Cancellation of Spurious Arrivals in Green’s Function Extraction

The extraction of the Green\u27s function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green\u27s function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium

Physical Modeling and Analysis of P-Wave Attenuation Anisotropy

Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group (effective) attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles (from 0° to 90°) with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient A governed by the Thomsen-style attenuation-anisotropy parameters εQ and δQ. Whereas the symmetry axis of the angle-dependent coefficient practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor Q increases more than tenfold from the symmetry axis (slow direction) to the isotropy plane (fast direction). Inversion of the coefficient using the Christoffel equation yields large negative values of the parameters εQ and δQ. . The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO (amplitude-variation-with-offset) analysis, amplitude-preserving migration, and seismic fracture detection

Modified Kubelka-Munk Equations for Localized Waves Inside a Layered Medium

We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We numerically solve the modified Kubelka-Munk equations and compare the results to radiative transfer as well as to simulations of the wave equation with randomly located thin layers

Monitoring a Passive Seismic Network at Neal Hot Springs Geothermal Plant

The Neal Hot Springs Project, currently under construction, will produce 23 MW of geothermal electric power once online. The project is located near Vale, Oregon (approx. 90 miles northwest of Boise) and consists of about 9.6 square miles of land, which is leased by U.S. Geothermal Inc. During construction the Geosciences department at Boise State University set up a network of 11 passive seismic stations in the area to monitor seismic activity. The goal is to obtain a large collection of seismic data during construction and testing, and to continue seismic monitoring during production. The data will be used to determine natural seismic activity, if any, in the area, seismic activity directly related to testing and production, and to determine the effects of fluid flow in the subsurface. These data sets may also be useful in targeting future geothermal reservoirs within the project area

Clustering Revisited: A Spectral Analysis of Microseismic Events

Identifying individual subsurface faults in a larger fault system is important to characterize and understand the relationship between microseismicity and subsurface processes. This information can potentially help drive reservoir management and mitigate the risks of natural or induced seismicity. We have evaluated a method of statistically clustering power spectra from microseismic events associated with an enhanced oil recovery operation in southeast Utah. Specifically, we were able to provide a clear distinction within a set of events originally designated in the time domain as a single cluster and to identify evidence of en echelon faulting. Subtle time-domain differences between events were accentuated in the frequency domain. Power spectra based on the Fourier transform of the time-domain autocorrelation function were used, as this formulation results in statistically independent intensities and is supported by a full body of statistical theory upon which decision frameworks can be developed

Noncontacting Benchtop Measurements of the Elastic Properties of Shales

We evaluated a laser-based noncontacting method to measure the elastic anisotropy of horizontal shale cores. Whereas conventional transducer data contained an ambiguity between phase and group velocity measurements, small laser source and receiver footprints on typical core samples ensured group velocity information in our laboratory measurements. With a single dense acquisition of group velocity versus group angle on a horizontal core, we estimated the elastic constants C11, C33, and C55 directly from ultrasonic waveforms, and C13 from a least-squares fit of modeled to measured group velocities. The observed significant P-wave velocity and attenuation anisotropy in these dry shales were almost surely exaggerated by delamination of clay platelets and microfracturing, but provided an illustration of the new laboratory measurement technique. Although challenges lay ahead to measure preserved shales at in situ conditions in the lab, we evaluated the fundamental advantages of the proposed method over conventional transducer measurements

Characterizing Phantom Arteries with Multi-Channel Laser Ultrasonics and Photo-Acoustics

Multi-channel photo-acoustic and laser ultrasonic waves are used to sense the characteristics of proxies for healthy and diseased vessels. The acquisition system is non-contacting and non-invasive with a pulsed laser source and a laser vibrometer detector. As the wave signatures of our targets are typically low in amplitude, we exploit multi-channel acquisition and processing techniques. These are commonly used in seismology to improve the signal-to-noise ratio of data. We identify vessel proxies with a diameter on the order of 1 mm, at a depth of 18 mm. Variations in scattered and photo-acoustic signatures are related to differences in vessel wall properties and content. The methods described have the potential to improve imaging and better inform interventions for atherosclerotic vessels, such as the carotid artery

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

Changes in Elastic Wave Velocity and Rock Microstructure Due to Basalt-CO\u3csub\u3e2\u3c/sub\u3e-Water Reactions

The chemical interaction between carbon dioxide, water, and basalt is a common process in the earth, which results in the dissolution of primary minerals that later precipitate as alteration minerals. This occurs naturally in volcanic settings, but more recently basalts have been suggested as reservoirs for sequestration of anthropogenic CO2. In both the natural and man-made cases, rock-fluid reactions lead to the precipitation of carbonates. Here, we quantify changes in ultrasonic wave speeds, associated with changes in the frame of whole-rock basalts, as CO2 and basalt react. After 30weeks of reactions and carbonate precipitation, the ultrasonic wave speed in dry basalt samples increases between 4% and 20% and permeability is reduced by up to an order of magnitude. However, porosity decreases only by 2% to 3%. The correlation between significant changes in wave speed and permeability indicates that a precipitate is developing in fractures and compliant pores. Thin sections, XRF-loss on ignition, and water chemistry confirm this observation. This means time-lapse seismic monitoring of a CO2-water-basalt system cannot assume invariance of the rock frame, as typically done in fluid substitution models. We conclude that secondary mineral precipitation causes a measurable change in the velocities of elastic waves in basalt-water-CO2 systems, suggesting that seismic waves could be used to remotely monitor future CO2 injection sites. Although monitoring these reactions in the field with seismic waves might be complicated due to the heterogeneous nature of basalt, quantifying the elastic velocity changes associated with rock alteration in a controlled laboratory experiment forms an important step toward field-scale seismic monitoring