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Spatial patterns of aftershocks of shallow focus earthquakes in California and implications for deep focus earthquakes

Previous workers have pioneered statistical techniques to study the spatial distribution of aftershocks with respect to the focal mechanism of the main shock. Application of these techniques to deep focus earthquakes failed to show clustering of aftershocks near the nodal planes of the main shocks. To better understand the behavior of these statistics, this study applies them to the aftershocks of six large shallow focus earthquakes in California (August 6, 1979, Coyote Lake; May 2, 1983, Coalinga; April 24, 1984, Morgan Hill; August 4, 1985, Kettleman Hills; July 8, 1986, North Palm Springs; and October 1, 1987, Whittier Narrows). The large number of aftershocks accurately located by dense local networks allows us to treat these aftershock sequences individually instead of combining them, as was done for the deep earthquakes. The results for individual sequences show significant clustering about the closest nodal plane and the strike direction for five of the sequences and about the presumed fault plane for all six sequences. This implies that the previously developed method does work properly. Nonrandom behavior was also found about the slip directions, the P axis, the T axis, and the B axis, but this is probably caused by the lack of independence between these axes and the previously mentioned features of the focal mechanisms. Given that the method does work and that deep aftershocks were not shown to cluster about the main shock nodal planes, the shallow focus data were used to simulate the deep focus study. The goal is to determine if there are artificial factors that make clustering in the deep focus data unobservable. To more closely mimic the work on deep earthquakes, the largest aftershocks from each of the six sequences were combined and studied with respect to their respective main shock focal mechanisms. This reduced the significance of the clustering about the focal mechanism parameters, but not below 95% confidence. Gaussian noise was then added to the aftershock hypocenters in order to determine if the larger hypocentral and focal mechanism errors in the deep focus data could account for the previous negative result. The conclusion is that the following reasons are sufficient to explain the lack of clustering about the main shock nodal planes for the deep focus aftershocks: the need to combine aftershocks from several sequences, the size of the hypocentral location and focal mechanism errors, and the alignment of distant aftershocks with the Wadati-Benioff zone.

Journal of Geophysical Research Solid Earth

RMT focal plane sensitivity to seismic network geometry and faulting style

Modern tectonic studies often use regional moment tensors (RMTs) to interpret the seismotectonic framework of an earthquake or earthquake sequence; however, despite extensive use, little existing work addresses RMT parameter uncertainty. Here, we quantify how network geometry and faulting style affect RMT sensitivity. We examine how data-model fits change with fault plane geometry (strike and dip) for varying station configurations. We calculate the relative data fit for incrementally varying geometries about a best-fitting solution, applying our workflow to real and synthetic seismograms for both real and hypothetical station distributions and earthquakes. Initially, we conduct purely observational tests, computing RMTs from synthetic seismograms for hypothetical earthquakes and a series of well-behaved network geometries. We then incorporate real data and station distributions from the International Maule Aftershock Deployment (IMAD), which recorded aftershocks of the 2010 M W 8.8 Maule earthquake, and a set of regional stations capturing the ongoing earthquake sequence in Oklahoma and southern Kansas. We consider RMTs computed under three scenarios: (1) real seismic records selected for high data quality; (2) synthetic seismic records with noise computed for the observed source-station pairings and (3) synthetic seismic records with noise computed for all possible station-source pairings. To assess RMT sensitivity for each test, we observe the ‘fit falloff’, which portrays how relative fit changes when strike or dip varies incrementally; we then derive the ranges of acceptable strikes and dips by identifying the span of solutions with relative fits larger than 90 per cent of the best fit. For the azimuthally incomplete IMAD network, Scenario 3 best constrains fault geometry, with average ranges of 45° and 31° for strike and dip, respectively. In Oklahoma, Scenario 3 best constrains fault dip with an average range of 46°; however, strike is best constrained by Scenario 1, with a range of 26°. We draw two main conclusions from this study. (1) Station distribution impacts our ability to constrain RMTs using waveform time-series; however, in some tectonic settings, faulting style also plays a significant role and (2) increasing station density and data quantity (both the number of stations and the number of individual channels) does not necessarily improve RMT constraint. These results may be useful when organizing future seismic deployments (e.g. by concentrating stations in alignment with anticipated nodal planes), and in computing RMTs, either by guiding a more rigorous data selection process for input data or informing variable weighting among the selected data (e.g. by eliminating the transverse component when strike-slip mechanisms are expected).

Geophysical Journal International

Three-dimenstional crustal velocity structure beneath the Strait of Georgia, British Columbia

The Strait of Georgia is a topographic depression straddling the boundary between the Insular and Coast belts in southwestern British Columbia. Two shallow earthquakes located within the strait ( M = 4.6 in 1997 and M = 5.0 in 1975) and felt throughout the Vancouver area illustrate the seismic potential of this region. As part of the 1998 Seismic Hazards Investigation of Puget Sound (SHIPS) experiment, seismic instruments were placed in and around the Strait of Georgia to record shots from a marine source within the strait. We apply a tomographic inversion procedure to first-arrival traveltime data to derive a minimum-structure 3-D P -wave velocity model for the upper crust to about 13 km depth. We also present a 2-D velocity model for a profile orientated across the Strait of Georgia derived using a minimum-parameter traveltime inversion approach. This paper represents the first detailed look at crustal velocity variations within the major Cretaceous to Cenozoic Georgia Basin, which underlies the Strait of Georgia. The 3-D velocity model clearly delineates the structure of the Georgia Basin. Taking the 6 km s −1 isovelocity contour to represent the top of the underlying basement, the basin thickens from between 2 and 4 km in the northwestern half of the strait to between 8 and 9 km at the southeastern end of the study region. Basin velocities in the northeastern half are 4.5–6 km s −1 and primarily represent the Upper Cretaceous Nanaimo Group. Velocities to the south are lower (3–6 km s −1 ) because of the additional presence of the overlying Tertiary Huntingdon Formation and more recent sediments, including glacial and modern Fraser River deposits. In contrast to the relatively smoothly varying velocity structure of the basin, velocities of the basement rocks, which comprise primarily Palaeozoic to Jurassic rocks of the Wrangellia Terrane and possibly Jurassic to mid-Cretaceous granitic rocks of the Coast Belt, show significantly more structure, probably an indication of the varying basement rock lithologies. The 2-D velocity model more clearly reveals the velocity layering associated with the recent sediments, Huntingdon Formation and Nanaimo Group of the southern Georgia Basin, as well as the underlying basement. We interpret lateral variation in sub-basin velocities of the 2-D model as a transition from Wrangellian to Coast Belt basement rocks. The effect of the narrow, onshore–offshore recording geometry of the seismic experiment on model resolution was tested to allow a critical assessment of the validity of the 3-D velocity model. Lateral resolution throughout the model to a depth of 3–5 km below the top of the basement is generally 10–20 km.

British Columbia

Seismic source dynamics of gas-piston activity at Kı̄lauea Volcano, Hawai‘i

Since 2008, eruptive activity at the summit of Kı̄lauea Volcano, Hawai‘i has been confined to the new Overlook pit crater within the Halema‘uma‘u Crater. Among the broad range of magmatic processes observed in the new pit are recurring episodes of gas pistoning. The gas-piston activity is accompanied by seismic signals that are recorded by a broadband network deployed in the summit caldera. We use raw data recorded with this network to model the source mechanism of representative gas-piston events in a sequence that occurred on 20–25 August 2011 during a gentle inflation of the Kı̄lauea summit. To determine the source centroid location and source mechanism, we minimize the residual error between data and synthetics calculated by the finite difference method for a point source embedded in a homogeneous medium that takes topography into account. We apply a new waveform inversion method that accounts for the contributions from both translation and tilt in horizontal seismograms through the use of Green's functions representing the seismometer response to translation and tilt ground motions. This method enables a robust description of the source mechanism over the period range 1–10,000 s. Most of the seismic wavefield produced by gas-pistoning originates in a source region ∼1 km below the eastern perimeter of the Halema‘uma‘u pit crater. The observed waveforms are well explained by a simple volumetric source with geometry composed of two intersecting cracks featuring an east striking crack (dike) dipping 80°to the north, intersecting a north striking crack (another dike) dipping 65° to the east. Each gas-piston event is marked by a similar rapid inflation lasting a few minutes, trailed by a slower deflation ramp extending up to 15 min, attributed to the efficient coupling at the source centroid location of the pressure and momentum changes accompanying the growth and collapse of a layer of foam at the top of the lava column. Assuming a simple lumped parameter representation of the shallow magmatic system, the observed pressure and volume variations can be modeled with the following attributes : foam thickness (10–50 m), foam cell diameter (0.04–0.10 m), and gas-injection velocity (0.01–0.06 m s −1 ). Gas-piston activity occurs in a narrow pipe with diameter of 6 m connecting the Halema‘uma‘u pit crater to the subjacent dike system. The height of the magma column is estimated at ∼104 m at the start of the sequence based on the period of very long period (VLP) oscillations accompanying the onset of the gas-piston signal. Based on the change in the period of VLP oscillations and tilt evidence, the height of the magma column is inferred to have risen by up to ∼23 m by the end of the 5 day long sequence. A penny-shaped crack model of the dike geometry yields effective diameters of ∼1.2–2.9 km for the east dike and 0.7 km for the north dike. The shallower north dike segment is embedded in a relatively weak medium, compatible with expected mechanical properties in the hydrothermal environment of this dike.

Hawaii

Modification of wave-cut and faulting-controlled landforms

From a casual observation that the form of degraded fault scarps resembles the error function, this investigation proceeds through an elementary diffusion equation representation of landform evolution to the application of the resulting equations to the modern topography of scarplike landforms. The morphologic observations can be analyzed either in the form of one or more cross-strike elevation profiles or in the form of the slope-offset plot, a point plot of maximum scarp slope versus scarp offset. Working with either or both of these data representations for nine geologic structures, which range in age from 3 to 400 ka B.P. and in offset from 1 to 50 m, we apply analytical solutions for the vertical initial value scarp, the vertical continuous offset scarp, and the finite slope, initial value scarp. The model calculations are intrinsically ambiguous, yielding as the final answer only the product κ t (in the case of the initial value problem) or the product κ A −1 (in the case of the repeated faulting problem); here t is the age of a single scarp-forming event, 2 A is the vertical slip rate, and κ is the “mass diffusivity.” A single profile across three sea cliffs along the Santa Cruz, California, coast is analyzed as three separate initial value problems. A reasonably constrained age for the sea cliff standing above the Highway 1 platform returns κ = 11 GKG (1 GKG = 1 m 2 /ka). With this κ, we can date the two older sea cliffs. In fact, we do the converse: age estimates for these two older sea cliffs based on a uniform rate of uplift both yield the same κ as for the lower sea cliff. We treat a single profile of the Raymond fault in Pasadena/San Marino in terms of the repeated faulting problem; for it the uplift rate of R. Crook and others yields κ = 16 GKG. The very substantial preexisting offset across the Raymond fault must have been buried/leveled some 230 ka B.P., when the modern topography began to form. Our analysis of the Lake Bonneville shoreline scarps reveals a dependence of κ t on 2a, suggestive of nonlinear modification processes. This appearance is treated with the finite slope initial value scarp model to determine κ=1.1 GKG for the Lake Bonneville shoreline scarps. The suggestion of M. N. Machette that approximately 100,000-year-old, meter-high scarps are “unobservable” in weakly consolidated alluvial terranes of the Basin and Range and Rio Grande Rift Valley provinces can be formulated as κ ≳ 1 GKG. The coincidence between this inequality and the Lake Bonneville shoreline κ is striking, and it suggests that the value of κ = 1 GKG may be generally applicable, as a good first approximation, to the modification of alluvial terranes within the semiarid regions of the western United States. The Lake Bonneville shoreline κ is the basis for dating four sets of fault scarps in west-central Utah. The Drum Mountains fault scarps can be modeled in several different circumstances, but the most likely interpretation is that these fault scarps formed as the result of a single episode of normal faulting 3.6 to 5.7 ka B.P. The younger age is associated with quite low initial slope angles (25°). The other three sets of fault scarps show no evidence for finite initial value slopes. Fault scarps along the eastern base of the Fish Springs Range are very young, 3 ka B.P. We estimate the age of fault scarps along the western flank of the Oquirrh Mountains to be 32 ka B.P., which meets the weak geologic constraint that they be older than the Lake Bonneville shoreline. Fault scarps along the northeastern margin of the Sheeprock Mountains are even older, 53 ka B.P. An intriguing consequence of our single-event analysis of these scarps is that an 11.5-m offset occurred in a single earthquake.

Journal of Geophysical Research Solid Earth

Resonance of a fluid-driven crack: Radiation properties and implications for the source of long-period events and harmonic tremor

A dynamic source model is presented, in which a three-dimensional crack containing a viscous compressible fluid is excited into resonance by an impulsive pressure transient applied over a small area ΔS of the crack surface. The crack excitation depends critically on two dimensionless parameters called the crack stiffness, C = ( b /μ)( L / d ), and viscous damping loss, F = (12η L )/(ρ ƒ d 2 α), where b is the bulk modulus, η is the viscosity, ρ ƒ is the density of the fluid, μ is the rigidity, α is the compressional velocity of the solid, L is the crack length, and d is the crack thickness. The first parameter characterizes the ability of the crack to vibrate and shapes the spectral signature of the source, and the second quantifies the effect of fluid viscosity on the duration of resonance. Resonance is sustained by a very slow wave trapped in the fluid-filled crack. This guided wave, called the crack wave, is similar to the tube wave propagating in a fluid-filled borehole; it is inversely dispersive, showing a phase velocity that decreases with increasing wavelength, and its wave speed is always lower than the acoustic velocity of the fluid, decreasing rapidly as the crack stiffness increases. The source spectrum shows many sharp peaks characterizing the individual modes of vibration of the crack; the variation of spectral shape, both in the number and width of peaks, is surprisingly complex, reflecting the interference between the lateral and longitudinal modes of resonance, as well as nodes for these modes. The far-field spectrum is marked by narrow-band dominant and subdominant peaks that reflect the interaction of the various source modes. The frequency of the dominant spectral peak radiated by the source is independent of the radiation direction. The frequency, bandwidth, and spacing of the resonant peaks are strongly dependent on the crack stiffness, larger values of the stiffness factor shifting these peaks to lower frequencies and decreasing their bandwidth. The excitation of a particular mode depends on the position of the trigger and on the extent of the crack surface affected by the pressure transient. Fluid viscosity decreases the amplitudes of the main spectral peaks, smears out the finer structure of the spectrum, and greatly reduces the duration of the radiated signal. The energy loss by radiation is stronger for high frequencies, producing a seismic signature that is marked by a high-frequency content near the onset of the signal and dominated by a longer-period component of much longer duration in the signal coda. Such signature is in harmony with those displayed by long-period events observed on active volcanoes and in hydrofracture experiments. The very low velocity which is possible in a crack with high stiffness ( C ≥ 100) also provides an attractive explanation for very long period tremor, such as type 2 tremor at Aso volcano, Japan, without the requirement of an unrealistically large magma container. The standing wave pattern set up on the crack surface by the sustained resonance in the fluid is observable in the near field of the crack, suggesting that the location and extent of the source may be estimated from the mapping of the pattern of nodes and antinodes seen in its vicinity. According to the model, the long-period event and harmonic tremor share the same source but differ in the boundary conditions for fluid flow and in the triggering mechanism setting up the resonance of the source, the former being viewed as the impulse response of the tremor generating system and the latter representing the excitation due to more complex forcing functions.

Journal of Geophysical Research Solid Earth