Vernon F. Cormier

Seismic attenuation of the inner core : Viscoelastic or stratigraphic?

Broadband velocity waveforms of PKIKP in the distance range 150° to 180° are inverted for inner core attenuation. A mean Qα of 244 is determined at 1 Hz from 8 polar and 9 equatorial paths. The scatter in measured Q−1 exceeds individual error estimates, suggesting significant variation in attenuation with path. These results are interpreted by (1) viscoelasticity, in which the relaxation spectrum has a low-frequency corner near or slightly above the frequency band of short-period body waves, and by (2) stratigraphic (scattering) attenuation, in which attenuation and pulse broadening are caused by the interference of scattered multiples in a velocity structure having rapid fluctuations along a PKIKP path. In the scattering interpretation, PKIKP attenuation is only weakly affected by the intrinsic shear attenuation measured in the free-oscillation band. Instead, its frequency dependence, path variations, and fluctuations are all explained by scattering attenuation in a heterogeneous fabric resulting from solidification texturing of intrinsically anisotropic iron. The requisite fabric may consist of either single or ordered groups of crystals with P velocity differences of at least 5% and as much as 12% between two crystallographic axes at scale lengths of 0.5 to 2 km in the direction parallel to the axis of rotation and longer in the cylindrically radial direction, perpendicular to the axis of rotation.

D as a transition in the heterogeneity spectrum of the lowermost mantle

Broadband SH and P wave fields are pseudospectrally modeled in three forms of the heterogeneity spectrum of the mantle, each having a transition in the power spectrum of heterogeneity in the lowermost mantle. With D″ defined as a zone of increased heterogeneity, low-pass and high-pass filters of models of the heterogeneity spectrum demonstrate that the thickness of D″ inferred from an incident seismic wave field can depend on the dominant wavelength of that wave field. A model of D″ heterogeneity that agrees with the coda power between S and ScS and between P and PcP is a simple linear extrapolation of the spectrum of heterogeneity power versus depth determined from global tomography to wavenumbers corresponding to short-period body waves. The negligible decay in the power spectrum of heterogeneity across a band of wavenumbers from 0.0001 to 1 km−1 is consistent with a pervasive entrainment of small scale chemical heterogeneities by convective motions. The lack of strong scattering attenuation in observed ScS and PcP waveforms is used to establish upper bounds in this wavenumber band of 3% and 1.5% on the root-mean-square variations of S and P velocity, respectively. Some realizations of the preferred model of the heterogeneity spectrum generate an SdS waveform from scattering by an elongated, high velocity anomaly, roughly parallel to the core-mantle boundary. The high topography of similarly shaped anomalies needed to account for the amplitude of narrow angle scattering observed from D″ argues against such anomalies having the high-density perturbation expected for a chemically distinct or phase-transformed layer.

Unsolved problems in the lowermost mantle

In an amplifier circuit, bias feedback to an amplifying transistor is provided by interconnecting the DC bias voltage applied to the transistor output and the transistor input with a feedback circuit consisting of a switching transistor and bias resistors. Bias current and stable operation is provided by this design. In a particular embodiment two common emitter amplifying transistors are connected to a common output and each has a separate bias feedback circuit including a respective switching transistor. A single DC control input connected to the inputs of both switching transistors can be used to switch between the two amplifying transistors depending on the value of the control voltage thereby amplifying either an input signal of the first amplifying transistor or an input signal of the second amplifying transistor.

Earth’s solid inner core: Seismic implications of freezing and melting

Seismic P velocity structure is determined for the upper 500 km of the inner core and lowermost 200 km of the outer core from differential travel times and amplitude ratios. Results confirm the existence of a globally uniform F region of reduced P velocity gradient in the lowermost outer core, consistent with iron enrichment near the boundary of a solidifying inner core. P velocity of the inner core between the longitudes 45°E and 180°E (quasi-Eastern Hemisphere) is greater than or equal to that of an AK135-F reference model whereas that between 180°W and 45°E (quasi-Western Hemisphere) is less than that of the reference model. Observation of this heterogeneity to a depth of 550 km below the inner core and the existence of transitions rather than sharp boundaries between quasi-hemispheres favor either no or very slow inner core super rotation or oscillations with respect to the mantle. Degree-one seismic heterogeneity may be best explained by active inner core freezing beneath the equatorial Indian Ocean dominating structure in the quasi-Eastern Hemisphere and inner core melting beneath equatorial Pacific dominating structure in the quasi-Western Hemisphere. Variations in waveforms also suggest the existence of smaller-scale (1 to 100 km) heterogeneity.

A Comparison of Synthetic Seismograms for 2D Structures: Semianalytical versus Numerical

Teleseismic wave fields occasionally exhibit rapid changes in travel times and waveforms over distances less than several great-circle degrees when observed at broadband arrays. These rapid changes in wave field suggest the existence of significant structural transitions occurring over scales of several hundred kilometers or less in the mid- and deep mantle. Although approximate analytical methods based on raytracing can be readily adapted to structures having arbitrarily small scale lengths, it is important to validate their accuracy against the predictions of numerical methods. Here we compare synthetics from an approximate ray-based method WKBJ modified (WKM) against the pseudospectral method for a 2D model of the S-velocity anomaly associated with the South African plume. This model consists of a uniform 3% decrease in S velocity over a broad (>10°) region of the mid- and deep mantle beneath South Africa, contiguous at its bottom with a thin (100- to 200-km-thick) zone of low velocity extending 30° westward toward South America along the core-mantle boundary. Transitions between anomalous and radially symmetric structures of the test model are sharp, occurring over l0 km or less. SV and SH wave fields synthesized by the WKM and pseudospectral methods in this model generally agree with each other well. Slight mismatches in the two methods can be understood as the result of either differences in model parameterization or the effects of asymptotic approximations in the ray-based WKM method.

Attenuation tomography of the upper inner core

The solidification of the Earths inner core shapes its texture and rheology, affecting the attenuation and scattering of seismic body waves transmitted through it. Applying attenuation tomography in a Bayesian framework to 398 high-quality PKIKP waveforms, we invert for the apparent Qp for the uppermost 400 km below the inner core boundary at latitudes 45°S to 45°N. We use damping and smoothing for regularization of the inversion, and it seems that the smoothing regularization combined with the discrepancy principle works better for this particular problem of attenuation tomography. The results are consistent with a regional variation in inner core attenuation more complex than hemispherical, suggesting coupling between inner core solidification and the thermal structure of the lowermost mantle.

High Frequency Earthquake Strong Ground Motion in Laterally Varying Media: The Effect of a Fault Zone

Crustal heterogeneity and the effects of a complex earthquake source may account for observations of strong ground motion not easily explained by simplified source models in a laterally homogeneous medium. Both the effects of a complex source and lateral heterogeneity can be examined using a forward modeling technique that combines distributed, non-uniform slip on a fault plane with dynamic ray tracing in a three dimensional medium. Iterative paraxial ray tracing is used to solve the two point ray tracing problem. The validity of the results are limited to relatively high frequencies at which ray theory provides and accurate approximation to the Green’s function; however, these frequencies are often those of greatest interest in seismic engineering