High frequency wave propagation in the earth: theory and observation

The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:

1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.

2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.

3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.

New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.

Control of polarization signal distortion by frequency domain phase conjugation in optical fiber systems

Optical frequency domain phase conjugation (FDPC) is based on phase conjugation of spectrum of an input signal. It is equivalent to the phase conjugation and the time reversal of the temporal envelope of an input signal. The use of FDPC to control polarization signal distortion in birefringent optical fiber systems is proposed. Evolution of polarization signals in the system using midway FDPC is analyzed theoretically and simulated numerically. It is shown that the distortion of polarization signals can be controlled effectively by FDPC. The impairments due to dispersion and nonlinear effects can be suppressed simultaneously.

One-shot parallel complex Fourier-domain optical coherence tomography using a spatial carrier frequency

We propose a novel method of one-shot parallel complex Fourier-domain optical coherence tomography using a spatial carrier frequency for full range imaging. The spatial carrier frequency is introduced into the 2-D spectral interferogram in the lateral direction by using a tilted reference wavefront. This spatial-carrier- contained 2-D spectral interferogram is recorded with one shot of a 2-D CCD camera, and is Fourier-transformed in the lateral direction to obtain a 2-D complex spectral interferogram by a spatial-carrier technique. A full-range tomogram is reconstructed from the 2-D complex spectral interferogram. The principle of this method is confirmed by cross-sectional imaging of a glass slip object. (c) 2008 Society of Photo-Optical Instrumentation Engineers.

The ionic basis of frequency selectivity in hair cells of the bullfrog's sacculus

Hair cells from the bull frog's sacculus, a vestibular organ responding to substrate-borne vibration, possess electrically resonant membrane properties which maximize the sensitivity of each cell to a particular frequency of mechanical input. The electrical resonance of these cells and its underlying ionic basis were studied by applying gigohm-seal recording techniques to solitary hair cells enzymatically dissociated from the sacculus. The contribution of electrical resonance to frequency selectivity was assessed from microelectrode recordings from hair cells in an excised preparation of the sacculus.

Electrical resonance in the hair cell is demonstrated by damped membrane-potential oscillations in response to extrinsic current pulses applied through the recording pipette. This response is analyzed as that of a damped harmonic oscillator. Oscillation frequency rises with membrane depolarization, from 80-160 Hz at resting potential to asymptotic values of 200-250 Hz. The sharpness of electrical tuning, denoted by the electrical quality factor, Q_e, is a bell-shaped function of membrane voltage, reaching a maximum value around eight at a membrane potential slightly positive to the resting potential.

In whole cells, three time-variant ionic currents are activated at voltages more positive than -60 to -50 mV; these are identified as a voltage-dependent, non-inactivating Ca current (I_ca), a voltage-dependent, transient K current (I_a), and a Ca-dependent K current (I_c). The C channel is identified in excised, inside-out membrane patches on the basis of its large conductance (130-200 pS), its selective permeability to Kover Na or Cl, and its activation by internal Ca ions and membrane depolarization. Analysis of open- and closed-lifetime distributions suggests that the C channel can assume at least two open and three closed kinetic states.

Exposing hair cells to external solutions that inhibit the Ca or C conductances degrades the electrical resonance properties measured under current-clamp conditions, while blocking the A conductance has no significant effect, providing evidence that only the Ca and C conductances participate in the resonance mechanism. To test the sufficiency of these two conductances to account for electrical resonance, a mathematical model is developed that describes I_ca, I_c, and intracellular Ca concentration during voltage-clamp steps. I_ca activation is approximated by a third-order Hodgkin-Huxley kinetic scheme. Ca entering the cell is assumed to be confined to a small submembrane compartment which contains an excess of Ca buffer; Ca leaves this space with first-order kinetics. The Ca- and voltage-dependent activation of C channels is described by a five-state kinetic scheme suggested by the results of single-channel observations. Parameter values in the model are adjusted to fit the waveforms of I_ca and I_c evoked by a series of voltage-clamp steps in a single cell. Having been thus constrained, the model correctly predicts the character of voltage oscillations produced by current-clamp steps, including the dependencies of oscillation frequency and Q_e on membrane voltage. The model shows quantitatively how the Ca and C conductances interact, via changes in intracellular Ca concentration, to produce electrical resonance in a vertebrate hair cell.

Analysis of beam-quality degradation in nonlinear frequency conversion

Based on the ripple transfers of electric-field amplitude and phase in frequency tripling, simple formulas are derived for the harmonic laser's beam-quality factor M-3omega(2), with an arbitrary fundamental incidence to ideal nonlinear crystals. Whereas the harmonic beam's quality is generally degraded, the beam's divergence is similar to that of the fundamental after nonlinear frequency conversion. For practical crystals with periodic surface ripples that are caused by their machining, a multiorder diffractive model is presented with which the focusing properties of harmonic beams can be studied. Predictions of the theories are shown to be in excellent agreement with full numerical simulations. (C) 2002 Optical Society of America.

Detection of Brillouin scattering temperature signal in Brillouin optical time-domain reflectometer sensing system based on instantaneous frequency measurement technology

We present a simple and practical method for the single-ended distributed fiber temperature measurements using microwave (11-GHz) coherent detection and the instantaneous frequency measurement (IFM) technique to detect spontaneous Brillouin backscattered signal in which a specially designed rf bandpass filter at 11 GHz is used as a frequency discriminator to transform frequency shift to intensity fluctuation. A Brillouin temperature signal can be obtained at 11 GHz over a sensing length of 10 km. The power sensitivity dependence on temperature induced by frequency shift is measured as 2.66%/K. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases. (C) 2005 Elsevier B.V. All rights reserved.

Detection of Brillouin scattering temperature signal in Brillouin optical time-domain reflectometer sensing system based on instantaneous frequency measurement technology

abstract {We present a simple and practical method for the single-ended distributed fiber temperature measurements using microwave (11-GHz) coherent detection and the instantaneous frequency measurement (IFM) technique to detect spontaneous Brillouin backscattered signal in which a specially designed rf bandpass filter at 11 GHz is used as a frequency discriminator to transform frequency shift to intensity fluctuation. A Brillouin temperature signal can be obtained at 11 GHz over a sensing length of 10 km. The power sensitivity dependence on temperature induced by frequency shift is measured as 2.66%/K. © 2007 Society of Photo-Optical Instrumentation Engineers.}

Stable single frequency and single polarization DFB fiber lasers operated at 1053 nm

Stable single-frequency and single-polarization distributed-feedback (DFB) fiber laser was realized by giving a pressure on the phase shift region of the fiber grating. The output wavelength of the DFB fiber laser is 1053 nm. When the pump power of 980 nm laser diode is 100 and 254 mW, the output power can reach 8.3 and 37.1 mW and the polarization extinction ratio was 26 and 20 dB, respectively. After chopped by Acousto-optic modulator (0.3 Hz), the pulse peak value variance is 4.65%(peak to peak) and 1.098% (RMS) for 31 min. (C) 2006 Elsevier Ltd. All rights reserved.

75 mW robust single frequency Yb-doped DFB fiber Bragg grating laser

Incorporating the shielded method and post-processing method, a 75 mW single frequency Yb-doped DFB fiber laser was obtained with a 250 mW laser diode pump source at 978 nm. The threshold of the laser is 2 mW. The laser is single-polarization operation and the output power fluctuation is less than 0.2 mW in one hour when the pump power is 250 mW.