Waveform Tomography Research Articles

Passive Adjoint Tomography of the Crustal and Upper Mantle Beneath Eastern Tibet With a W2‐Norm Misfit Function

AbstractFull waveform tomography is an effective method to obtain high‐resolution subsurface velocity structures. It is, however, difficult for the conventional L2‐norm‐based inversion to reach the global minimum because of cycle‐skipping problem. In this study, we investigated the feasibility of using the quadratic Wasserstein metric distance (W2 norm) as the misfit function for passive adjoint tomography. We first derived equations of the Fréchet gradient and adjoint source under W2‐norm misfit function. We then conducted numerical experiments to illustrate the effectiveness of the proposed method in avoiding cycle skipping. We finally applied the adjoint tomography to eastern Tibet and obtained a 3‐D velocity model of the lithosphere. The adjoint tomography revealed two low‐velocity channels beneath the NE and SE margins of the Tibetan plateau, which were also observed by previous studies. Our results are consistent with the lower crust flow model that was proposed to explain the deformation occurring at the two margins.

Accelerating full waveform inversion via source stacking and cross-correlations

SUMMARYAccurate synthetic seismic wavefields can now be computed in 3-D earth models using the spectral element method (SEM), which helps improve resolution in full waveform global tomography. However, computational costs are still a challenge. These costs can be reduced by implementing a source stacking method, in which multiple earthquake sources are simultaneously triggered in only one teleseismic SEM simulation. One drawback of this approach is the perceived loss of resolution at depth, in particular because high-amplitude fundamental mode surface waves dominate the summed waveforms, without the possibility of windowing and weighting as in conventional waveform tomography.This can be addressed by redefining the cost-function and computing the cross-correlation wavefield between pairs of stations before each inversion iteration. While the Green’s function between the two stations is not reconstructed as well as in the case of ambient noise tomography, where sources are distributed more uniformly around the globe, this is not a drawback, since the same processing is applied to the 3-D synthetics and to the data, and the source parameters are known to a good approximation. By doing so, we can separate time windows with large energy arrivals corresponding to fundamental mode surface waves. This opens the possibility of designing a weighting scheme to bring out the contribution of overtones and body waves. It also makes it possible to balance the contributions of frequently sampled paths versus rarely sampled ones, as in more conventional tomography.Here we present the results of proof of concept testing of such an approach for a synthetic 3-component long period waveform data set (periods longer than 60 s), computed for 273 globally distributed events in a simple toy 3-D radially anisotropic upper mantle model which contains shear wave anomalies at different scales. We compare the results of inversion of 10 000 s long stacked time-series, starting from a 1-D model, using source stacked waveforms and station-pair cross-correlations of these stacked waveforms in the definition of the cost function. We compute the gradient and the Hessian using normal mode perturbation theory, which avoids the problem of cross-talk encountered when forming the gradient using an adjoint approach. We perform inversions with and without realistic noise added and show that the model can be recovered equally well using one or the other cost function.The proposed approach is computationally very efficient. While application to more realistic synthetic data sets is beyond the scope of this paper, as well as to real data, since that requires additional steps to account for such issues as missing data, we illustrate how this methodology can help inform first order questions such as model resolution in the presence of noise, and trade-offs between different physical parameters (anisotropy, attenuation, crustal structure, etc.) that would be computationally very costly to address adequately, when using conventional full waveform tomography based on single-event wavefield computations.

Evaluation of Bridge Abutment with Ultraseismic Waveform Tomography: Field Data Application

This paper presents an application of ultraseismic waveform tomography for condition evaluation (determination of elastic properties) and the unknown depth of a concrete bridge abutment. A newly developed waveform tomography technique for bounded medium (e.g. thin plate) was applied to an ultraseismic dataset collected on a 30-m long bridge in New York City. The dataset was measured on the top of abutment using 24 100-Hz vertical geophones uniformly spaced at 1.2 m apart, and a 3-lb hammer source to induce wave energy. The results revealed that the waveform analysis was able to characterize both the S-wave and P-wave velocities (Vs and Vp) of the abutments and the supporting soils. The true abutment depth of 5.7 m was generally identified in both inverted Vs and Vp profiles. The main advantages of this approach include: (1) data acquisition on top of the abutment is more convenient and cost effective compared to measurements from the ground, boreholes, or river-beds for water bridges; and (2) abutment concrete physical elastic properties are characterized at high resolution in cells. To our best understanding, this is the first reported study using the waveform tomography on field data for assessment of concrete abutments or wall-type structures.

Slab behavior beneath Eastern Asia from full waveform tomography

Slab behavior beneath Eastern Asia from full waveform tomography

Eastward expansion of the eastern Tibetan margin revealed by adjoint waveform tomography

Eastward expansion of the eastern Tibetan margin revealed by adjoint waveform tomography

Characterization of Concrete Pile Groups with 2-D Seismic Waveform Tomography

Currently, about 28,000 bridges over water in the United States are classified as having missing key foundation information such as number and distribution of piles and pile lengths. The as-built drawings of buried concrete piles or drilled shafts are critical in assessing the hydraulic scour vulnerability of bridges. This paper presents an application of seismic waveform tomography for characterization of shaft groups. The capability of an existing 2-D Gauss–Newton seismic waveform tomography method was investigated on challenging subsurface conditions for groups of drilled shafts with various lengths within each group. The method was applied to field experimental datasets collected at the National Geotechnical Experimental Site (NGES) at College Station, Texas. The site contains two groups of four and five drilled shafts with various lengths from 10.4 to 24.1 m. Seismic wave fields were measured on the ground surface at the edges of the two pile groups, and analyzed by the 2-D waveform tomography method. Seismic results showed that waveform analysis was able to well characterize the pile groups. Individual drilled shafts and soil between them are distinguished, and lengths were also generally predicted.

Seismic Waveform Tomography With Simplified Restarting Scheme

For shot-encoded seismic waveform tomography, the restarted limited-memory BFGS (L-BFGS) algorithm is an effective technique to suppress the crosstalk effect among encoded seismic shots. It restarts the L-BFGS calculation at each iteration segment, consisted of a group of iterations, and recodes the individual shots randomly not only at the beginning but also at the inside of the iteration segment. Here, we simplified this scheme using an invariant shot-encoding within each iteration segment and recoding individual shots only at the beginning of the segment. This simplification did compromise the image quality at the early stage of inversion, as the crosstalk effect appeared on the inversion result of the low-frequency data. However, it eventually achieved both the computation efficiency and the good quality for a multiscale inversion procedure, which inverts the seismic data from low-frequency components to high-frequency components in sequence.

Anisotropic full-waveform inversion of crosshole seismic data: A vertical symmetry axis field data application

Anisotropic waveform tomography (AWT) uses anisotropic traveltime tomography followed by anisotropic full-waveform inversion (FWI). Such an approach is required for FWI in cases in which the geology is likely to exhibit anisotropy. An important anisotropy class is that of transverse isotropy (TI), and the special case of TI media with a vertical symmetry axis (VTI) media is often used to represent elasticity in undeformed sedimentary layering. We have developed an approach for AWT that uses an acoustic approximation to simulate waves in VTI media, and we apply this approach to crosshole data. In our approach, the best-fitting models of seismic velocity and Thomsen VTI anisotropy parameters are initially obtained using anisotropic traveltime tomography, and they are then used as the starting models for VTI FWI within the acoustic approximation. One common problem with the acoustic approach to TI media is the generation of late-arriving (spurious) S-waves as a by-product of the equation system. We used a Laplace-Fourier approach that effectively damps the spurious S-waves to suppress artifacts that might otherwise corrupt the final inversion results. The results of applying AWT to synthetic data illustrate the trade-offs in resolution between the two parameter classes of velocity and anisotropy, and they also verify anisotropic traveltime tomography as a valid method for generating starting models for FWI. The synthetic study further indicates the importance of smoothing the anisotropy parameters before proceeding to FWI inversions of the velocity parameter. The AWT technique is applied to real crosshole field gathers from a sedimentary environment in Western Canada, and the results are compared with the results from a simpler (elliptical) anisotropy model. The transversely isotropic approach yields an FWI image of the vertical velocity that (1) exhibits a superior resolution and (2) better predicts the field data than does the elliptical approach.

Imaging high-resolution velocity and attenuation structures from walkaway vertical seismic profile data in a carbonate reservoir using visco-acoustic waveform inversion

Frequency domain visco-acoustic waveform inversion is applied to multi-offsets vertical seismic profile data acquired over a carbonates reservoir in an oil field offshore Abu Dhabi in the United Arab Emirates, to produce high resolution seismic velocity and attenuation structures. The starting velocity and attenuation models are obtained from traveltime tomography, and from the centroid frequency-shift method, respectively. Waveform tomography is performed between the frequencies 4 and 50 Hz. To reduce coupling between velocity and attenuation parameters during model updates, a two stage inversion strategy is adopted. During the first stage, only the velocity model is recovered and, during the second stage, velocity and attenuation models are recovered. The density is estimated from empirical correlation derived from sonic and density logs at the borehole location. A judicious selection of the time-damping constant [Formula: see text], used to suppress late arrivals in the Laplace-Fourier domain is critical to mitigate nonlinearities. Prior to the inversion, data preconditioning is done to transform the data in a form convenient for the visco-acoustic wave equation. High resolution final velocity and attenuation models are obtained. Extracted 1D profiles from the final models generally correlate well with the sonic log and estimated clay content from the gamma-ray log. These observations give confidence to the results. A comparison of the synthetic data generated from the final models and the field data shows a high degree of similarity. The high resolution of the results enables us to readily identify layers and provide a geologic interpretation from Quaternary to Late Jurassic. The inverted models show a stack of layers with alternating relatively high and low velocity values associated with relatively high- and low-attenuation values defining anticlines, as we progressed deeper into the subsurface. The two main reservoirs units in the Lower Cretaceous are clearly identified.

Insights on Upper Mantle Melting, Rheology, and Anelastic Behavior From Seismic Shear Wave Tomography.

In seismic tomography we map the wave speed structure inside the Earth, but we ultimately seek to interpret those images in terms of physical parameters. This is challenging because many parameters can trade‐off with each other to produce a given wave speed. The problem is compounded by the convention of mapping seismic structures as perturbations relative to a 1‐D reference model, rather than absolute wave speeds. Using a full waveform tomography model of Europe as a case study, we quantify the extent to which thermochemical and dynamic properties can be constrained using only S wave speed, expressed in absolute values. The wave speed distributions of this tomography model are compared with 4 million thermochemical models, whose seismic properties are computed via thermodynamic modeling. These models sample the full range of realistic mantle compositions, including variable water and melt contents, and mineral intrinsic anelasticity is taken into account. Intrinsic anelasticity causes waves to travel more slowly at higher temperatures, leading to seismic attenuation, but the sensitivity of the wave speed reduction to temperature is, in turn, controlled by the wave frequency. Global studies of surface waves indicate an anticorrelation between S wave speed and attenuation. We therefore only retain thermochemical models satisfying this anticorrelation. Our study indicates that the frequency dependence of anelasticity, α, depends on temperature or rheology, with α ≈ 0.1 being most appropriate in cold or lithospheric mantle and α ≈ 0.3 in warmer regions (i.e., the asthenosphere). Additionally, the slowest regions require specific compositions and/or a velocity‐weakening mechanism, such as partial melting, elastically accommodated grain boundary sliding, or water.

Frequency-Domain Multi-Scale Early-Arrival Waveform Tomography with a Time-Domain Wavefield Modeling Engine

Early-arrival waveform tomography (EWT) is one of the most promising techniques for building near-surface velocity model. Based on finite-frequency wave equation, EWT estimates velocities by matching calculated early-arrival waveforms with the observed ones. However, the objective function of EWT can easily converge to local minimum because of the cycle-skipping phenomenon. In order to reduce the cycle-skipping problem, a hybrid-domain early-arrival waveform tomography (HEWT) is proposed in this paper. The forward modeling of HEWT is realized in the time domain where early-arrival waveforms are easier to be selected from seismic data and less memory is needed than they are in the frequency domain. The inversion is implemented in the frequency domain where multi-scale strategy is more convenient to be realized than that in the time domain. Discrete Fourier transformation (DFT) is used to transform the time-domain wavefield to the frequency-domain wavefield. Test results show that HEWT is more competitive than EWT in both accuracy and computational time.

Imaging high-resolution seismic velocity from walkaway vertical seismic profile data in a carbonate reservoir using acoustic waveform tomography

High-resolution seismic velocity was obtained using acoustic full-waveform tomography of walkaway vertical seismic profile (VSP) data from an oil field dominated by carbonate rocks, offshore Abu Dhabi in the United Arab Emirates. The data were collected in a deviated borehole with receivers located from 521 to 2742 m depth. The inversion was performed in the frequency domain. The success of the inversion was determined by three important factors: the starting model, the preconditioning of the input data, and the inversion strategy, which included an appropriate selection of a damping term [Formula: see text] in the Laplace–Fourier transformation. The inversion was performed between the frequencies of 4 and 50 Hz, and a logarithmic data residual was used. The extracted 1D velocity profiles from the final high-resolution velocity model correlate well with the sonic log, and estimated vertical incidence VSP velocities. The predicted data obtained by the final velocity model indicate a generally good fit with the field data, thus confirming the success of the inversion. A reverse time migrated section derived by the final velocity model provides additional structural details. The velocity model indicates anomalous zones of low-velocity values that correlate with known locations of hydrocarbon reservoirs.

Application of 2D full-waveform tomography on land-streamer data for assessment of roadway subsidence

Roadways are key components of the modern transportation system. Therefore, assessment of roadway subsidence is critical to the health and safety of the traveling public. Existing seismic refraction and waveform tomography methods can be used for subsidence evaluation; however, the data acquisition time is significant because they require multiple source impacts (shots) along a test line. To mitigate the negative impact caused by closing the traffic flow under seismic testing, a land-streamer seismic testing system and waveform analysis are developed. An existing 2D Gauss-Newton full-waveform inversion (FWI) method is extended for analysis of the land-streamer waveform data. The main advantage of using land-streamer waveform data is that geophones are not coupled to test materials and source-receiver offsets are fixed; thus, the whole test system can be moved along the roadway quickly for data acquisition. To demonstrate the effectiveness of land-streamer waveform data, the FWI method was tested on synthetic and field data sets. The synthetic result reveals that buried voids can be well-characterized by the land-streamer waveform analysis. Field data were collected on asphalt pavement using a 24 channel land streamer and a propelled energy generator to induce seismic wave energy. The test system was towed by a pickup truck along a roadway with an on-going subsidence (repaired sinkhole). The data were collected over 277.5 m distance at a 3 m interval, and the total data acquisition time was approximately 1 h. The field data result indicates that the waveform analysis was able to delineate low-velocity soil zones and laterally variable bedrock. The FWI results are also compared with multichannel analysis of surface wave (MASW) results. The 2D [Formula: see text] profiles from the FWI and MASW methods are consistent; however, the FWI method provides more detailed information ([Formula: see text] of [Formula: see text] cells) of low-velocity anomalies for assessment of roadway subsidence.

Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method

Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method

P and S Wave Receiver Function Imaging of Subduction With Scattering Kernels

AbstractA method for scattered wave imaging in 3‐D with both teleseismic P and S wave receiver function data is introduced. The approach relies on body‐wave scattering kernels that are derived from the adjoint data sensitivity kernels which are typically used for full waveform tomography. The forward problem is approximated using ray theory, yielding a computationally efficient imaging algorithm that can resolve dipping and discontinuous interfaces using both P and S wave receiver functions. Traveltime fields for the incident teleseismic arrivals and the receiver point‐sources are obtained by solving the Eikonal equation using a Fast Marching code which can handle a 3‐D reference velocity model. An energy stable finite‐difference method is used to simulate elastic wave propagation in a 2‐D hypothetical subduction zone model. The resulting synthetic P and S wave receiver function data sets are used to validate the imaging method. The kernel images are compared with those generated by the Generalized Radon Transform and Common Conversion Point Stacking methods. These results demonstrate the potential of the kernel imaging approach for constraining lithospheric structure in complex geologic environments with sufficiently dense recordings of teleseismic data. Potential imaging targets include short‐wavelength compositional variations in the mantle wedge and the slab's lithosphere‐asthenosphere boundary.

Evaluation of Bridge Abutments and Bounded Wall Type Structures with Ultraseismic Waveform Tomography

Abstract A new ultraseismic waveform tomography technique for a bounded medium is presented for evaluation of concrete bridge abutments, or wall piers, and the supporting soil and rock underneath t...

Ultrasonic wavefield inversion and migration in complex heterogeneous structures: 2D numerical imaging and nondestructive testing experiments

Delaminations, cracks and other defects in engineered structures often lie close to the theoretical resolution limit for ultrasonic waves. While ultrasonic waveform tomography has succeeded in detecting such features, recovery is difficult because it requires computationally expensive high-frequency numerical wave simulations and an accurate understanding of large-scale background variations of the engineered structure. Without such knowledge, small defects may be incorrectly imaged or go undetected altogether. To reduce computational cost and improve detection of small defects, a useful approach is to divide the waveform tomography procedure into two steps: first, a low-frequency model-building step aimed at recovering background structure, and second, a high-frequency imaging step targeting defects. The first is naturally formulated as waveform inversion for wavespeed parameters and the second as time reversal migration for reflectivity. Through synthetic test cases, we show that the two-step workflow appears more promising in most cases than a single-step inversion. In particular, we find that new workflow succeeds in the challenging scenario where the defect lies along preexisting layer interface in a composite bridge deck and in related experiments involving noisy data or inaccurate source parameters.

Quantitative seismic characterization of CO2 at the Sleipner storage site, North Sea

Reliable quantification of carbon dioxide ([Formula: see text]) properties and saturation is crucial in the monitoring of [Formula: see text] underground storage projects. We have focused on quantitative seismic characterization of [Formula: see text] at the Sleipner storage pilot site. We evaluate a methodology combining high-resolution seismic waveform tomography, with uncertainty quantification and rock physics inversion. We use full-waveform inversion (FWI) to provide high-resolution estimates of P-wave velocity [Formula: see text] and perform an evaluation of the reliability of the derived model based on posterior covariance matrix analysis. To get realistic estimates of [Formula: see text] saturation, we implement advanced rock physics models taking into account effective fluid phase theory and patchy saturation. We determine through sensitivity tests that the estimation of [Formula: see text] saturation is possible even when using only the P-wave velocity as input. After a characterization of rock frame properties based on log data prior to the [Formula: see text] injection at Sleipner, we apply our two-step methodology. The FWI result provides clear indications of the injected [Formula: see text] plume being observed as low-velocity zones corresponding to thin [Formula: see text] filled layers. Several tests, varying the rock physics model and [Formula: see text] properties, are then performed to estimate [Formula: see text] saturation. The results suggest saturations reaching 30%–35% in the thin sand layers and up to 75% when patchy mixing is considered. We have carried out a joint estimation of saturation with distribution type and, even if the inversion is not well-constrained due to limited input data, we conclude that the [Formula: see text] has an intermediate pattern between uniform and patchy mixing, which leads to saturation levels of approximately [Formula: see text]. It is worth noting that the 2D section used in this work is located 533 m east of the injection point. We also conclude that the joint estimation of [Formula: see text] properties with saturation is not crucial and consequently that knowing the pressure and temperature state of the reservoir does not prevent reliable estimation of [Formula: see text] saturation.

The SCEC Unified Community Velocity Model Software Framework

ABSTRACT Crustal seismic‐velocity models and datasets play a key role in regional 3D numerical earthquake ground‐motion simulation, full waveform tomography, and modern physics‐based probabilistic earthquake‐hazard analysis, as well as in other related fields, including geophysics and earthquake engineering. Most of these models and datasets, often collectively identified as Community Velocity Models (CVMs), synthesize information from multiple sources and are delivered to users in variable formats, including computer applications that allow for interactive querying of material properties, namely P ‐ and S ‐wave velocities and density ρ . Computational users often require massive and repetitive access to velocity models and datasets, and such access is often unpractical and difficult due to a lack of standardized methods and procedures. To overcome these issues and to facilitate access by the community to these models, the Southern California Earthquake Center developed the Unified CVM (UCVM) software framework, an open‐source collection of tools that enables users to access one or more seismic‐velocity models, while providing a standard query interface. Here, we describe the research challenges that motivated the development of UCVM, its software design, development approach, and basic capabilities, as well as a few examples of seismic‐modeling applications that use UCVM.

Seismic waveform tomography with shot-encoding using a restarted L-BFGS algorithm.

In seismic waveform tomography, or full-waveform inversion (FWI), one effective strategy used to reduce the computational cost is shot-encoding, which encodes all shots randomly and sums them into one super shot to significantly reduce the number of wavefield simulations in the inversion. However, this process will induce instability in the iterative inversion regardless of whether it uses a robust limited-memory BFGS (L-BFGS) algorithm. The restarted L-BFGS algorithm proposed here is both stable and efficient. This breakthrough ensures, for the first time, the applicability of advanced FWI methods to three-dimensional seismic field data. In a standard L-BFGS algorithm, if the shot-encoding remains unchanged, it will generate a crosstalk effect between different shots. This crosstalk effect can only be suppressed by employing sufficient randomness in the shot-encoding. Therefore, the implementation of the L-BFGS algorithm is restarted at every segment. Each segment consists of a number of iterations; the first few iterations use an invariant encoding, while the remainder use random re-coding. This restarted L-BFGS algorithm balances the computational efficiency of shot-encoding, the convergence stability of the L-BFGS algorithm, and the inversion quality characteristic of random encoding in FWI.