Frank L. Vernon

A Fortran 90 library for multitaper spectrum analysis

The spectral analysis of geological and geophysical data has been a fundamental tool in understanding Earths processes. We present a Fortran 90 library for multitaper spectrum estimation, a state-of-the-art method that has been shown to outperform the standard methods. The library goes beyond power spectrum estimation and extracts for the user more information including confidence intervals, diagnostics for single frequency periodicities, and coherence and transfer functions for multivariate problems. In addition, the sine multitaper method can also be implemented. The library presented here provides the tools needed in multiple fields of the Earth sciences for the analysis of data as evident from various examples.

Breathing of the seafloor: Tidal correlations of seismicity at Axial volcano

Tidal effects on seafloor microearthquakes have been postulated, but the search has been hindered by a lack of continuous long-term data sets. Making this observation is further complicated by the need to distinguish between Earth and ocean tidal influences on the seafloor. In the summer of 1994, a small ocean-bottom seismograph array located 402 microseismic events, over a period of two months, on the summit caldera of Axial volcano on the Juan de Fuca Ridge. Harmonic tremor was also observed on all instruments, and Earth and ocean tides were recorded on tiltmeters installed within the seismometer packages. Microearthquakes show a strong correlation with tidal lows, suggesting that faulting is occurring preferentially when ocean loading is at a minimum. The harmonic tremor, interpreted as the movement of superheated fluid in cracks, also has a tidal periodicity.

Lithospheric seismic velocity discontinuities beneath the Arabian Shield

We determined crustal and lithospheric mantle velocity structure beneath the Arabian Shield through the modeling of receiver function stacks obtained from teleseismic P waves recorded by the 9 station temporary broadband array in western Saudi Arabia. The receiver function deconvolution technique was used to isolate the receiver-side PS mode conversions. A grid search method, which should yield an unbiased global minimum, was used to solve for a shear wave velocity model that is optimal and has the minimum number of layers needed to fit the receiver function waveform. Results from this analysis show that the crustal thickness in the shield area varies from 35 to 40 km in the west, adjacent to the Red Sea, to 45 km in central Arabia. Stability tests of each solution indicate that the models are relatively well constrained. We have also observed evidence for a large positive velocity contrast at sub-Moho depths at four stations at depths of 80 to 100 km. This discontinuity may represent a change in rheology in the lower part of the lithosphere or remnant structure from the formation of the Arabian Shield.

Broadband seismology in the oceans: Lessons from the Ocean Seismic Network Pilot Experiment

The fundamental objective of the Ocean Seismic Network Pilot Experiment (OSNPE)—which was carried out over a period of about 4 months at a site 225 km southwest of Oahu, Hawaii—was to learn how to make high-quality, broadband seismic measurements in the deep oceans. The OSNPE results demonstrate that broadband data of quality similar to that of quiet land stations can be acquired with seafloor seismographs, but that the location of the seismometer—whether it be on the seafloor, surficially buried within the seabed, or in a deep borehole—has a profound effect on data quality. At long-periods ( 0.1 Hz), data quality was best for a seismometer deployed 242 m below the seafloor in a borehole.

The generalized earthquake-location (GENLOC) package: an earthquake-location library

We describe a library and associated set of applications for locating seismic events. The library is called the GENeralized LOCation (GENLOC) library because it is a general library that implements most methods commonly used for single event locations. The library has a flexible implementation of the standard Gauss-Newton method with many options for weighting schemes, inversion methods, and algorithms for choosing an initial location estimate. GENLOC also has a grid-search algorithm that makes no assumptions about the geometry of the grid it is searching returning only the point with a best fit solution for the specified residual norm. GENLOC supports both arrival time and array slowness vector measurements. A unique feature is the strong separation between the travel time/earth model problem and the location estimations. GENLOC can utilize data from any seismic phase for which the user can supply an earth model and method to compute theoretical travel times and/or slowness values. The GENLOC library has been used in five different working applications: (1) a simple command line program, (2) an interactive graphical user interface version used in an analyst information system, (3) a database-driven relocation program, (4) a recent implementation of the progressive multiple event location method, and (5) a real-time location program. We ran a validation test against LOCSAT and found reasonable consistency in estimated locations. We attribute observed differences in the solutions to roundoff errors in different calculators used by the two programs.

Crustal thickness of the Peninsular Ranges and Gulf Extensional Province in the Californias

We estimate crustal thickness along an east-west transect of the Baja California peninsula and Gulf of California, Mexico, and investigate its relationship to surface elevation and crustal extension. We derive Moho depth estimates from P-to-S converted phases identified on teleseismic recordings at 11 temporary broadband seismic stations deployed at ;318N latitude. Depth to the Moho is ;33 (63) km near the Pacific coast of Baja California and increases gradually toward the east, reaching a maximum depth of ;40 (64) km beneath the western part of the Peninsular Ranges batholith. The crust then thins rapidly under the topographically high eastern Peninsular Ranges and across the Main Gulf Escarpment. Crustal thickness is ;15-18 (62) km within and on the margins of the Gulf of California. The Moho shallowing beneath the eastern Peninsular Ranges represents an average apparent westward dip of ;258. This range of Moho depths within the Peninsula Ranges, as well as the sharp ;east-west gradient in depth in the eastern part of the range, is in agreement with earlier observations from north of the international border. The Moho depth variations do not correlate with topography of the eastern batholith. These findings suggest that a steeply dipping Moho is a regional feature beneath the eastern Peninsular Ranges and that a local Airy crustal root does not support the highest elevations. We suggest that Moho shallowing under the eastern Peninsular Ranges reflects extensional deformation of the lower crust in response to adjacent rifting of the Gulf Extensional Province that commenced in the late Cenozoic. Support of the eastern Peninsular Ranges topography may be achieved through a combination of flexural support and lateral density variations in the crust and/or upper mantle.

Shear-wave splitting at central Tien Shan: Evidence for rapid variation of anisotropic patterns

At active collisional belts, the fast polarization axis of shear-wave splitting is generally aligned parallel to the strike of the belt, which has been proposed to indicate mantle strain that is coherent with crustal deformation. A notable exception is central Tien Shan, where anomalous patterns of splitting have previously been observed. We here analyze shear-wave splitting of SKS phases across north central Tien Shan using digital data from the Kyrgyzstan Broadband Seismic Network (KNET). We find a pattern of short-wavelength anisotropic heterogeneity that supports complex mantle flow due to small-scale convection. The along-strike variations in mantle structure contrast with the coherent pattern of crustal shortening, and indicate that mantle flow is not directly coupled to crustal deformation in this region.

Coherence of seismic body waves from local events as measured by a small‐aperture array

Eight local earthquakes were recorded during the operation of a small-aperture seismic array at Pinyon Flat, California. The site was chosen for its homogeneous granitic geology and its planar topography. Amplitude spectral ratios for the same signal measured at different stations had average values of less than 2 and maximum values of 7. Magnitude-squared coherences were estimated for all station pairs. These estimates were highest for the P wave arrivals on the vertical component and lowest for the P wave recorded on the transverse component. At 500 m station separation the P and S waves were incoherent above 15 Hz and 10 Hz, respectively. Coherence for both the P and S waves decrease as frequency increases and as distance increases. The coherence of signals from borehole sensors located at 300 and 150 m depth displays higher average coherence than equally spaced sites located on the surface. The results here suggest that even for sites that appear to be very similar, that is, those which are located on a planar surface within a few meters of granite bedrock, the measured seismic wavefield can be distorted substantially over scale lengths of 500 m. Coherence properties were calculated from synthetic seismograms which were computed for velocity models with exponential and self similar distribution perturbations. Standard deviations of 10% are not sufficient for the random velocity distributions to approximate the results from the small-aperture array.

Shear‐wave splitting across western Saudi Arabia: The pattern of upper mantle anisotropy at a Proterozoic Shield

We constrain upper mantle anisotropy across the Arabian Shield from shear-wave splitting analyses of SKS phases at eight temporary broadband stations that operated in Saudi Arabia. The direction of fast polarization is consistently aligned north-south and the delay time between fast and slow shear waves is generally 1.0 to 1.5 s, indicating that the mantle anisotropy is relatively homogeneous and coherent. We cannot distinguish between two possible models for the origin of this signal. The observed splitting may reflect fossil upper mantle anisotropy associated with the dominantly east-west accretion of oceanic terranes and formation of the Proterozoic Arabian lithosphere. Our results may also be compatible with present-day asthenospheric anisotropy caused by the northward absolute plate motion of the Arabian plate or northward asthenospheric flow from an Ethiopian mantle plume.

Regional crustal thickness variations of the Peninsular Ranges, southern California

We used the teleseismic receiver function technique to obtain a profile of the crustal thickness of the northern Peninsular Ranges, California. Depth to the Moho varies from ∼37 km beneath the western Peninsular Ranges batholith to ∼27 km at the western edge of the Salton trough, an average apparent dip of ∼10° to the west over a lateral distance of 60 km. We previously obtained a similar result for a profile ∼100 km to the south (a Moho dip of ∼20° over 30 km lateral distance). In both cases, the Moho depth variations do not correlate with topography of the eastern batholith, but rather appear to parallel the trend of a boundary that separates compositionally distinct eastern and western terranes. These observations suggest that a steeply dipping Moho is a regional feature beneath the eastern Peninsular Ranges, and that compensation is through lateral variations in crustal or upper mantle density rather than through an Airy root.