Robert W. Clayton

Time series modelling and maximum entropy

This paper briefly reviews the principles of maximum entropy spectral analysis and the closely related problem of autoregressive time series modelling. The important aspect of model identification is discussed with particular emphasis on the representation of harmonic processes with noise in terms of autoregressive moving-average models. It is shown that this representation leads to a spectral estimator proposed by Pisarenko in 1973.

The SCEC Southern California Reference Three-Dimensional Seismic Velocity Model Version 2

We describe Version 2 of the three-dimensional (3D) seismic velocity model of southern California developed by the Southern California Earthquake Center and designed to serve as a reference model for multidisciplinary research activities in the area. The model consists of detailed, rule-based representations of the major southern California basins (Los Angeles basin, Ventura basin, San Gabriel Valley, San Fernando Valley, Chino basin, San Bernardino Valley, and the Salton Trough), embedded in a 3D crust over a variable depth Moho. Outside of the basins, the model crust is based on regional tomographic results. The model Moho is represented by a surface with the depths determined by the receiver function technique. Shallow basin sediment velocities are constrained by geotechnical data. The model is implemented in a computer code that generates any specified 3D mesh of seismic velocity and density values. This parameterization is convenient to store, transfer, and update as new information and verification results become available.

Origin of High Mountains in the Continents: The Southern Sierra Nevada

Active and passive seismic experiments show that the southern Sierra, despite standing 1.8 to 2.8 kilometers above its surroundings, is underlain by crust of similar seismic thickness, about 30 to 40 kilometers. Thermobarometry of xenolith suites and magnetotelluric profiles indicate that the upper mantle is eclogitic to depths of 60 kilometers beneath the western and central parts of the range, but little subcrustal lithosphere is present beneath the eastern High Sierra and adjacent Basin and Range. These and other data imply the crust of both the High Sierra and Basin and Range thinned by a factor of 2 since 20 million years ago, at odds with purported late Cenozoic regional uplift of some 2 kilometers.

Subducting slab ultra-slow velocity layer coincident with silent earthquakes in southern Mexico.

Seismic mapping suggests that silent earthquakes may be related to an ultralow velocity layer on top of a subducting slab. Hot Silent Quakes Subduction zones tend to produce the largest and potentially most destructive earthquakes. Recent observations show that some deformation in several subduction zones seems to be occurring through small or “silent” quakes. The origin of these silent quakes, and their effect on the seismic hazard, is uncertain. Song et al. (p. 502) use a specific seismic signal to map out thin regions with low seismic velocities on the subduction zone beneath southern Mexico. The regions seem to occur at depths below the seismogenic zone where temperatures are higher. These high temperatures and the silent quakes may reflect the release and episodic trapping of fluids from metamorphic reactions. Great earthquakes have repeatedly occurred on the plate interface in a few shallow-dipping subduction zones where the subducting and overriding plates are strongly locked. Silent earthquakes (or slow slip events) were recently discovered at the down-dip extension of the locked zone and interact with the earthquake cycle. Here, we show that locally observed converted SP arrivals and teleseismic underside reflections that sample the top of the subducting plate in southern Mexico reveal that the ultra-slow velocity layer (USL) varies spatially (3 to 5 kilometers, with an S-wave velocity of ~2.0 to 2.7 kilometers per second). Most slow slip patches coincide with the presence of the USL, and they are bounded by the absence of the USL. The extent of the USL delineates the zone of transitional frictional behavior.

Nonvolcanic tremor observed in the Mexican subduction zone

Nonvolcanic tremor (NVT) activity is revealed as episodes of higher spectral amplitude at 1–8 Hz in daily spectrograms from the continuous seismological records in Guerrero, Mexico. The analyzed data cover a period of 2001–2007 when in 2001–2002 a large slow slip event (SSE) had occurred in the Guerrero-Oaxaca region, and then a new large SSE occurred in 2006. The tremor burst is dominated by S-waves. More than 100 strong NVT bursts were recorded in the narrow band of ~40 × 150 km^2 to the south of Iguala City and parallel to the coastline. Depths of NVT hypocenters are mostly scattered in the continental crust between 5 and 40 km depth. Tremor activity is higher during the 2001–2002 and 2006 SSE compared with that for the “quiet” period of 2003–2005. While resistivity pattern in Guerrero does not correlate directly with the NVT distribution, gravity and magnetic anomaly modeling favors a hypothesis that the NVT is apparently related to the dehydration and serpentinization processes.

Mantle Heterogeneities and the SCEC Reference Three-Dimensional Seismic Velocity Model Version 3

We determine upper mantle seismic velocity heterogeneities below Southern California from the inversion of teleseismic travel-time residuals. Teleseismic P-wave arrival times are obtained from three temporary passive experiments and Southern California Seismic Network (SCSN) stations, producing good raypath coverage. The inversion is performed using a damped least-squares conjugate gradient method (LSQR). The inversion model element spacing is 20 km. Before the inversion, the effects of crustal velocity heterogeneities represented by the Southern California Earthquake Center (SCEC) seismic velocity model version 2 are removed from the teleseismic travel times. The P-wave inversion produces a variance reduction of 43%. S-wave velocities are determined from laboratory Vp/Vs ratios. The most prominent features imaged in the results are high P-wave velocities (+3%) in the uppermost mantle beneath the northern Los Angeles basin, and the previously reported tabular high-velocity anomaly (+3%) to depths of 200 km beneath the Transverse Ranges, crosscutting the San Andreas fault. We incorporate the upper mantle seismic velocity heterogeneities into the SCEC Southern California reference seismic velocity model. The prior accounting for the crustal velocity heterogeneity demonstrates the utility of the top-down method of the SCEC seismic velocity model development.

Geometry and seismic properties of the subducting Cocos plate in central Mexico

The geometry and properties of the interface of the Cocos plate beneath central Mexico are determined from the receiver functions (RFs) utilizing data from the Meso America Subduction Experiment (MASE). The RF image shows that the subducting oceanic crust is shallowly dipping to the north at 15° for 80 km from Acapulco and then horizontally underplates the continental crust for approximately 200 km to the Trans-Mexican Volcanic Belt (TMVB). The crustal image also shows that there is no continental root associated with the TMVB. The migrated image of the RFs shows that the slab is steeply dipping into the mantle at about 75° beneath the TMVB. Both the continental and oceanic Moho are clearly seen in both images, and modeling of the RF conversion amplitudes and timings of the underplated features reveals a thin low-velocity zone between the plate and the continental crust that appears to absorb nearly all of the strain between the upper plate and the slab. By inverting RF amplitudes of the converted phases and their time separations, we produce detailed maps of the seismic properties of the upper and lower oceanic crust of the subducting Cocos plate and its thickness. High Poissons and Vp/Vs ratios due to anomalously low S wave velocity at the upper oceanic crust in the flat slab region may indicate the presence of water and hydrous minerals or high pore pressure. The evidence of high water content within the oceanic crust explains the flat subduction geometry without strong coupling of two plates. This may also explain the nonvolcanic tremor activity and slow slip events occurring in the subducting plate and the overlying crust.

Absorbing boundary conditions for wave-equation migration

The standard boundary conditions used at the sides of a seismic section in wave-equation migration generate artificial reflections. These reflections from the edges of the computational grid appear as artifacts in the final section. Padding the section with zero traces on either side adds to the cost of migration and simply delays the inevitable reflections. We develop stable absorbing boundary conditions that annihilate almost all of the artificial reflections. This is demonstrated analytically and with synthetic examples. The absorbing boundary conditions presented can be used with any of the different types of finite-difference wave-equation migration, at essentially no extra cost.

Inversion of refraction data by wave field continuation

The process of wave equation continuation (migration) is adapted for refraction data in order to produce velocity-depth models directly from the recorded data. The procedure consists of two linear transformations: a slant stack of the data produces a wave field in the p - τ plane which is then downward continued using τ = O as the imaging condition. The result is that the data wave field is linearly transformed from the time-distance domain into the slowness-depth domain, where the velocity profile can be picked directly. No travel-time picking is involved, and all the data are present throughout the inversion. The method is iterative because it is necessary to specify a velocity function for the continuation. The solution produced by a given iteration is used as the continuation velocity function for the next step. Convergence is determined when the output wave field images the same velocity-depth function as was input to the continuation. The method obviates the problems associated with determining the envelope of solutions that are consistent with the observations, since the time resolution in the data is transformed into a depth resolution in the slowness-depth domain. The method is illustrated with several synthetic examples, and with a refraction line recorded in the Imperial Valley, California.

The 2006 slow slip event and nonvolcanic tremor in the Mexican subduction zone

The last decade featured an explosive sequence of discoveries of slow slip events (SSE) and nonvolcanic tremor (NVT) in different subduction zones and continental faults. Many observations show that SSE is usually associated with an increased NVT activity but it is not clear yet if those events are the result of the same process or are independent expressions of a common underlying seismotectonic source. A large SSE in Central Mexico occurred in 2006 during the Meso-American Subduction Experiment (MASE) which provided continuous observations of the NVT for the years 2005-2007. GPS and abundant seismic data show that although the NVT energy increased notably during the 2006 SSE, the two phenomena were separated spatially and not completely synchronized in time. Significant NVT episodes occur during the period between SSEs, suggesting again that large slow slip events and NVT observed in the Mexican subduction zone are of different origins. The results presented here contribute to uncovering the nature of these two separate phenomena that have been indistinguishable in some other regions.