Elastic Waveform Inversion Research Articles

Monitoring spatiotemporal evolution of fractures during hydraulic stimulations at the first EGS collab testbed using anisotropic elastic-waveform inversion

The EGS Collab project acquired continuous active-source seismic monitoring (CASSM) data before, during, and after hydraulic stimulations at the first testbed at the depth of 4850 ft (1478 m) at the Sanford Underground Research Facility in Lead, South Dakota, for monitoring fracture creation and evolution. CASSM acquisition was conducted using 24 hydrophones, 18 accelerometers, and 17 piezoelectric sources within four fracture-parallel wells and two orthogonal wells. 3D anisotropic traveltime tomography and anisotropic elastic-waveform inversion of the campaign cross-borehole seismic data show that the rock within the stimulation region is a heterogeneous horizontal transverse isotropic medium. We use these inversion results as the initial models and apply 3D anisotropic first-arrival traveltime tomography and 3D anisotropic elastic-waveform inversion to the CASSM data acquired after each stimulation in May, 2018 and December, 2018. We observe the spatiotemporal evolution of seismic velocities and anisotropic parameters caused by hydraulic fracture stimulations, showing the regions of rock alternation caused by hydraulic fracture stimulation.

Characterizing the target of interest underlying a complex overburden with target-oriented elastic waveform inversion

Abstract It remains challenging for elastic full waveform inversion (EFWI) to characterize the elastic properties of a target reservoir deep beneath complex overburden media. This can be attributed to two factors. 1) The complex wavefield distortions arising from the overburden obscure the target reflection properties, resulting in a target zone with limited energy illumination. 2) High-resolution EFWI for the whole inversion domain is computationally expensive. To overcome these challenges, instead of directly inverting for the subsurface model using surface seismic data, we develop a target-oriented elastic waveform inversion scheme. We first retrieve the elastic reflection response to the target zone of interest by projecting seismic data from surface to the datum level. Then, we can apply high-resolution EFWI on the target zone by using the retrieved elastic reflection data. To better handle the complex overburden, which may include anisotropy and salt bodies, we make full use of the prior estimate of the overburden in the redatuming process to obtain a reliable reflection response to the target zone. In the numerical examples, we use the SEAM model with an anisotropic overburden and a salt body model to demonstrate the feasibility and effectiveness of the proposed method and analyze the influence of anisotropy and high-contrast salt in the overburden on the redatuming and inversion results, respectively.

Robust Elastic Full-Waveform Inversion Based on Normalized Cross-Correlation Source Wavelet Inversion

The elastic full-waveform inversion (EFWI) method efficiently utilizes the amplitude, phase, and travel time information present in multi-component seismic recordings to create detailed parameter models of subsurface structures. Within full-waveform inversion (FWI), accurate source wavelet estimation significantly impacts both the convergence and final result quality. The source wavelet, serving as the initial condition for the wave equation’s forward modeling algorithm, directly influences the matching degree between observed and synthetic data. This study introduces a novel method for estimating the source wavelet utilizing cross-correlation norm elastic waveform inversion (CNEWI) and outlines the EFWI algorithm flow based on this CNEWI source wavelet inversion. The CNEWI method estimates the source wavelet by employing normalized cross-correlation processing on near-offset direct waves, thereby reducing the susceptibility to strong amplitude interference such as bad traces and surface wave residuals. The proposed CNEWI method exhibits a superior computational efficiency compared to conventional L2-norm waveform inversion for source wavelet estimation. Numerical experiments, including in ideal scenarios, with seismic data with bad traces, and with multi-component data, validate the advantages of the proposed method in both source wavelet estimation and EFWI compared to the traditional inversion method.

Elastic waveform inversion in the frequency domain for an application in mechanized tunneling

The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the frequency domain, is investigated for the application in tunneling. The approach tries to minimize the difference of seismic records from field observations and from a discretized ground model by changing the ground properties. The final ground model might be a representation of the geology. The used elastic wave modeling approach is described as well as the application of convolutional perfectly matched layers. The proposed inversion scheme uses the discrete adjoint gradient method, a multi-scale approach as well as the L-BFGS method. Numerical parameters are identified as well as a validation of the forward wave modeling approach is performed in advance to the inversion of every example. Two-dimensional blind tests with two different ground scenarios and with three different source and receiver station configurations are performed and analyzed, where only the seismic records, the source functions and the ambient ground properties are provided. Finally, an inversion for a three-dimensional tunnel model is performed and analyzed for three different source and receiver station configurations.

Can elastic waveform inversion benefit from inverting multicomponent data?

Waveform inversion aims to retrieve high-resolution earth parameter volumes. Due to its high computational cost, acoustic approaches using low to mid seismic data frequencies are often applied in velocity model building. However, in the presence of large parameter contrasts, an elastic formulation should be preferred due to wave interferences that limit the applicability of phase- and kinematics-only approaches. The benefits of elastic waveform inversion have been demonstrated with inversion of hydrophone data in marine environments. Here, we extend the approach to inversion of the vertical geophone component. We propose a weighted cost function in the waveform inversion algorithm to jointly invert multicomponent data sets, and we compare the results to the inversion of single-component data. For this study, we use an ocean-bottom-node data set from the deepwater Gulf of Mexico around a salt dome. We show that slightly different velocity models, reverse time migration images, and angle gathers are retrieved when using hydrophone or vertical geophone data, further improving either the shallow or deeper sediments. The joint inversion combines the improvements brought by the single-component inversions. Though it doubles the cost, joint elastic waveform inversion of hydrophone and vertical geophone data can help velocity model building around salt bodies.

Early arrival waveform inversion using data uncertainties and matching filters with application to near-surface seismic refraction data

We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ([Formula: see text]) waveform misfit of one is achieved, and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.

Data-driven prestack-waveform inversion using genetic algorithm: Methodology and examples

The choice of an initial model for seismic waveform inversion is important. In matured exploration areas with adequate well control, we can generate a suitable initial model using well information. However, in new areas where well control is sparse or unavailable, such an initial model is compromised and/or biased by the regions with more well controls. Even in matured exploration areas, if we use time-lapse seismic data to predict dynamic reservoir properties, an initial model that we obtain from the existing preproduction wells could be incorrect. In this work, we outline a new methodology and workflow for a nonlinear prestack isotropic elastic waveform inversion. We call this method a data-driven inversion, meaning that we derive the initial model entirely from the seismic data without using any well information. By assuming a locally horizontal stratification for every common midpoint and starting from the interval P-wave velocity, estimated entirely from seismic data, our method generates pseudowells by running a two-pass 1D isotropic elastic prestack-waveform inversion that uses the reflectivity method for forward modeling and the genetic algorithm for optimization. We then use the estimated pseudowells to build the initial model for seismic inversion. By applying this methodology to real seismic data from two different geologic settings, we determine the usefulness of our method. We believe that our new method is potentially applicable for subsurface characterization in areas where well information is sparse or unavailable. Additional research is, however, necessary to improve the computational efficiency of the methodology.

Shear reflectivity compensation in full-waveform inversion using least-squares reverse-time migration

SUMMARY The computational cost of elastic-waveform inversion is too high for inverting PP reflections, while using acoustic full-waveform inversion (FWI) is inaccurate because it does not depend on the shear modulus/velocity/impedance that affects elastic PP wavefield amplitudes. To solve this problem, we develop a waveform inversion method that uses acoustic least-squares reverse-time migration (LSRTM) to compensate the shear reflectivity for acoustic FWI. Our method is based on the quasi-elastic-wave equation developed by Chapman et al. (2014). The quasi-elastic-wave equation uses a linearized acoustic-wave equation with shear modulus μ as a virtual source to correct the acoustic PP wavefield amplitudes toward elastic ones. Our waveform inversion method inverts for elastic parameters by minimizing the L2 norm of the difference between recorded and predicted PP reflections modelled using the quasi-elastic-wave equation. Numerical tests on synthetic and field data show that our method can properly handle the amplitudes of elastic PP reflections and provides an accurate estimate of the P- and S-wave velocities/impedances and, in some cases, the density. The method does not need the computationally expensive numerical solution to the elastic-wave equation. It also gives a better estimate of elastic parameters than a pure LSRTM method for elastic PP reflections.

Low-frequency, long-offset elastic waveform inversion in the context of velocity model building

Classic imaging approaches consist of splitting the earth into background and reflectivity models. When justified, this separation of scale is quite powerful, although this approach relies on some smoothness and weak contrast assumptions. This approach allows for the imaging methods to be based on acoustic wave propagation after having identified the compressional waves through picking or signal processing. Over the past years, wave-equation tomography and waveform inversion approaches have become routine, complementing the classic approaches to derive background models. They do not rely on high-frequency picks, unlike ray-based traveltime tomography, but on low-frequency cross-correlation to define time shifts and on waveform matching. In the presence of large earth parameter contrasts, time shifts and waveforms of compressional waves may depend on elastic parameters when interferences occur within the Fresnel zones. This challenges the recovery of the background model under an acoustic assumption with low-frequency data. Accounting for an elastic propagation in waveform inversion, even in the context of model building, could help to reduce the artifacts seen in acoustic results. A synthetic and a real data example are presented to illustrate the potential benefit of using an elastic waveform inversion approach when inverting long-offset, low-frequency seismic data.

Elastic-waveform inversion and imaging of 2010 walkaway VSP data from the Raft River geothermal field

A vertical seismic profiling (VSP) survey conducted in 2010 in the original RRG-9 well at the Raft River geothermal field is to understand the subsurface geologic structures for geothermal reservoir characterization. This survey consists of 40 three-component (3C) geophones deployed in the upper 600 m of the well and 255 vibroseis sources positioned along eight walkaway lines at the surface. We perform elastic-waveform inversion and reserve-time migration of the VSP data to obtain high-resolution subsurface images. We first process the raw walkaway 3C VSP data and separate the upgoing compressional-to-compressional (PP) and compressional-to-shear (PS) wavefields. We then build an initial velocity model based on sonic logging and zero-offset VSP data, update the initial model with first-arrival traveltime tomography, and refine the model using elastic-waveform inversion to reveal high-resolution velocity variations. We finally apply reverse-time migration to the upgoing wavefields to obtain high-resolution PP and PS migration images of the lithologies encountered in the well. The refined velocity models obtained using elastic-waveform inversion improve the subsurface migration imaging results. Our elastic-waveform inversion and reverse-time migration confirm the lithology interfaces revealed from well logs and provide images of subsurface geologic layers away from well RRG-9 at the Raft River geothermal field.

Application of 2D full-waveform inversion on exploration land data

Estimating subsurface seismic properties is an important topic in civil engineering, oil and gas exploration, and global seismology. We have developed an application of 2D elastic waveform inversion with an active-source on-shore data set, as is typically acquired in exploration seismology on land. The maximum offset is limited to 12 km, and the lowest available frequency is 5 Hz. In such a context, surface waves are generally treated as noise and are removed as a part of data processing. In contrast to the conventional approach, our workflow starts by inverting surface waves to constrain shallow parts of the shear wavespeed model. To mitigate cycle skipping, frequency- and offset-continuation approaches are used. To accurately take into account free-surface effects (and irregular topography), a spectral-element-based wave propagation solver is used for forward modeling. To reduce amplitude influences, a normalized crosscorrelation (NC) objective function is used in conjunction with systematic updates of the source wavelet during the inversion process. As the inversion proceeds, body waves are gradually incorporated in the process. At the final stage, surface and body waves are inverted together using the entire offset range over the band between 5 and 15 Hz. The inverted models include high-resolution features in the first 500 m of compressional and shear wavespeeds, with some model updates down to 4.0 km in the first parameter. The inversion results confirmed by well-log information, indicate a better fit of compressional to shear wavespeeds ratios compared with the initial model. The final data fit is also noticeably improved compared to the initial one. Although our results confirm previous studies demonstrating that an NC norm combined with a source time function correction can partly stabilize purely elastic inversions of viscoelastic data, we believe that including an attenuation depth model in the forward simulation gives better results.

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.

Acoustic- and elastic-waveform inversion with total generalized p-variation regularization

Geophysical models usually contain both sharp interfaces and smooth variations, and it is difficult to accurately account for both of these two types of medium parameter variations using conventional full-waveform inversion methods. We develop a novel full-waveform inversion method for acoustic and elastic waves using a total generalized p-variation regularization scheme to address these challenging problems. We decompose the full-waveform inversion into two subproblems and solve these two minimization subproblems using an alternating-direction minimization strategy. One important advantage of the total generalized p-variation regularization scheme is that it can simultaneously reconstruct sharp interfaces and smooth background variations of geophysical parameters. Such capability can also effectively suppress the noises in source-encoded inversion and sparse-data inversion, or inversion of noisy data. We demonstrate the advantages of our full-waveform inversion method using a checkerboard model, a modified elastic SEG/EAGE overthrust model, and a land field seismic data set. Our results of synthetic and field seismic data demonstrate that our method reconstructs both smooth background variations and sharp interfaces of subsurface geophysical properties accurately, and provides a useful tool for accurate and reliable inversion of field seismic data.

Reconstructing disturbance zones ahead of the tunnel face by elastic waveform inversion supported by a parametric level-set representation

This work presents a flexible and effective methodology for locating and characterizing the disturbance zones ahead of the underground tunnel face by elastic full-waveform inversion (FWI) enhanced with the parametric level-set representation. By using the unscented Kalman filter as the inversion machinary, the inversion process is completely free from gradient calculations and able to provide uncertainty bounds of the estimated model. The conceptual methodology is verified through successful reconstructions of single- and multiple-disturbance objects in a simple 2D frequency domain model. In the synthetic tunnel reconnaissance tests, the special characteristics of the tunnel seismic waves in the time domain are described, and the results of SPECFEM2D simulation and a qualitative evaluation of the simulated tunnel seismic waveforms are shown. The computer model and its simulated tunnel seismic waveform data are eventually used to reconstruct the geological scenarios, whose disturbance is present in the form of a single object and multiple discontinuous objects, in a parsimonious and flexible manner. Although further validations using laboratory or in-situ measurements and the use of fully 3D model are needed to prove the practicality of this approach, the current results are encouraging and promising to apply FWI in tunneling practice as an advanced tool for looking ahead of the tunnel face.

Building Subsurface Velocity Models with Sharp Interfaces Using Interface-Guided Seismic Full-Waveform Inversion

Reverse-time migration has the potential to image complex subsurface structures, including steeply-dipping fault zones, but the method requires an accurate velocity model. Acoustic- and elastic-waveform inversion is a promising tool for high-resolution velocity model building. Because of the ill-posedness of acoustic- and elastic-waveform inversion, it is a great challenge to obtain accurate velocity models containing sharp interfaces. To improve velocity model building, we develop an acoustic- and elastic-waveform inversion method with an interface-guided modified total-variation regularization scheme to improve the inversion accuracy and robustness, particularly for models with sharp interfaces and steeply-dipping fault zones with widths much smaller than the seismic wavelength. The new regularization scheme incorporates interface information into seismic full-waveform inversion. The interface information of subsurface interfaces is obtained iteratively using migration imaging during waveform inversion. Seismic migration is robust for subsurface imaging. Our new acoustic- and elastic-waveform inversion takes advantage of the robustness of migration imaging to improve velocity estimation. We use synthetic seismic data for a complex model containing sharp interfaces and several steeply-dipping fault zones to validate the improved capability of our new acoustic- and elastic-waveform inversion method. Our inversion results are much better than those produced without using interface-guided regularization. Acoustic- and elastic-waveform inversion with an interface-guided modified total-variation regularization scheme has the potential to accurately build subsurface velocity models with sharp interfaces and/or steep fault zones.

Pseudo 2D elastic waveform inversion for attenuation in the near surface

Seismic waveform propagation could be significantly affected by heterogeneities in the near surface zone (0m–500m depth). As a result, it is important to obtain as much near surface information as possible. Seismic attenuation, characterized by QP and QS factors, may affect seismic waveform in both phase and amplitude; however, it is rarely estimated and applied to the near surface zone for seismic data processing. Applying a 1D elastic full waveform modelling program, we demonstrate that such effects cannot be overlooked in the waveform computation if the value of the Q factor is lower than approximately 100. Further, we develop a pseudo 2D elastic waveform inversion method in the common midpoint (CMP) domain that jointly inverts early arrivals for QP and surface waves for QS. In this method, although the forward problem is in 1D, by applying 2D model regularization, we obtain 2D QP and QS models through simultaneous inversion. A cross-gradient constraint between the QP and Qs models is applied to ensure structural consistency of the 2D inversion results. We present synthetic examples and a real case study from an oil field in China.

Localized time-lapse elastic waveform inversion using wavefield injection and extrapolation: 2-D parametric studies

Localized time-lapse elastic waveform inversion using wavefield injection and extrapolation: 2-D parametric studies

Extracting Low-Frequency Information from Time Attenuation in Elastic Waveform Inversion

Low-frequency information is crucial for recovering background velocity, but the lack of low-frequency information in field data makes inversion impractical without accurate initial models. Laplace–Fourier domain waveform inversion can recover a smooth model from real data without low-frequency information, which can be used for subsequent inversion as an ideal starting model. In general, it also starts with low frequencies and includes higher frequencies at later inversion stages, while the difference is that its ultralow frequency information comes from the Laplace–Fourier domain. Meanwhile, a direct implementation of the Laplace-transformed wavefield using frequency domain inversion is also very convenient. However, because broad frequency bands are often used in the pure time domain waveform inversion, it is difficult to extract the wavefields dominated by low frequencies in this case. In this paper, low-frequency components are constructed by introducing time attenuation into the recorded residuals, and the rest of the method is identical to the traditional time domain inversion. Time windowing and frequency filtering are also applied to mitigate the ambiguity of the inverse problem. Therefore, we can start at low frequencies and to move to higher frequencies. The experiment shows that the proposed method can achieve a good inversion result in the presence of a linear initial model and records without low-frequency information.

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.

Modified surface boundary conditions for elastic waveform inversion of low-frequency wide-angle active land seismic data

Modified surface boundary conditions for elastic waveform inversion of low-frequency wide-angle active land seismic data