Seismic Wavefield Research Articles

Multi-source wavefield reconstruction combining interferometry and compressive sensing: application to a linear receiver array

SUMMARY Seismic interferometry (SI) is a technique that allows one to estimate the wavefields accounting for the wave propagation between seismometers, any of which can act as a virtual source (VS). Interferometry, particularly noise interferometry, has been applied to several geophysical disciplines such as passive monitoring and distributed acoustic sensing. In practice, one requires long recordings of seismic noise for noise interferometry. Additionally, one can have missing seismic interferometric traces because some receivers in seismic arrays may be absent or inoperative due to issues of receiver installation and malfunction. Thus, filling the gap of seismic interferometric profile requires wavefield reconstruction and regularization techniques. Compressive sensing (CS) is one such method that can reconstruct seismic interferometric wavefields and help mitigate the limitations by exploiting the sparsity of seismic waves. In our work, we use CS to reconstruct missing seismic interferometric wavefields. One can interpolate interferometric wavefields using correlograms provided by one VS. We call this method of reconstructing an individual VS gather single-source wavefield reconstruction. We propose an alternative technique called multi-source wavefield reconstruction, which applies CS to reconstruct multiple interferometric wavefields using a volume of VS gathers provided from all available VSs. Using numerical examples, we show that one can apply CS to recover interferometric wavefields resulting from interferometry of a linear seismic array. To exploit the sparsity of interferometric wavefields, we apply the Fourier and Curvelet transforms to the two reconstruction schemes. Using the signal-to-noise ratio (SNR) to compare reconstruction of interferometric wavefields, the Fourier multi-source method improves the recovery of interferometric wavefields by approximately 50 dB compared to the Fourier and Curvelet single-source wavefield reconstructions.

Overview of seismo-acoustic tremor at Oldoinyo Lengai, Tanzania: Shallow storage and eruptions of carbonatite melt

We analyze volcanic tremor from Oldoinyo Lengai, Tanzania, which is currently the only active volcano on Earth producing carbonatitic lavas. Here, we use data from the recent SEISVOL deployment and focus on a co-located seismic and infrasound station about 200 m below the summit. We show the very first observations of seismo-acoustic tremor caused by carbonatitic eruptions. This seismo-acoustic tremor is highly variable throughout the ∼one year of data which we characterize by analyzing its seismic amplitude, duration, recurrence, dominant seismic frequency and harmonics. Frequency gliding occurs frequently and over short (minutes to hours) to long time scales (hours to days) and likely reflects different time-dependent mechanisms, such as evenly-spaced repeating events with a change in inter-event times, crater dynamics that alter resonators, and dike intrusions. Seismic and acoustic wavefields correlate well for stronger eruptive sequences but are only partially coherent which suggests that high-frequency seismic tremor (up to 25 Hz) may be caused by the low viscosity of the carbonatitic melt and not by ground-coupled airwaves. In addition, the comparison between seismic-acoustic and satellite InfraRed thermal data allows us to infer different volcanic activity styles which partially alternate throughout the year: intrusive activity and the construction of hornitos, degassing, activity from a lava pond, and varying styles of extrusive activity, in particular spattering. Our study provides important insights into the eruption dynamics of this peculiar volcano which suggests shallow melt storage within the crater floor.

Influence of the Yucatan earthquake event

In recent years, seismic wave effects caused by meteorite impacts have been widely observed. The meteorite impact event that occurred 66 million years ago is one of the most famous impact events in Earth’s history. The influences of the seismic wave field generated by this collision event on the solid Earth itself is worth exploring. Therefore, this study initially estimated the seismic source parameter information based on the multiring structure of the meteorite crater, and then simulates the seismic event. The results of this study provide a possible explanation for the formation of the Earth’s tectonic plates. The findings of this study suggest that the seismic wave field generated by the meteorite impact event 66 million years ago may have caused the destruction of the Solid Earth, leading to the formation of the boundary between the Indian Ocean and the Pacific Plate. Simultaneously, this study has important significance for inspiring the development of new geoscientific methods.

Vector Decomposition of Elastic Seismic Wavefields Using Self-Attention Deep Convolutional Generative Adversarial Networks

Vector decomposition of P- and S-wave modes from elastic seismic wavefields is a key step in elastic reverse-time migration (ERTM) to effectively improve the multi-wave imaging accuracy. Most previously developed methods based on the apparent velocities or the polarization characteristics of different wave modes are unable to accurately achieve the vector decomposition of P- and S-wave modes. To effectively overcome the shortcomings of conventional methods, we develop a vector decomposition method of P- and S-wave modes using self-attention deep convolutional generative adversarial networks (SADCGANs) to effectively separate the horizontal and vertical components of P- and S-wave modes from elastic seismic wavefields and accurately preserve their amplitude and phase characteristics for isotropic elastic media. For an elastic model, we use many time slices for a given source position to train the neural network, and use other time slices not in this training dataset to test the neural network. Numerical examples of different models demonstrate the effectiveness and feasibility of our developed method and indicate that it provides an effective intelligent data-driven vector decomposition method of P- and S-wave modes.

The impact of seismic noise produced by wind turbines on seismic borehole measurements

Abstract. Seismic signals produced by wind turbines can have an adverse effect on seismological measurements up to distances of several kilometres. Based on numerical simulations of the emitted seismic wave field, we study the effectivity of seismic borehole installations as a way to reduce the incoming noise. We analyse the signal amplitude as a function of sensor depth and investigate effects of seismic velocities, damping parameters and geological layering in the subsurface. Our numerical approach is validated by real data from borehole installations affected by wind turbines. We demonstrate that a seismic borehole installation with an adequate depth can effectively reduce the impact of seismic noise from wind turbines in comparison to surface installations. Therefore, placing the seismometer at greater depth represents a potentially effective measure to improve or retain the quality of the recordings at a seismic station. However, the advantages of the borehole decrease significantly with increasing signal wavelength.

Q-Compensated Gaussian Beam Migration under the Condition of Irregular Surface

The viscosity of actual underground media can cause amplitude attenuation and phase distortion of seismic waves. When seismic images are processed assuming elastic media, the imaging accuracy for the deep reflective layer is often reduced. If this attenuation effect is compensated, the imaging quality of the seismic data can be significantly improved. Q-compensated Gaussian beam migration (Q-GBM) is an effective seismic imaging method for viscous media, and it has the advantages of both wave equation and ray-based Q-compensated imaging methods. This study develops a Q-GBM method in visco-acoustic media with an irregular surface. Initially, the basic principles of Gaussian beam in visco-acoustic media are introduced. Then, by correcting the complex-value time of the Gaussian beam in visco-acoustic media, energy compensation and phase correction are carried out for the forward continuation wavefield at the seismic source of the irregular surface and the reverse continuation wavefield at the beam center, which effectively compensates the absorption and attenuation effects of visco-acoustic media on the seismic wavefield. Further, a Q-GBM method under the irregular surface is proposed using cross-correlation imaging conditions. Through migration tests for three numerical models of visco-acoustic media with irregular surfaces, it is verified that our method is an effective depth domain imaging technique for seismic data in visco-acoustic media under the condition of irregular surfaces.

Reverse time migration imaging method for tunnel seismic forward‐prospecting in viscoacoustic media

AbstractThe imaging of geological structure in front of a tunnel face is conducive to the safe construction of tunnels. The reverse time migration (RTM) method is popular for its high imaging accuracy. However, most of the current tunnel seismic RTM methods assume complete elasticity, ignoring the nature of wave propagation attenuation, resulting in a poor imaging outcome, especially when tunnelling in the shallow subsurface. Thus, it is necessary to study tunnel RTM suitable for attenuating strata. First, considering the frequency of tunnel seismic forward‐prospecting is usually higher than that of ground surface seismic exploration, we established a corresponding tunnel viscous media model to enable viscoacoustic forward modelling of seismic wavefield. Then, a simultaneous compensation approach for its amplitude and phase velocity is proposed based on the combination of the real and imaginary parts of the complex modulus. After the compensation of seismic wavefields, the tunnel Q‐RTM imaging method in viscoacoustic media is formed, and its effectiveness is verified by numerical examples. Compared with RTM without attenuation compensation, tunnel Q‐RTM effectively enhances the imaging energy and has higher positioning accuracy, improving the imaging effect of complex structures (especially at larger distances from the tunnel face). In the end, a detailed case study is presented to demonstrat the potential of the proposed method for field application.

Numerical investigation of seismic wavefield characteristics induced by a tensile source in a heterogeneous mining environment

Mining-induced tremors serve as the main dynamic stress source of coal bursts which represent one type of the most critical mining disasters in underground coal mines. To evaluate coal burst risks and comprehend the response of the coal-rock mass to seismic waves, microseismic monitoring stands as the principal method. By inferring the zones with elevated coal burst risks based on the seismic event clusters, valuable insights can be gained. However, because of limited seismic monitoring results generated from an individual seismic event, the recognition of the corresponding dynamic disturbance process remains ambiguous. The dynamic disturbance process presents immense complexity due to the focal mechanism and heterogeneous medium, particularly under the effect of structural heterogeneity induced by large-scale mining operations. In this study, forward numerical modelling was employed to gain the comprehension of seismic wave propagation affected by extraction zones. The findings revealed heightened intricacy of the wavefields and increased displacement concentrations around the working face. The characteristics of peak particle velocity (PPV) and displacement spectra were investigated in the near- and far-field zones, respectively. Owing to the existence of the extraction zone, both a significant amplification effect and the redistribution of PPV were observed around the near-field zone. The intricate wavefield caused by the focal mechanism and extraction zones resulted in more scattered distributions of the low-frequency spectral level, which can potentially cause an overestimation of source intensity. However, the impact of the complex wavefield on the corner frequency was limited. Through the analysis of the PPV attenuation law, as well as the distribution of both seismic moment and source radius, this study offered valuable insights for seismic risk assessment. The forward modelling approach facilitated the identification of high-risk potential areas resulting from seismic events, which deepened our comprehension of the dynamic disturbance process in the complex underground mine environment.

Past Earthquake Simulations Using Ambient Seismic Noise in Vrancea, Romania

Abstract The Vrancea seismic zone (VSZ), located in Romania, at the sharp bend of the southeast Carpathians, is an anomalous intraplate seismic nest releasing the largest strain in continental Europe. The last powerful earthquake in Vrancea occurred in 1977 causing significant damage to the densely populated cities in southeast Romania. The seismic infrastructure was underdeveloped at that time and the earthquake was not well recorded locally. Using ambient seismic noise recorded at modern broadband seismic stations around Vrancea in the year 2020, and the approximate moment tensor solutions of significant earthquakes Mw>6 since 1977, we reconstruct ground-motion waveforms recorded by modern seismometers decades after their occurrence. The virtual earthquake approach uses empirical Green’s functions from ambient noise cross correlations between pairs of seismic stations and adds the signatures of a model earthquake: double couple mechanism, buried source, and a realistic earth model in the epicentral area. Ambient noise data capture the signatures of complex subsurface structures and the 3D path effects, providing a more physically accurate representation of the seismic wavefield than purely synthetic data. Our new results demonstrate the viability of this innovative method and provide a unique opportunity for more accurate seismic hazard analysis in intraplate seismic zones with insufficient instrumental data.

Retrieval of surface waves from high-speed-train-induced vibrations using seismic interferometry

Train traffic has recently been realized as a potential seismic source for imaging and monitoring shallow subsurface structures. High-speed trains usually move on viaducts and generate seismic wavefields through bridge piers. This kind of source is not randomly distributed in space and time and thus indicates the characteristic of self-correlation. We find that correlated sources of one high-speed train running over piers make time-delayed spurious signals in the crosscorrelation functions. The direct-wave interferometry with correlated sources is proposed and demonstrates that stacking the interferometric responses from high-speed trains with different speeds may reduce the spurious imprint of source self-correlations, but it cannot remediate the problem. The influence of the source wavelet can be eliminated by using cross coherence. Stationary-phase segment selection and stacking can reduce the bias generated by trains moving out of the stationary-phase zone of station pairs. The validity is demonstrated by using synthetic data with inline and out-of-line linear arrays. We apply the proposed scheme to field data with nine high-speed train events. Multimodal Rayleigh waves were retrieved and shallow shear-wave velocities were inverted from multimodal dispersion data in a range of 4–25 Hz. The results bring a novel approach for the imaging and monitoring of the shallow subsurface using high-speed-train-induced vibrations.

Analytic formula for the group velocity and its derivatives with respect to elastic moduli for a general anisotropic medium

Studying the anisotropy of seismic wave velocity can provide a theoretical basis for understanding the characteristics of seismic wave propagation in anisotropic media, such as forward modeling of seismic wavefield and simultaneous inversion of anisotropic parameters. It is an important work to calculate the group velocities of three kinds of seismic waves (qP, qS1, and qS2) and the analytical expressions of the partial derivatives of the group velocities with respect to 21 elastic parameters in general anisotropic media. Therefore, a new relationship between the phase and group velocity in the general anisotropic medium is introduced first, and then the analytical expressions of the group velocity of three kinds of waves are deduced. Then, the analytical formulas of partial derivatives of the group (or phase) velocity with respect to 21 elastic parameters are derived. Finally, the distribution of partial derivatives of group slowness with respect to 21 elastic parameters with varied ray angles is analyzed and discussed. The final analytical expressions of group velocity and its partial derivatives are relatively concise and can deal with the singular points and multivalued problems of qS waves. By drawing comparison to the numerical solution of the eigenvector method, the accuracy of the analytical formula of group velocity and its partial derivatives with respect to elastic parameters are verified. The numerical simulation results indicate that the algorithm can accurately obtain the partial derivatives of group slowness with respect to 21 elastic parameters and would provide a theoretical basis for seismic ray tracing and traveltime inversion in general anisotropic media.

Research on the evolution law of the seismic wave field based on the explosive source parameters

We present a numerical model for blast-induced seismic waves. This model is based on the transformation mechanism of the seismic wave field, and the process of the seismic wave’s generation is divided into two stages. The first stage is the generation of elastic waves. Due to the plastic deformation of the geotechnical medium in this stage, we have established the Euler model to describe it. The second stage is the prorogation of the elastic waves; we have established the Lagrange models to describe this stage. Finally, the influence of the main parameters of the explosive sources (detonation pressure and expansion index) on the seismic wave is analyzed by the established model. The results show that the proposed model in this paper can reasonably predict the evolution law of the seismic wave field based on the explosive source parameters.

Seismic response of a single-layer reticulated dome: Fault-to-structure simulation

Seismic response of large-span spatial structures is particularly susceptible to soil-structure interaction and spatial variability of ground motions. Yet existing seismic analysis fail to properly account for the foundation soil, and the ground motions are commonly determined based on empirical formulas. Physics-based 3D seismic simulation has recently been developed to provide site-specific ground motions, and the fault-to-structure simulation facilitates the incorporation of seismic wave field and soil-structure interaction into the analysis of engineering structures. This article innovatively implements the fault-to-structure simulation on a single-layer reticulated dome. Structural response of fault-to-structure model and two commonly used models is compared and discussed. Results show that the damping of soil reduces the stress and horizontal acceleration of the reticulated dome, while the soil movement leads to an increase in displacement. Noticeably, the seismic propagation characteristics increase vertical acceleration of the inner rings. Compared with fault-to-structure model, the multi-support excitation model and uniform excitation model reduce the vertical displacement of 29.1% and 50.1%, respectively, and reduce the vertical acceleration of the inner rings of 59.9% and 69.0%, respectively.

Elastic full-waveform inversion on Caesar-Tonga — Case study

Full-waveform inversion (FWI) has been widely used on 3D data sets to build detailed velocity models over the past 10 years. Most of these projects used pressure data and an acoustic approximation, with the assumption that the field data were dominated with P-waves. This approach of FWI can determine parameters related to the acoustic wave equation. It focuses on updating velocities by minimizing the misfit between observed and model data. Acoustic FWI, using the pressure component of collected data, has shown tremendous potential in simple geologic settings. Successful FWI projects, using wide-azimuth streamer, ocean bottom, and land survey geometries, have convinced the oil industry to pursue the next step by involving more physical properties. However, questions remain on how far we can properly describe field data with the acoustic approximation and at what point we need to switch to a much more expensive elastic wave equation implementation. In a complicated geologic region such as the Gulf of Mexico (GoM), the seismic wavefield can be complex and elastic FWI is needed to achieve a better velocity model, even when using mostly pressure data alone. We demonstrate the application of elastic FWI on sparse-node ocean-bottom-node data from the GoM and show comparisons to the acoustic solution. The comparisons demonstrate the benefits of the elastic FWI implementation when applied to image steeply dipping Miocene sands beneath a complex salt canopy, despite the increased computational expense. Furthermore, we demonstrate that when elastic FWI is applied to sufficiently high frequencies, the FWI-derived reflectivity product and velocity model are reliable interpretation products.

3-D crustal shear wave velocity model derived from full-waveform tomography for Central Honshu Island, Japan

SUMMARY We present a crustal shear wave (S-wave) velocity model for central Japan that accurately captures the previously mapped geology and lithology of the region. We perform a full-waveform tomographic inversion using a large seismic data volume that was recorded by the dense, permanent seismic monitoring network that spans the Japan Islands to resolve the seismic structure beneath central Honshu Island. The inversion reduces the time–frequency phase misfit by 16.4 and 6.7 per cent in the 20–50-s and 10–30-s period ranges, respectively. We infer that the resolved seismic velocity anomalies in our inversion reflect a range of subsurface features, including volcanic fluids, dehydration fluids from the subducted crust and sedimentary basins. In contrast to previous S-wave velocity models of the same region, which have been based primarily on first-arrival tomography, our S-wave velocity model is based on the explicit computation of the full seismic wavefield. This approach makes our model more suitable for modelling seismic wavefields in the 10–50-s period range and enables high-resolution imaging of the subsurface.

Determination of effective seismic wave velocities using time gradients obtained from response and CDP reflection hodographs

Seismic wave velocities, including effective velocities, play a critical role in the kinematic processing and interpretation of 2D and 3D seismic data. Along with other parameters of elastic waves, the geological efficiency of seismic exploration also depends on the level of knowledge of the velocity model of the medium, on the accuracy of information about velocities. The article briefly lists the main methods for determining the effective velocities according to the seismic wave field, developed and applied in the practice of seismic research. The methods used to determine the effective velocities of reflected waves can be divided into two groups: methods for determining the effective velocities based on automatic or visual tracking of the in-phase axes (i.e. hodographs) of reflected waves on seismic records, then their approximation by hyperbolas constitute the first group, and the second the group consists of methods based on the application of the analysis of the seismic wave field in controlled directions on the seismograms of a common depth point (CDP). Each proposed method for determining effective speeds has advantages and disadvantages. The article focuses on the industrial method, widely used at present, based on the analysis of the wave field in controlled directions, which do not provide sufficient information to solve the main problems of kinematic interpretation. The main disadvantages of the existing methods are indicated. The article describes a new method for determining the effective velocity, which is fundamentally different from the methods that are still used in the practice of seismic exploration. The fact is that in this method, seismic survey data of single and multiple profiling are not used separately, as it was in the methods used in seismic survey practice so far, but together. Formulas have been derived for determining the effective velocity based on the time gradients of the travel time curves of the CSP and CDP of reflected waves, which makes it possible to determine the speeds even from incomplete travel time curves. A technique for determining the effective speed has been developed and a sequence of procedures has been determined for solving the problem. The results of research are given on a specific example by solving the direct and inverse problems for the Sazhdag area between the Kura and Gabyrra rivers. The influence of errors in the values of the parameters included in the formula for calculating the effective speed on the final results is studied. At the end of the article, the main advantages of the proposed method are indicated.

Seismic ahead-prospecting based on deep learning of retrieving seismic wavefield

Unknown geology ahead of the tunnel boring machine (TBM) brings a large safety risk for tunnel construction. Seismic ahead-prospecting using TBM drilling noise as a source can achieve near-real-time detection, meeting the requirements of TBM rapid drilling. Seismic wavefield retrieval is the key data processing step for the efficient utilization of TBM drilling noise. The traditional solution is based on cross-correlation to extract reflected waves, but the reference waves remain in the result, disturbing the imaging and interpretation of the adverse geology. To solve this problem, the deep learning method was introduced in wavefield retrieval to improve the accuracy of geological prospecting. We trained a deep neural network (DNN) with its strong nonlinear mapping capability to transform seismic data from TBM drilling noise to data from the active source. The issue lies in its features for this specific tunnel task, including the decay of the seismic signal with time and the incomplete spatial correspondence. Thus, we improved a classical DNN with the time constraint as an additional input, and an additional pre-decoder to enlarge the receptive field. Additionally, a loss function weighted by the ground truth and time constraint is improved to achieve an accurate retrieval of the effective signal, considering the little effective information in tunnel data. Finally, the workflow of the proposed method was given, and a dataset designed with reference to the field case was employed to train the network. The proposed method accurately retrieved the reflection signal with higher dominant frequencies, which helped improve the accuracy of imaging. Numerical simulations and imaging on typical geological models show that the proposed method can suppress reference waves and get more accurate results with fewer artifacts. The proposed method has been applied in the Gaoligongshan Tunnel and imaged two abnormal zones, providing meaningful geological information for TBM drilling and tunnel construction.

Quantitative analysis of surface‐wave propagation in the Mexico City Valley

AbstractThe Mexico City basin is an extreme example of an alluvial geological structure that induces long duration and large amplification on ground motions. Researchers have established that the seismic wavefield within the Mexico City basin is composed primarily of surface waves. In the present work, we present a quantitative analysis of the surface‐wave field propagating in the Mexico City basin and generated by thrust‐ and normal‐faulting events. Surface waves are identified and extracted from three‐component ground motion recordings using a technique that exploits the polarization of ground motion. The spatial analysis of the extracted waves clearly shows that the basin response, is strongly dominated by low‐frequency ( to ) Love waves. For all seismic events considered, we found that the identified Love waves can reach amplitudes three times larger as compared to Rayleigh waves. Our analysis indicates that surface wave amplification (as defined in the present work) increases with the 1D fundamental resonant site‐period T1, and appears to be independent of earthquake magnitude. We also quantify the mean delay time of the central frequency f0 of the extracted waves. We found that the of Love waves is spatially more coherent as compared to that of Rayleigh waves. The parameter T1 appears to be a good “proxy” of surface wave effects. This is manifested by a reciprocal relation that was established between T1 and the frequency f0 of the extracted Love waves. Equally important, the latter reciprocal relation turns out to be independent of earthquake magnitude.

Effects of non-ideal seabed topography on low frequency sound propagation in shallow sea

In order to study the influence of seabed topography on sound propagation under non-ideal conditions, a simulation model of low frequency sound propagation of whole waveguide is established by using finite element method (FEM). The action mechanism of the topography with seamounts on the components of the seismic wave field is studied in time domain. The simulation results show that the propagation of various seismic wave components can be seen intuitively from the time domain. Scholte waves can be excited easily in a suitable range from the seabed, and can propagate along the seabed for a long distance with small attenuation and strong stability. The presence of a seamount allows Scholte waves to scatter, and Scholte waves can travel along the surface of the seamount to the back of the seamount. The path and energy intensity of sound wave change with the change of terrain.

P- and S-wave energy current density vectors dot product imaging condition of source time-reversal imaging

SUMMARY Source time-reversal imaging (TRI) based on decoupled elastic wave equation can utilize vector P- and S-wave time differences and achieve high-precision source location in complex geological models. The imaging condition is critical for TRI. However, because of the orthogonally polarized properties of P and S waves, traditional vector dot product imaging condition directly applied to TRI will decrease the effective imaging values. In contrast, the energy current density vectors of P and S waves represent the propagation directions of the wavefields and are almost parallel. Their dot product can result in the maximum imaging energy. Based on this principle, we propose a P- and S-wave energy current density vectors dot product imaging condition (PSEDPIC), which uses the propagation direction information of P and S waves at the source point to suppress imaging artefacts generated by waves with inconsistent propagation directions. Numerical tests reveal that PSEDPIC can (1) reduce the image artefacts, (2) improve the imaging spatial resolution and (3) allow a shallower imaging region. In addition, if the numerical simulation algorithm used in TRI can reconstruct the seismic wavefield accurately in the presence of surface topography, the impact of an observation system with elevation differences on imaging can be eliminated automatically. For this reason, we use the curvilinear grid finite-difference method to directly reconstruct the wavefield in TRI to solve the problem of data elevation correction. The test results of 3-D synthetic and field data for microseismic monitoring demonstrate the effectiveness of the proposed method.