Lane R. Johnson

Tomographic inversions for mantle P wave velocity structure based on the minimization of l 2 and l 1 norms of International Seismological Centre Travel Time Residuals

We use International Seismological Centre (ISC) P arrival data (1964–1987) and iterative algorithms which minimize the l1 and l2 residual norms to solve simultaneously for three-dimensional P velocity variations in Earths mantle, source mislocations, and station corrections. We find that the maximum velocity perturbations produced by the l1 minimization (approximately ±4% in our final model) are relatively insensitive to smoothing and damping constraints. Therefore, using an l1 norm criterion allows us to keep the bias introduced to the inversion to a minimum. Among the well-resolved features contained in both the l1 and the l2 velocity models are a fast anomaly in the lower mantle beneath the Tonga-New Hebrides subduction zone to a depth of 1670 km and another fast anomaly beneath the Japanese island arc and eastern Asia. Continuity between these anomalies and shallower fast anomalies is not clear. A fast anomaly extending from 670 km to 2070 km depth appears beneath eastern North America, the Caribbean, and north central South America. A broad, fast anomaly appears beneath eastern Asia just above the core-mantle boundary as well as several slow anomalies under the Pacific basin of comparable size. Both models contain a circum-Pacific ring of 2% lower velocities in the depth range 0–200 km, associated with back arc basins. High velocities (over 2%) associated with the continental shields tend to disappear below 400 km, though a significant region of high velocity remains beneath the Siberian platform in the 400 to 670 km depth interval.

Lateral variations in mantle velocity structure and discontinuities determined from P, PP, S, SS, and SS — SdS travel time residuals

On the basis of P, PP, S, SS arrival times and SS - S410S, SS - S660S differential times, we construct models of mantle P and S velocity structure and boundary topography of the 410-km and 660-km discontinuities. Events from the catalog of the International Seismological Centre (ISC) are relocated relative to the International Association of Seismology and Physics of the Earths Interior 1991 (IASP91) velocity model using both P and S arrival times. The arrival times are corrected for ellipticity and the PP and SS residuals are corrected for the topography at the bounce point. The cap-averaged PP - P and SS - S differential time residuals, plotted at the PP and SS surface reflection points, form broad coherent patterns. The geographic distribution of the cap averaged residuals agrees quite well with PP - P and SS-S differential time residuals derived from long period Global Digital Seismograph Network (GDSN) data. A robust lp inversion scheme is used to infer global mantle structure. Synthetic tests indicate that for regions well sampled by SS - S410S and SS - S660S differential times, the velocity estimates are not seriously contaminated by the topography of the 410- and 660-km discontinuities. However, estimates of boundary deflections may be influenced by extensive P and S velocity variations of 3% or greater. We find the 410-km discontinuity to be depressed by as much as 24 km beneath North America. Conversely, the discontinuity is deflected upward underneath Eurasia. In some regions the topography of the 660-km discontinuity is quite distinct from that of the 410-km discontinuity, but the two appear to be positively correlated. A series of depressions are found at several intersections of the 660-km discontinuity with known subduction zones. The elevated topography in the 410-km discontinuity beneath Europe is underlain by a trough in the 660-km discontinuity. A number of subduction zones are characterized by a thinning of the transition zone. Negative P and S velocity anomalies, underlying back-arc basins and tectonically active continental regions, encircle the Pacific. Where they are resolved, the stable continental cratons are systematically positive velocity features that extend below 200 km. With the inclusion of PP and SS travel time residuals we are better able to constrain midmantle structure. Most notably, in the depth range 35–660 km beneath the Northwest Pacific we observe high P velocity. Where they are resolved, mid-ocean ridges are most clearly imaged as low velocity features in the S model. The northern portion of the Mid-Atlantic Ridge is underlain by negative S velocity anomalies. In the Pacific, the East Pacific Rise is an extensive low S velocity anomaly.

Robust inversion of IASP91 travel time residuals for mantle P and S velocity structure, earthquake mislocations, and station corrections

Using both P and S arrival time information, 41,108 events in the International Seismological Centre (ISC) catalog for the years 1964 to 1987 are relocated relative to the IASP91 velocity model. The mean absolute horizontal relocation is 7.7 km and the mean absolute depth relocation is 9.1 km, The mean absolute origin time shift is 1.2 s. The relocation procedure increased the P residual standard deviation slightly from 2.3 s to 2.5 s while decreasing the S residual standard deviation from 6.8 s to 6.1 s. When plotted as bottoming point averages, the resulting IASP91 P and S arrival time residuals show coherent patterns as a function of geographic location. An iterative lp residual norm minimization algorithm is used to estimate the set of P and S velocity variations as well as the earthquake relocation and seismographic station parameters which best explain the travel time residuals. The procedure is robust in that extremely large travel time residuals, which are common in the ISC data, do not unduly influence the velocity estimates. Both the P and S models of lateral heterogeneity contain prominent circum-Pacific low velocities, 1% to 2% perturbations, underlying the back arc basins between 35 and 200 km depth. This ring of negative deviations continues into the depth interval 200–400 km. The continental cratons are underlain by high-velocity anomalies with maximum amplitudes of 2%. Iceland and the Azores are underlain by low-velocity mantle material that extends down to at least 400 km. The Benioff zones are only intermittently imaged as 1–2% high-velocity regions in the uppermost 400 km. They are best resolved in the P velocity variations. Both the P and S velocity models contain a circum-Pacific ring, beneath the Benioff zones, of 1–2% positive velocity deviations in the depth range 660–870 km. Coherent high-velocity features are seen below South America, Borneo, Tonga-Fiji, the Marianas, and the northern Kuriles. The anomalies beneath South America and Borneo extend into the 870–1070 km depth range. Below depths of 1270 km for P variations and 1070 km for S variations the amplitude of the heterogeneity has decreased significantly. It is only in the lowermost mantle, 2670 km to the core-mantle boundary, that the level of P heterogeneity rises significantly above the estimated noise level. In this depth range a partial ring around the Pacific basin is observed, although this.

Moment tensor inversions of M ~ 3 earthquakes in the Geysers geothermal fields, California

Microearthquakes have come into high public awareness due to being induced by the development and exploitation of enhanced and natural geothermal fields, hydrofracturing, and CO2 sequestration sites. Characterizing and understanding the faulting process of induced earthquakes, which is generally achieved through moment tensor inversion, could both help in risk prediction and in reservoir development monitoring. However, this is a challenging task because of their lower signal-to-noise ratio at frequencies typically used in earthquake source analyses. Therefore, higher-resolution velocity models and modeling of seismic waves at higher frequencies are required. In this study, we examine both the potentials to obtain moment tensor solutions for small earthquakes and the uncertainty of those solutions. We utilize a short-period seismic network located in the Geysers geothermal field in northern California and limit our study to that which would be achieved by industry in a typical reservoir environment. We obtain full moment tensor solutions of Mu2009~u20093 earthquakes using waveform modeling and first-motion inversions. We find that these two data sets give complimentary but yet different solutions. Some earthquakes correspond possibly to complex processes in which both shear and tensile failures occur simultaneously or sequentially. This illuminates the presence of fluids at depth and their role for the generation of these small-magnitude earthquakes. Finally, since first motions are routinely obtained for all magnitude earthquakes, our approach could be extended to small earthquakes where noise level and complex Greens functions prohibit using waveforms in moment tensor inversions.

Q in the inner core

Short-period vertical seismograms from ten earthquakes and one nuclear explosion in the distance range of 140-170 degrees are examined for a study of the anelastic properties of the inner core. The depth of the earthquake foci varies between 116 and 625 km. The phases of interest are PKP(BC branch) and PKIKP with bottoming depths in the upper few hundred kilometers of the inner core. The data consist of high-quality digital data at sampling rates 20/40 samples per second selected after an extensive search of the 1985-1986 GDSN event tapes for short-period P waves with a high signal-to-noise ratio. The results are based primarily upon observations between distances of 147° and 154°.

Source Mechanisms of Induced Earthquakes at The Geysers Geothermal Reservoir

At The Geysers geothermal reservoir in northern California, evidence strongly suggests that activities associated with production of electric power cause an increase in the number of small earthquakes. First-degree dynamic moment tensors are used to investigate the relationship between induced earthquakes and injection of water into a well as part of a controlled experiment in the northwest Geysers. The estimation of dynamic moment tensors in the complex shallow crust at The Geysers is challenging, so the method is described in detail with particular attention given to the uncertainty in the results. For seismic events in the moment magnitude range of 0.9–2.8, spectral moduli of dynamic moment tensors are reliably recovered in the frequency range of 1–100xa0Hz, but uncertainty in the associated spectral phases limits their use to a few simple results. A number of different static moment tensors are investigated, with the preferred one obtained from parameters of a model fitted to the spectral modulus of the dynamic moment tensor. Moment tensors estimated for a group of 20 earthquakes exhibit a range of source mechanisms, with over half having significant isotropic parts of either positive or negative sign. Corner frequencies of the isotropic part of the moment tensor are about 40 % larger than the average of the deviatoric moment tensor. Some spatial patterns are present in source mechanisms, with earthquakes closely related in space tending to have similar mechanisms, but at the same time, some nearby earthquakes have very different mechanisms. Tensional axes of displacement in the source regions are primarily horizontal, while the pressure axes range from near horizontal to vertical. Injection of water into the well in the center of the study area clearly causes an increase in the number of earthquakes per day, but an effect upon source mechanisms is not evident.

Effect of P-wave scattering on velocity and attenuation in unconsolidated sand saturated with immiscible liquids

Seismic wave tomography is a potentially powerful tool for detecting and delineating nonaqueous phase liquid (NAPL) contaminants in the shallow subsurface. To develop this application, we are conducting laboratory and numerical studies to understand the mechanisms of P-wave transmission through NAPL-water‐sand systems. P-wave measurements of traveltime and amplitude were taken in the 100–900 kHz frequency range through saturated sand with variable NAPL content. To simulate the stress conditions of the shallow surface, a low confining and axial pressure of 60 and 140 kPa, respectively, was applied. The measurements show a significant change in the traveltime and amplitude of the primary arrival as a function of NAPL saturation. To simulate the laboratory measurements, we performed numerical calculations of P-wave propagation through a 1-D medium. The results show that the main behavior of traveltime and amplitude variation can be explained by P-wave scattering. This represents an alternative explanation to...

A Source Model for Induced Earthquakes at the Geysers Geothermal Reservoir

The results of a previous study on source mechanisms of small earthquakes at the Geysers geothermal reservoir in northern California are used to investigate an extended crack model for seismic events. The seismic events are characterized by their first-degree moment tensors and interpreted in terms of a model that is a combination of a shear crack and wing cracks. Solutions to both forward and inverse problems are obtained that can be used with either dynamic or static moment tensors. The model contains failure criteria, explains isotropic parts that are commonly observed in induced earthquakes, and produces estimates of crack dimensions and maximum amount of slip. Effects of fluid pressure are easily incorporated into the model as an effective stress. The model is applied to static moment tensors of 20 earthquakes that occurred during a controlled injection project in the northwest Geysers. For earthquakes in the moment magnitude range of 0.9–2.8, the model predicts shear crack radii in the range of 10–150 m, wing crack lengths in the range of 2–25 m, and maximum slips in the range of 0.3–1.1 cm. Only limited results are obtained for the time-dependence of the earthquake process, but the model is consistent with corner frequencies of the isotropic part of the moment tensor being greater than the deviatoric part and waveforms of direct p waves that become more emergent for larger events.

What patterns of heterogeneity in the Earth's mantle can be revealed by seismic travel time tomography?

Abstract We investigate which patterns of seismic heterogeneity in the mantle would be returned reliably by a tomographic inversion in which the model mantle is parametrized by a set of discrete, non-overlapping voxels. We construct synthetic data sets based on real ray sampling of the mantle by introducing spherical harmonic patterns of velocity heterogeneity and perform inversions of the synthetic data. We expand the resulting voxel model in spherical harmonics and compare the power at each degree and in each model layer with the input spherical harmonics in order to determine which patterns produced by inversions of real data may be deemed reliable and to identify patterns which must be viewed with skepticism. We find that while the power input to a particular pattern of heterogeneity in the 0–200 km layer is generally recovered accurately, the pattern itself is poorly determined in this layer. A pattern in the 200–400 km layer is more precisely determined though the power contained in the pattern is consistently underestimated and more leakage occurs to the layers above and below. The transition zone, 400–670 km, shows similarly strong control of lateral heterogeneity patterns but tests return a more accurate estimate of input powre than for the second layer. The l = 2, 4, and 6 components all show accurate recovery in the 400–670 km layer. This result supports previous findings, from inversions with real data, that l = 2 is a significant pattern of heterogeneity in the mantles transition zone and that l = 4 is not a significant pattern. For the entire upper mantle, l = 6 would be retrieved reliably and its constructive behavior in upper mantle models derived with real data is confirmed. These tests also demonstrate the inability of our inversion procedure to retrieve shorter wavelength features in the lower mantle. The results for our lowermost layer, D″, must be considered suspect due to the inadequate constraints placed on model values by our ray coverage and the sensitivity of these results to noise in the data.

Low frequency elastic wave scattering by an inclusion: Limits of applications

The present investigation considers various approximations for the problem of low frequency elastic waves scattered by a single, small inclusion of constant elastic parameters. For the Rayleigh approximation containing both near and far field terms, the scattered amplitudes are investigated as a function of distance from the scatterer. Near field terms are found to be dominant for distances up to two wavelengths, after which far field solutions correctly describe the scattered field. At a distance of two wavelengths the relative error between the total and the far field solution is about 15% and decreases with increasing, distance. Deriving solutions for the linear and quadratic Rayleigh-Born approximation, the relative error between the nonlinear Rayleigh approximation and the linear and quadratic Rayleigh-Born approximation as a function of the scattering angle and the parameter perturbation is investigated. The relative error reveals a strong dependence on the scattering angle, while the addition of the quadratic term significantly improves the approximation for all scattering angles and parameter perturbations. An approximation for the error caused by linearization of the problem, based entirely on the perturbations of the parameters from the background medium, and its validity range given. We also investigate the limit of the wave parameter for Rayleigh scattering and find higher values than previously assumed. By choosing relative errors of 5%, 10% and 20% between the exact solution and the Rayleigh approximation, we find the upper limits for the parameter k{sub p}R to be 0.55, 0.7 and 0.9, respectively.