Compression approaches for the regularized solutions of linear systems from large-scale inverse problems

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a large matrix through a sparser matrix with fewer nonzero elements, by borrowing from ideas used in wavelet image compression. Next, we describe and compare approaches based on the use of the low rank singular value decomposition (SVD), which can result in further size reductions. We describe how to obtain the approximate low rank SVD of the original matrix using the sparser wavelet compressed matrix. Some analytical results concerning the various methods are presented and the results of the proposed techniques are illustrated using both synthetic data and a very large linear system from a seismic tomography application, where we obtain significant compression gains with our methods, while still resolving the main features of the solutions.European Research Council (Advanced Grant 226837)United States. Defense Advanced Research Projects Agency (Contract N66001-13-1-4050)National Science Foundation (U.S.) (Contracts 1320652 and 0748488

A comparison of methods to estimate seismic phase delays: numerical examples for coda wave interferometry

Time-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross-correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here we implement Dynamic Time Warping (DTW) to estimate the warping function – a vector of local time shifts that globally minimizes the misfit between two seismic traces. We compare all three methods using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross-correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has good time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements

The Virtual Refraction: Useful Spurious Energy in Seismic Interferometry

Seismic interferometry is rapidly becoming an established technique to recover the Green’s function between receivers, but practical limitations in the source-energy distribution inevitably lead to spurious energy in the results. Instead of attempting to suppress all such energy, we use a spurious wave associated with the crosscorrelation of refracted energy at both receivers to infer estimates of subsurface parameters. We named this spurious event the virtual refraction. Illustrated by a numerical two-layer example, we found that the slope of the virtual refraction defines the velocity of the faster medium and that the stationary-phase point in the correlation gather provides the critical offset. With the associated critical time derived from the real shot record, this approach includes all of the necessary information to estimate wave speeds and interface depth without the need of inferences from other wave types

Scanning for Velocity Anomalies in the Crust and Mantle with Diffractions from the Core-Mantle Boundary

A novel method, based on differential arrival times of diffractions from the core-mantle boundary, swiftly scans for seismic velocity anomalies in the crust and mantle below an array of seismometers. The method is applied to data from the USArray and the large-scale structural features in the western United States are resolved. High lateral resolution is achieved, but structure is averaged over depth. As such, this method is complementary to surface-wave and tomographic body-wave methods, where averaging takes place in the lateral sense. Processing and data-volume requirements involved are minimal. Therefore, this method can be applied during the early stages of array deployment, before the necessary data is acquired to obtain accurate inversion images. The quick scanner can be used to identify features of interest, upon which the array could be refined

Isolating Retrograde and Prograde Rayleigh-Wave Modes Using a Polarity Mute

Estimates of S-wave velocity with depth from Rayleigh-wave dispersion data are limited by the accuracy of fundamental and/or higher mode signal identification. In many scenarios, the fundamental mode propagates in retrograde motion, whereas higher modes propagate in prograde motion. This difference in particle motion (or polarity) can be used by joint analysis of vertical and horizontal inline recordings. We have developed a novel method that isolates modes by separating prograde and retrograde motions; we call this a polarity mute. Applying this polarity mute prior to traditional multichannel analysis of surface wave (MASW) analysis improves phase velocity estimation for fundamental and higher mode dispersion. This approach, in turn, should lead to improvement of S-wave velocity estimates with depth. With two simple models and a field example, we have highlighted the complexity of the Rayleigh-wave particle motions and determined improved MASW dispersion images using the polarity mute. Our results show that we can separate prograde and retrograde signals to independently process fundamental and higher mode signals, in turn allowing us to identify lower frequency dispersion when compared with single component data. These examples demonstrate that the polarity mute approach can improve estimates of S-wave velocities with depth

Estimating the Rayleigh-Wave Impulse Response Between Seismic Stations with the Cross Terms of the Green Tensor

The development of ambient noise tomography has provided a powerful tool to investigate the Earth\u27s subsurface with increased resolution. Most commonly, surface-wave tomography is performed on inter-station estimates of the vertical component of Rayleigh waves, stemming from crosscorrelations of ocean-generated noise. Here, we estimate the cross terms of the Rayleigh-wave Green tensor, and show this is less sensitive to signal not in-line with the seismic stations. We illustrate this result with the Batholiths temporary seismic deployment, showing estimates of the Rayleigh wave with a higher signal-to-noise ratio and a consequently better phase-velocity dispersion curve. This approach provides an opportunity for reliable ambient noise crosscorrelations over shorter time windows and more closely spaced stations in the future

Using SVD for improved interferometric Green's function retrieval

Seismic interferometry (SI) is a technique used to estimate the Green's function (GF) between two receiver locations, as if there were a source at one of the receiver locations. However, in many applications, the requirements to recover the exact GF are not satisfied and SI yields a poor estimate of the GF. For these non-ideal cases, we improve the interferometric GFs, by applying singular value decomposition (SVD) to the cross-correlations before stacking. The SVD approach preserves energy that is stationary in the cross-correlations, which is the energy that contributes most to the GF recovery, and attenuates non-stationary energy, which leads to artefacts in the interferometric GF. We apply this method to construct virtual shot gathers (for both synthetic and field data) and demonstrate how using SVD enhances physical arrivals in these gathers. We also find that SVD is robust with respect to weakly correlated random noise, allowing a better recovery of events from noisy data, in some cases recovering energy that would otherwise be completely lost in the noise and that the standard SI technique fails to recover

Subsurface Characterization Using Head-Wave Artifacts in Seismic Interferometry

Seismologists continually work to improve images of the Earth\u27s interior. One new approach is seismic interferometry, which involves cross-correlating the seismic wave field recorded at two receivers to generate data as if one of the receivers was a source. Over the past decade, seismic interferometry has become an established technique to estimate the surface-wave part of the impulse response between two receivers; however, practical limitations in the source-energy distribution have made body-wave recovery difficult and causes spurious energy in the estimated impulse response. Rather than suppress such spurious energy, it can be useful to analyze coherent spurious events to help constrain subsurface parameters. With this in mind, we examine a particular spurious event we call the virtual refraction. This event comes from cross-correlating head-wave (or critically refracted) energy at one receiver with reection and refraction energy at the other receiver. For this particular spurious event, we find that, similar to surface waves, the important part of the source-energy distribution is readily available. The sources need to be at or past the critical offset from both receivers. In a horizontal, two-layer subsurface model, the slope of the virtual refraction defines the velocity of the fast layer (V2). Furthermore, the stationary-phase point in the correlation gather defines the critical offset, a property that depends on the thickness (H) and velocity (V1) of the slow layer. A two-layer numerical example is presented to illustrate the origin of the virtual refraction. After estimating the refractor velocity, a semblance analysis can be used to estimate H and V1. In field data from the Boise Hydrogeophysical Research Site, the virtual refraction alone is used to the estimate H, V1, and V2. This is an improvement over methods that rely on several wave types to fully characterize seismic properties above and below an interface. An exploration-scale active source seismic data set illustrates how we can use the method to build near-surface seismic models that can then be used for statics estimation in standard reection processing. Finally, we investigate multi-component seismic interferometry for the virtual refraction, a technique that has recently been developed to more accurately estimate the surface-wave impulse response with higher signal-to-noise than traditional single component estimates. We find that using multi-component correlations to estimate shear wave virtual refractions also improves signal-to-noise, but with a dependence on the incidence angle of the incoming wavefield

Seismic Constraints on Geothermal Resources Beneath the Western and Central Snake River Plain

Using geophysical data, we identify crustal sills that presumably produce the high heat flow expression within the central and western Snake River Plain (SRP) region of southern Idaho. We invert receiver function waveforms and analyze seismic velocity datasets from IRIS to identify anomalous velocity layers in the mid-crust that may relate to either partial melt or cooled sills. Gravity and magnetic data is used to further constrain the locations of these sills. We find the majority of identified sills to be located along the southern portions of the western SRP, which is coincident with locations of high geothermal gradient

Source Mechanism of Small Long-Period Events at Mount St. Helens in July 2005 Using Template Matching, Phase-Weighted Stacking, and Full-Waveform Inversion

Long-period (LP, 0.5-5 Hz) seismicity, observed at volcanoes worldwide, is a recognized signature of unrest and eruption. Cyclic LP “drumbeating” was the characteristic seismicity accompanying the sustained dome-building phase of the 2004–2008 eruption of Mount St. Helens (MSH), WA. However, together with the LP drumbeating was a near-continuous, randomly occurring series of tiny LP seismic events (LP “subevents”), which may hold important additional information on the mechanism of seismogenesis at restless volcanoes. We employ template matching, phase-weighted stacking, and full-waveform inversion to image the source mechanism of one multiplet of these LP subevents at MSH in July 2005. The signal-to-noise ratios of the individual events are too low to produce reliable waveform inversion results, but the events are repetitive and can be stacked. We apply network-based template matching to 8 days of continuous velocity waveform data from 29 June to 7 July 2005 using a master event to detect 822 network triggers. We stack waveforms for 359 high-quality triggers at each station and component, using a combination of linear and phase-weighted stacking to produce clean stacks for use in waveform inversion. The derived source mechanism points to the volumetric oscillation (∼10 m3) of a subhorizontal crack located at shallow depth (∼30 m) in an area to the south of Crater Glacier in the southern portion of the breached MSH crater. A possible excitation mechanism is the sudden condensation of metastable steam from a shallow pressurized hydrothermal system as it encounters cool meteoric water in the outer parts of the edifice, perhaps supplied from snow melt