[1] We demonstrate that the coherent information about the Earth structure can be extracted from the ambient seismic noise We compute cross-correlations of vertical component records of several days of seismic noise at different pairs of stations separated by distances from about one hundred to more than two thousand kilometers Coherent broadband dispersive wavetrains clearly emerge with group velocities similar to those predicted from the global Rayleigh-wave tomographic maps that have been constrained using ballistic surface waves Those results show that coherent Rayleigh waves can be extracted from the ambient seismic noise and that their dispersion characteristics can be measured in a broad range of periods This provides a source for new types of surface-wave measurements that can be obtained for numerous paths that could not be sampled with the ballistic waves and, therefore, can significantly improve the resolution of seismic images

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Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise.

Deep long-period tremors were recognized and located in a nonvolcanic region in southwest Japan. Epicenters of the tremors were distributed along the strike of the subducting Philippine Sea plate over a length of 600 kilometers. The depth of the tremors averaged about 30 kilometers, near the Mohorovic discontinuity. Each tremor lasted for at most a few weeks. The location of the tremors within the subduction zone indicates that the tremors may have been caused by fluid generated by dehydration processes from the slab.

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Nonvolcanic deep tremor associated with subduction in southwest Japan.

Publisher Summary This chapter focuses on elastic wave propagation in stratified media. The development of the theory of elastic wave propagation in stratified media has been strongly influenced by the problems of seismic wave propagation and the nature of the seismograms recorded from earthquakes. For purely analytic developments of elastic wave propagation, the level of manageable algebraic complexity is reached in a model with one or two uniform layers overlying a uniform half space. This chapter shows how the excitation of elastic waves, within a horizontally stratified structure, can be conveniently developed in terms of reflection and transmission matrices. This procedure has allowed the construction of the full response of the medium or approximations with desired properties so that theoretical seismograms may be calculated for realistic distributions of elastic parameters. Although this development has been for isotropic media, nearly all the results apply directly to the case of full anisotropy if 3 × 3 reflection and transmission matrices allowing coupling between all wave types are employed. This development of the wavefield for both source and receiver within the stratification may be used for other classes of wave propagation.

Seismic Wave Propagation in Stratified Media

SUMMARY We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic seismograms in 3-D earth models. The method combines the £exibility of a ¢nite element method with the accuracy of a spectral method. One uses a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements that is adapted to the free surface and to the main internal discontinuities of the model. The wave¢eld on the elements is discretized using high-degree Lagrange interpolants, and integration over an element is accomplished based upon the Gauss^Lobatto^Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix, which greatly simpli¢es the algorithm. We illustrate the great potential of the method by comparing it to a discrete wavenumber/re£ectivity method for layer-cake models. Both body and surface waves are accurately represented, and the method can handle point force as well as moment tensor sources. For a model with very steep surface topography we successfully benchmark the method against an approximate boundary technique. For a homogeneous medium with strong attenuation we obtain excellent agreement with the analytical solution for a point force.

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Introduction to the spectral element method for three-dimensional seismic wave propagation

We present the spectral element method to simulate elastic-wave propagation in realistic geological structures involving complieated free-surface topography and material interfaces for two- and three-dimensional geometries. The spectral element method introduced here is a high-order variational method for the spatial approximation of elastic-wave equations. The mass matrix is diagonal by construction in this method, which drastically reduces the computational cost and allows an efficient parallel implementation. Absorbing boundary conditions are introduced in variational form to simulate unbounded physical domains. The time discretization is based on an energy-momentum conserving scheme that can be put into a classical explicit-implicit predictor/multi-corrector format. Long-term energy conservation and stability properties are illustrated as well as the efficiency of the absorbing conditions. The associated Courant condition behaves as Δ tC < O ( nel−1/nd N −2), with nel the number of elements, nd the spatial dimension, and N the polynomial order. In practice, a spatial sampling of approximately 5 points per wavelength is found to be very accurate when working with a polynomial degree of N = 8. The accuracy of the method is shown by comparing the spectral element solution to analytical solutions of the classical two-dimensional (2D) problems of Lamb and Garvin. The flexibility of the method is then illustrated by studying more realistic 2D models involving realistic geometries and complex free-boundary conditions. Very accurate modeling of Rayleigh-wave propagation, surface diffraction, and Rayleigh-to-body-wave mode conversion associated with the free-surface curvature are obtained at low computational cost. The method is shown to provide an efficient tool to study the diffraction of elastic waves by three-dimensional (3D) surface topographies and the associated local effects on strong ground motion. Complex amplification patterns, both in space and time, are shown to occur even for a gentle hill topography. Extension to a heterogeneous hill structure is considered. The efficient implementation on parallel distributed memory architectures will allow to perform real-time visualization and interactive physical investigations of 3D amplification phenomena for seismic risk assessment.

The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures

SUMMARY We analyzed 16 seismic events recorded by the Hawaiian broad-band seismic network at Kilauea Volcano during the period September 9-26, 1999. Two distinct types of event are identified based on their spectral content, very-long-period (VLP) waveform, amplitude decay pattern and particle motion. We locate the VLP signals with a method based on analyses of semblance and particle motion. Different source regions are identified for the two event types. One source region is located at depths of -1 km beneath the northeast edge of the Halemaumau pit crater. A second region is located at depths of ~8 km below the northwest quadrant of Kilauea caldera. Our study represents the first time that such deep sources have been identified in VLP data at Kilauea. This discovery opens the possibility of obtaining a detailed image of the location and geometry of the magma plumbing system beneath this volcano based on source locations and moment tensor inversions of VLP signals recorded by a permanent, large-aperture broad-band network.

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Identifying elements of the plumbing system beneath Kilauea Volcano, Hawaii, from the source locations of very‐long‐period signals

Although most volcanic seismicity is shallow (within several kilometers of the surface), some volcanoes exhibit deeper seismicity (10 to 30+ km) that may reflect active processes such as magma resupply and volatile transfer. One such volcano is Mammoth Mountain, California, which has also recently exhibited high rates of CO2 discharge at the surface. We perform high-resolution earthquake detection and relocation to reveal punctuated episodes of rapidly propagating seismicity at mid-crustal depths along a narrow fracture zone surrounding a body of partial melt. We infer that these earthquakes track dike intrusions or fluid pressure pulses associated with CO2 exsolution, suggesting that the deep plumbing system of Mammoth Mountain is an active conduit for fluid transport from the base of the crust to the surface.

https://advances.sciencemag.org/content/advances/4/8/eaat5258.full.pdf

Deep fluid pathways beneath Mammoth Mountain, California, illuminated by migrating earthquake swarms

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Nonlinear processes in volcanoes

The decay rate of local earthquake coda is characteristic of the area in which the epicenter and stations are located (Aki, 1969; Aki and Chouet, 1975; Rautian and Khalturin, 1978; Tsujiura, 1978). Aki (1980) interpreted the coda decay rate in terms of the attenuation property of S waves in the lithosphere under the area. The Q of S waves inferred from coda waves is called "coda Q." Recently, several papers reported temporal changes in coda Q prior to the occurrence of large earthquakes. They are: (1) the Tangshan earthquake (M = 7.8) of 1976 and the Haicheng earthquake (M = 7.4) of 1975 (Jin and Aki, 1986); (2) three earthquakes (M = 8) in the Kuril-Kamchatka region (Gusev and Lemzikov, 1985); (3) the Kalapana, Hawaii, earthquake (M = 7.2) of 1975 (Wilson et al., 1983); and (4) the eastern Yamanashi, Japan, earthquake (M = 6.0) of 8 August 1983 (Sato, 1986). In all these cases, the coda Q was reported to be anomalously low before the occurrence of the earthquake. However, in a detailed study by Chouet (1979), a strong fluctuation of coda Q with time was observed in Bear Valley, California, which was not followed by a significant earthquake. A recent coda Q study in the Adak seismic zone by Scherbaum and Kisslinger (1985) also did not find significant coda Q changes that could be related to a mb = 5.8 earthquake which occurred in the area of investigation. In order to evaluate the feasibility of using coda Q for earthquake prediction research in California and Nevada, we began a systematic study of coda Q using digital waveform data from the regional microearthquake networks operated by the U.S. Geological Survey and the University of Nevada.

A preliminary study of coda Q in California and Nevada

A hierarchical model of magma transport in Hawaii is developed from the seismic records of deep (30–60 km) and intermediate-depth (5–15 km) harmonic tremor between January 1, 1962, and December 31, 1983. We find two kinds of spatial distributions of magma fractions at depths below 5 km, defined by the fractal dimension D3, where the subscript is the embedding dimension. The first is a focused distribution with D3 = 0.28, and the second is a dispersed distribution with D3 = 1.52. The former dimension reflects conduitlike structures where the magma flow converges toward a summit magma chamber and the fractal dimension tends to zero. The latter dimension reflects multifractal clustering of dendritic fractures where hypocentral domains represent subsets of fractures within spherical domains with an average radius of about 1 km. These geometries constitute a percolation network of clustered intermittent fracture and magma transport. The magma volume of the average fracture is about 2 × 104 m3. A tremor model of magma transport is developed from mass balances of percolation that are proportional to tremor durations. It gives reasonable magma fractions and residence times for a vertical drift velocity of 4 km yr−1 and yields patterns of intermittency that are in accord with singularity analyses of the 22-year time series record. According to the model, sustained tremor is generated by the relaxation oscillations of the percolation network with a dominant frequency of about 1 Hz to obtain internally consistent values of fracture geometry, fracture opening force, and magma supply rate. Calculated tremor frequencies are higher in fracture networks of small volume in harmony with the observed relation between seismic amplitude and dominant frequency of tremor. Tectonic relaxation times of rock stresses versus magma pressures are in fair agreement with the average length of tremor episodes and average period of tremor intermittencies. These observations suggest that a high degree of self-organization is characteristic of the nonlinear dynamics of fracture percolation and coupled tremor processes. Logarithms of frequencies (in hertz) of high-amplitude tremor (1-s period), mean tremor duration (28-min period), and mean onset interval (14-day period) are 0, −3.2, and −6.1, implying broadband maxima in the frequency spectrum of transport at intervals of 103. The next longer period of this sequence, which corresponds to eruptions and shallow intrusions, is about 32 years (10 −9 Hz), comparable to the average eruption intermission of Mauna Loa during the last 150 years (about 20 years). This and other evidence suggest that spatiotemporal universality extends from small to large scales in Hawaiian and other magmatic systems. The apparent universal scaling of frequencies may be more than 15 decades in time (1 s to about 60 m.y.) and 10 decades in length (0.1 mm to 103 km).

Bernard Chouet

Papers

Identifying elements of the plumbing system beneath Kilauea Volcano, Hawaii, from the source locations of very‐long‐period signals

Deep fluid pathways beneath Mammoth Mountain, California, illuminated by migrating earthquake swarms

Nonlinear processes in volcanoes

A preliminary study of coda Q in California and Nevada

Fractal hierarchies of magma transport in Hawaii and critical self-organization of tremor