Acoustic Waveform Inversion Research Articles

Robust frequency-domain acoustic waveform inversion using a measurement of smooth radical function derived from compressive sensing

A smooth radical function derived from compressive sensing is introduced, aiming to measure the misfit in frequency-domain acoustic waveform inversion. The purpose of employing this function is to improve inverse accuracy and reliability. With a novel approximation of L1 norm, the objective function constructed by this measurement can exhibit favorable robustness throughout the inverse iteration. By exploiting the smoothness property, the misfit can be minimized through a cost-effective approach of taking derivatives. The inverse framework of the smooth radical function is derived which indicates comparable computing complexity per iterative step to L2 case, theoretically. The experiential data with outliers are employed for inversion and compared with the traditional optimization-based L1 norm and L2 norm. The obtained results are consistent with theoretical analysis and demonstrate the superiority of the proposed measurement.

Monitoring underground hydrogen storage migration and distribution using time-lapse acoustic waveform inversion

The ongoing global energy shift from fossil fuels to renewable sources highlights the importance of underground hydrogen storage (UHS) as a sustainable mechanism to counterbalance the seasonal inconsistencies of renewable energy. Comparable to geological CO2 sequestration, UHS necessitates precise subsurface imaging and a thorough understanding of hydrogen behavior within geological formations, including its location and migration patterns. Since direct subsurface measurement is unattainable, there is a pronounced need for robust subsurface characterization and monitoring techniques. This research focuses on UHS feasibility in enduring storage scenarios, employing seismic monitoring strategies adapted from CO2 storage practices. Specifically, we integrate Continuous Active Source Seismic Monitoring (CASSM) and Time-Lapse Full Waveform Inversion (TLFWI) to scrutinize UHS. The study employs synthetic crosshole surveys that initially model the coexistence of hydrogen and water within fractured reservoirs, aiming to pinpoint hydrogen-related velocity alterations in acoustic waveforms. Subsequently, we utilize a time-lapse synthetic model of hydrogen injection to emulate CASSM observations. Utilizing TLFWI in conjunction with White's model, we successfully process the CASSM data to discern and quantify temporal variations in velocity and saturation, which effectively maps the spatial and temporal distribution of mobile hydrogen. The results affirm the capabilities of TLFWI and CASSM as proficient monitoring systems for UHS. This study aspires to offer a dependable methodology for the administration of large-scale and long-term geological hydrogen storage.

Acoustic waveform inversion in frequency domain: Application to a tunnel environment

Waveform inversion is an approach used to find an optimal model for the velocity field of a ground structure such that the dynamic response is close enough to the given seismic data. First, a suitable numerical approach is employed to establish a realistic forward computer model. The forward problem is solved in the frequency domain using higher-order finite elements. The velocity field is inverted over a specific number of discrete frequencies, thereby reducing the computational cost of the forward calculation and the nonlinearity of the inverse problem. The results are presented for different frequency sets and with different source and receiver locations for a two-dimensional model. The influence of attenuation effects is also investigated. The results of two blind tests are presented where only the seismic records of an unknown synthetic model with an inhomogeneous material parameter distribution are provided to mimic a more realistic case. Finally, the result of the inversion in a three-dimensional space is illustrated.

An implementation of a recurrent neural network for 1D acoustic waveform inversion

Recurrent neural network (RNN) is a class of artificial neural networks widely used to model a temporal dynamic system. Recently, recurrent neural networks have been developed for acoustic waveform modelling in 1D and 2D bounded domains. Since the trainable parameters of the networks are the acoustic wave velocity, the process of network training is equivalent to solving an inverse problem of acoustic waveform inversion. In this work, we extend the previously proposed RNNs for acoustic waveform modelling/inversion in 1D unbounded domains by incorporating perfectly matched layers (PML) into the RNN cell. The proposed RNN architecture was implemented using Tensor Flow and has been successfully tested on a 1D synthetic data set. The results show that we have successfully implemented PML to RNN base acoustic full waveform inversion.

The influence of source wavelet estimation error in acoustic time domain full waveform inversion

Abstract Almost all forms of full waveform inversion use a source wavelet estimate in the extrapolation of the down-going wavefield to produce the forward modelled data and also to create the gradient. This source wavelet can be modelled, extracted from the recorded data during the pre-processing, or sometimes a zero-phase band-limited synthetic wavelet can be used instead. Alternatively, the source information can be regarded as another unknown and the initial source estimate then updated within the inversion. The importance of reliable source wavelet information during the waveform inversion implementation has been widely implied or briefly mentioned by multiple authors, but little detailed study of the effects of poor wavelets has been presented in the literature. It is the purpose of this study to examine if shape errors in the source wavelet manifest themselves in a significantly damaging way in the velocity model obtained using conventional time-domain acoustic waveform inversion, and also to assess what effect such velocity change has on the subsequent migrated image positions. We conclude that for modest structural complexity, acoustic time-domain least-squares waveform inversion for refractions with a maximum frequency of 9 Hz, commencing from a non-cycle skipped model, is surprisingly robust with respect to source wavelet error.

Acoustic multi-parameter full waveform inversion based on the wavelet method

In this paper, the acoustic full waveform inversion based on the wavelet method is proposed. It allows to determine density and velocity parameters simultaneously in the time domain. The forward problem is solved based on the wavelet method. The numerical schemes for modelling are constructed in detail. The stability condition is derived for the first time. The inversion is an optimization process for minimizing the mismatch between the synthetic data and the observed data. The computational scheme for the gradient of the objective function is constructed based on the matrix analysis technique. The inversion is implemented from low frequency to high frequency successively. Furthermore, the inversion result of current low frequency is served as the initial guess of next high frequency. This hierarchic strategy includes the smaller wavelengths progressively and improves the inversion robustness. Numerical computations for the benchmark Marmousi model demonstrate that the method has good ability to reconstruct media parameters in complex structures.

The effects of elastic data on acoustic and elastic full waveform inversion

Full waveform inversion (FWI) is regarded as an effective method to obtain high accuracy subsurface parameters like velocity and density. When it is applied to real seismic data, some challenges may appear. Real seismic data contain complex wavefields including compressional waves, shear waves and their interconversions, however, acoustic FWI only matches compressional waves but not including the converted compressional waves and treats others as noise. Though elastic FWI can take all types of wave modes into consideration, the inversion results will be compromised by the lack of multi-component input since only the vertical component is generally acquired in practice. It is interesting to investigate the effects of a single-component input generated by an elastic model on acoustic and elastic FWI. The investigation is carried out using a modified Marmousi2 model. Numerical examples illustrate that elastic FWI using a single vertical component observation data has an advantage in obtaining higher resolution inversion results than acoustic FWI. However, the ability of elastic FWI to recover more accurate velocities, especially for S-wave velocity, is limited to a degree if the horizontal component is missing. This situation will worsen in the presence of noise. It is also found that the inversion results of acoustic FWI from the elastic data generated by an explosive source are acceptable, whereas those of acoustic FWI from the elastic data created by a vertical-directional normal stress source are of very low accuracy.

Velocity-model building with enhanced shallow resolution using elastic waveform inversion — An example from onshore Oman

Full-waveform inversion is a powerful data-fitting technique that is used for velocity-model building in seismic exploration. The inversion approach exploits the sensitivity of long-offset, wide-aperture, low-frequency data to the P-wave velocity properties in the subsurface. In the geologically complex land context in which different lithologies interleave and create large elastic property contrasts, acoustic waveform inversion is challenged due to the elastic nature of the data. The large elastic property contrasts create mode conversions. At low-to-intermediate frequencies, due to tuning/interference effects, the changes in the amplitudes of the different events affect amplitude and phase of the waveforms. We found that elastic waveform inversion of the long-offset, wide-aperture, low-frequency data leads to better retrieval of the compressional velocity model than the acoustic inversion and it is more stable. To obtain a good resolution in the shallow part of the model in an efficient manner, we have developed a two-stage inversion workflow that combines offset and frequency continuation. We have evaluated the relevance of this workflow with a challenging data set from South Oman.

Volume Flow Rate Estimation for Small Explosions at Mt. Etna, Italy, From Acoustic Waveform Inversion

AbstractRapid assessment of the volume and the rate at which gas and pyroclasts are injected into the atmosphere during volcanic explosions is key to effective eruption hazard mitigation. Here, we use data from a dense infrasound network deployed in 2017 on Mt. Etna, Italy, to estimate eruptive volume flow rates (VFRs) during small gas‐and‐ash explosions. We use a finite‐difference time‐domain approximation to compute the acoustic Green's functions and perform a full waveform inversion for a multipole source, combining monopole and horizontal dipole terms. The inversion produces realistic estimates of VFR, on the order of 4 × 104 m3/s and well‐defined patterns of source directivity. This is the first application of acoustic waveform inversion at Mt. Etna. Our results demonstrate that acoustic waveform inversion is a mature and robust tool for assessment of source parameters and holds potential as a tool to provide rapid estimates of VFR in near real time.

Multi-parameter reconstruction of velocity and density using ultrasonic tomography based on full waveform inversion

In this paper, an ultrasonic tomography method based on acoustic multi-parameter full waveform inversion (FWI) is developed for high-resolution reconstructions of velocity and density in metal components. The challenging issue in multi-parameter FWI is to deal with the trade-off effects between different parameters of different natures. Moreover, different parameters have different orders of amplitudes in the wave-field which make the inversion ill-conditioned. The inverse Hessian has been shown to mitigate the coupling effects and rescale the amplitudes of different parameters, and then the reliable updates of different parameters are available. The simultaneous reconstructions of velocity and density by using the truncated Gauss–Newton method, in which the inverse Hessian can be considered through a matrix-free conjugate gradient solution of the Gauss–Newton normal equation, are investigated by simulation as well as experiment on the centred inclusions. The results show that this method can effectively alleviate the trade-off effects between velocity and density, and thus the velocity of the inclusion is accurately reconstructed and the reconstruction of the density is well achieved.

Using acoustic waveform inversion to quantify volcanic emissions

Volcanic eruptions produce immense sound, particularly in the infrasound band. Acoustic waveform inversion shows promise for improved eruption characterization by providing robust estimates of erupted volume and mass. Previous inversion studies have generally assumed a simple volumetric acoustic source (monopole) that radiates sound equally in all directions. However, more complex and complete source reconstructions are possible with a combination of equivalent sources (multipole). Recent work has made progress using Finite-Difference Time-Domain modeling over high-resolution topography to obtain the full three-dimensional Green’s functions. The source-time function can then be inverted for and converted to a volume and mass flow rate. We review the acoustic waveform inversion as it has been applied to volcanic eruptions and discuss current limitations and how they can be mitigated. In most cases, the simple (monopole) source mechanism is a good approximation for discrete volcanic explosions, but a small directionality (dipole) component may remain. Furthermore, the neglecting effects of topography can lead to the overestimation of both the monopole and dipole strengths. Volcano infrasound source mechanisms are also not well constrained due to infrasound sensors usually being deployed on the surface. The methods discussed here can be extended to anthropogenic explosions and monitoring efforts, potentially in near-real time.Volcanic eruptions produce immense sound, particularly in the infrasound band. Acoustic waveform inversion shows promise for improved eruption characterization by providing robust estimates of erupted volume and mass. Previous inversion studies have generally assumed a simple volumetric acoustic source (monopole) that radiates sound equally in all directions. However, more complex and complete source reconstructions are possible with a combination of equivalent sources (multipole). Recent work has made progress using Finite-Difference Time-Domain modeling over high-resolution topography to obtain the full three-dimensional Green’s functions. The source-time function can then be inverted for and converted to a volume and mass flow rate. We review the acoustic waveform inversion as it has been applied to volcanic eruptions and discuss current limitations and how they can be mitigated. In most cases, the simple (monopole) source mechanism is a good approximation for discrete volcanic explosions, but a small ...

Seismoacoustic Analysis of Chemical Explosions at the Nevada National Security Site

AbstractIn recent years, two sets of chemical explosions have been conducted at the Nevada National Security Site: six explosions from Phase I of the Source Physics Experiment and four explosions from the Forensics Surface Events. We have estimated the explosive yield and depth‐of‐burial/height‐of‐burst of both from the synthesis of seismic and low‐frequency acoustic data. Analysis of the seismic signal is performed using a waveform envelope technique. Using seismic data only, however, there is a trade‐off between the yield and depth or height of the explosion, which becomes especially acute for near‐surface events. This trade‐off between yield and depth/height can be broken by including complementary analysis of the acoustic signal using the acoustic waveform inversion method. The acoustic signal also has a strong trade‐off between a yield and depth/height, but the slope is opposite that of the seismic for near‐surface events. We use a likelihood function to combine the seismic and acoustic analysis and improve our estimates of yield and depth/height for these sets of explosions. The results are generally consistent with the known parameters, but can be improved upon by higher‐frequency seismic analysis and improved acoustic impulse scaling for large‐scaled depths‐of‐burial. These events serve as prime examples of data fusion from multiple data streams. The challenge will be to apply the method to events at longer regional distances where the seismic signals will include phases traveling in the upper mantle, and the acoustic signals will be recorded as infrasound signals, which are subject to atmospheric variability.

Uncertainty analysis for infrasound waveform inversion: Application to explosion yield estimation.

While the acoustic waveform inversion method is increasingly used in geophysical acoustics to constrain source parameters, the inversion results are often provided without any uncertainty analysis. This study presents a probabilistic representation for acoustic waveform inversion and method to evaluate the inversion uncertainty using ground-truth data. A posteriori probability distribution of source estimate is described by a priori waveform misfit covariance and the variance of acoustic source model. The probabilistic framework is applied to local explosion infrasound to estimate the yields of explosions and uncertainty. Estimated yields showed overall good agreement with the true yields (less than 25% errors). The uncertainty of the estimated yield is represented by the sum of the waveform inversion uncertainty and source model uncertainty. It is shown that the yield uncertainty attributed to local infrasound inversion (within 10 km) is as small as the uncertainty caused by 10% prediction errors in the acoustic source model. These results indicate that the acoustic source model uncertainty should also be considered for accurate yield estimation and that local infrasound can be a valuable tool to understand the magnitude of the source uncertainty.

Acoustic waveform inversion and uncertainty analysis for explosion yield estimation

Waveform inversion techniques are widely used to extract source information from acoustic signals. The methods exploit full-waveform information and provide further constraints on source inversion than other parameter-based inversions. Infrasound waveform inversion was recently applied to chemical explosions and showed promising results for the determination of explosion yield. The method can improve the accuracy of the estimated yield by using full 3-D numerical Green's functions and incorporating the propagation path effects into the inversion. However, the inversion results are often given without any uncertainty estimation, which is critical for a post-detonation forensic analysis. In this study, we evaluate the yield estimation errors associated with the uncertainty in the atmospheric representation. An ensemble of atmospheric realizations is obtained by adding random turbulence to an atmospheric model and the uncertainty of inversion solution depending on atmospheric variation is quantified. In addition, different atmospheric models derived from local weather data or numerical weather prediction models are validated for yield estimation by using a series of chemical explosion data.

Acoustic Wave Based Time-Domain Full Waveform Inversion and Its Application

In this paper, the acoustic wave-based time-domain full waveform inversion (FWI) is investigated. The FWI is a typical nonlinear ill-posed problem. In order to overcome its ill-posedness, the strategy of stepwise inversion is adopted. The inversion is carried out from low frequency to high frequency, and the inverse result at low frequency is chosen as the initial model for the high frequency inversion. This strategy effectively strengthens the robustness of inversion. The forward simulation is implemented efficiently with the explicit finite difference scheme while the inverse iteration is based on the LBFGS algorithm. The gradient of the objection function is computed by the wavefield backward technique. Numerical computations are not only completed for the benchmark Overthrust model but also for a real data set and good inversion results are yielded.

A discrepancy-based penalty method for extended waveform inversion

Extended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model, thus permitting it to fit the data well throughout the inversion process. These extra degrees of freedom must be curtailed at the solution, for example, by penalizing them as part of an optimization formulation. For separable (partly linear) models, a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical (linear) degrees of freedom. The linear variables are eliminated in an inner optimization step, leaving a function of the outer (nonlinear) variables to be optimized. This variable projection method is convenient for computation, but it requires that the penalty weight be increased as the estimated model tends to the (physical) solution. We describe an algorithm based on discrepancy, that is, maintaining the data residual at the inner optimum within a prescribed range, to control the penalty weight during the outer optimization. We evaluate this algorithm in the context of constant density acoustic waveform inversion, by recovering background model and perturbation fitting bandlimited waveform data in the Born approximation.

Acoustic Waveform Inversion for Ocean Turbulence

AbstractThe seismic oceanography method is based on extracting and stacking the low-frequency acoustic energy scattered by the ocean heterogeneity. However, a good understanding on how this acoustic wavefield is affected by physical processes in the ocean is still lacking. In this work an acoustic waveform modeling and inversion method is developed and applied to both synthetic and real data. In the synthetic example, the temperature field is simulated as a homogeneous Gaussian isotropic random field with the Kolmogorov–Obukhov spectrum superimposed on a background stratified ocean structure. The presented full waveform inversion method is based on the ray-Born approximation. The synthetic seismograms computed using the ray-Born scattering method closely match the seismograms produced with a more computationally expensive finite-difference method. The efficient solution to the inverse problem is provided by the multiscale nonlinear inversion approach that is specifically stable with respect to noise. Full waveform inversion tests are performed using both the stationary and time-dependent sound speed models. These tests show that the method provides a reliable reconstruction of both the spatial sound speed variation and the theoretical spectrum due to fully developed turbulence. Finally, the inversion approach is applied to real seismic reflection data to determine the heterogeneous sound speed structure at the west Barents Sea continental margin in the northeast Atlantic. The obtained model illustrates in more detail the processes of diapycnal mixing near the continental slope.

Monitoring gas leakages simulated in a near surface aquifer of the Ellerbek paleo-channel

Renewable energy resources are intermittent and need buffer storage to bridge the time-gap between production and demand peaks. The North German Basin has a very large capacity for compressed air/gas energy storage (CAES) in porous saltwater reservoirs and salt cavities. Even though these geological storage systems are constructed with high caution, accidental gas leakages occurred in the past. Stored gases migrated from deep reservoirs along permeable zones upwards into shallow potable aquifers. These CAES leakages cause changes in the electro-elastic properties, and density of the aquifers, and therefore justify investigations with the application of different geophysical techniques. A multiphase flow simulation has been performed to create a realistic virtual CAES leakage scenario into a shallow aquifer in Northern Germany. This scenario is used to demonstrate the detecting resolution capability of a combined geophysical monitoring approach, consisting of acoustic joint waveform inversion (FWI) of surface and borehole data, electrical resistivity tomography (ERT) and gravity. This combined approach of geophysical multi-techniques was able to successfully map the shape and determine the physical properties of the simulated gas phase body at a very early stage after leakage began. Techniques of FWI and ERT start to resolve CAES leakage anomalies only a few years and gravity even a few months after leakage began. Geophysical monitoring of vast areas may start by conducting time-effective aero-surveys (e.g. electromagnetic induction or gravity gradient methods) to isolate anomalous subareas of potential leakage risks. These subareas are then studied in detail using our combined high-resolution approach. In conclusion, our approach is sensitive to CAES leakages and can be used for monitoring.

Characterization of moderate ash-and-gas explosions at Santiaguito volcano, Guatemala, from infrasound waveform inversion and thermal infrared measurements.

The rapid discharge of gas and rock fragments during volcanic eruptions generates acoustic infrasound. Here we present results from the inversion of infrasound signals associated with small and moderate gas‐and‐ash explosions at Santiaguito volcano, Guatemala, to retrieve the time history of mass eruption rate at the vent. Acoustic waveform inversion is complemented by analyses of thermal infrared imagery to constrain the volume and rise dynamics of the eruption plume. Finally, we combine results from the two methods in order to assess the bulk density of the erupted mixture, constrain the timing of the transition from a momentum‐driven jet to a buoyant plume, and to evaluate the relative volume fractions of ash and gas during the initial thrust phase. Our results demonstrate that eruptive plumes associated with small‐to‐moderate size explosions at Santiaguito only carry minor fractions of ash, suggesting that these events may not involve extensive magma fragmentation in the conduit.

Full-waveform modeling and inversion of physical model data

Because full elastic waveform inversion requires considerable computation time for forward modeling and inversion, acoustic waveform inversion is often applied to marine data for reducing the computational time. To understand the validity of the acoustic approximation, we study data collected from an ultrasonic laboratory with a known physical model by applying elastic and acoustic waveform modeling and acoustic waveform inversion. This study enables us to evaluate waveform differences quantitatively between synthetics and real data from the same physical model and to understand the effects of different objective functions in addressing the waveform differences for full-waveform inversion. Because the materials used in the physical experiment are viscoelastic, we find that both elastic and acoustic synthetics differ substantially from the physical data over offset in true amplitude. If attenuation is taken into consideration, the amplitude versus offset (AVO) of viscoelastic synthetics more closely approximates the physical data. To mitigate the effect of amplitude differences, we apply trace normalization to both synthetics and physical data in acoustic full-waveform inversion. The objective function is equivalent to minimizing the phase differences with indirect contributions from the amplitudes. We observe that trace normalization helps to stabilize the inversion and obtain more accurate model solutions for both synthetics and physical data.