called surface operator. When the MPI scheme is used in the first phase it also significantly reduces the nonlinearity of the problem in the second phase that involves attenuating multiples without removing or altering primaries. The effectiveness of the MPI scheme is demonstrated by examples involving real marine seismic data.