Matthew J. Yedlin

A phenomenological approach to estimating transit times in GaAs HBTs

A method is proposed for estimating transit times in heterojunction bipolar transistors (HBTs) which are fabricated from semiconductor materials in which the conduction band can be represented by a two-valley model. The transition times for exchange of electrons between the conduction band valleys are treated as phenomenological parameters and are shown to be linked by the electric field in the device. Incorporation of the transition rates into the continuity equations for upper and lower valley electrons yields a set of equations which can be solved under transient conditions to yield directly the transit times of carriers across the base and the base-collector space-charge region. Results from this approach are compared with Monte Carlo calculations and shown to exhibit good agreement. >

Application of the Karhunen-Loève transform to diffraction separation

The Karhunen-Loeve (K-L) transform is applied to the separation of diffractions from reflections, for the model problem of a rigid half-plane. The basic transform and its interpretation in the context of seismic data are briefly reviewed. The transform, computed via the singular value decomposition, is applied to model data generated using an acoustic transceiver, which travels above a metal plate representing the half-plane. The K-L transform yields a clear separation between the edge diffraction and reflection. This is followed by an application of the slant K-L transform to remove dipping wall reflections which interfere with the edge diffraction.

A basic acoustic diffraction experiment for demonstrating the geometrical theory of diffraction

An apparatus is described in which acoustic diffractions are generated. Such diffractions are recorded in the field when seismic data is collected over a geological area that has many faults and truncated geological structures. The design of the experiment is considered from the point of view of theoretical feasibility and practical implementation. A computer‐controlled transceiver is guided on a traverse perpendicular to a model of a rigid half‐plane. At each transceiver location an acoustic pulse is emitted, and the scattered acoustic pulse is recorded. Results of this experiment are presented and analyzed from the perspective of Keller’s geometric theory of diffraction. The predicted asymmetry of the diffraction hyperbola is observed in the model data collected.

Acoustic pulse diffraction by step discontinuities on a plane

High‐frequency acoustic pulse diffraction of a point source by step discontinuities in a hard plane boundary is analyzed with the uniform geometrical theory of diffraction. Proper treatment of source and receiver locations at shadow boundaries provides a more complete analysis than before for the 90-degree step as evidenced by frequency‐domain numerical values. Time‐domain results for the 90-degree step, for a 30-degree inclined step, and for two offset half‐planes illustrate the significance of corner reflection and double diffraction missing from earlier numerical models based on Kirchhoff diffraction theory. Advantages in accuracy, computational efficiency, and scope of application of geometrical over Kirchhoff diffraction theory are indicated.

Incorporation of absorbing boundary conditions into acoustic and elastic wave propagation problems solved by spectral time-marching

Abstract The focus of this paper is a detailed description of the incorporation of absorbing boundary conditions in the symbolic solution of the two-dimensional elastic wave equation. This symbolic solution forms the basis for the spectral time-marching technique, which is also described. Application of the absorbing boundary conditions necessitates the employment of a spatial spectral discretization, yielding an algorithm whose accuracy is balanced in time and space. To illustrate the usefulness of the method, a numerical example of horizontally polarized shear waves is presented. The snapshots amply demonstrate how well the numerical absorbing condition works, a consequence of Chebyshev nodal clustering. The kernel operation of this time-stepping algorithm is matrix multiplication, efficiently implemented on existing supercomputers. Execution time for the numerical example, on the VPX 240 10 , was a sustained processing rate of 650 M-FLOPS or 37% of the achievable peak performance of 1·76 G-FLOPS.

ARMA implementation of diffraction operators with inverse-root singularities

The integral of a time-domain diffraction operator which has an integrable inverse-root singularity and an infinite tail is numerically differentiated to get a truncated digital form of the operator. This truncated difference operator effectively simulates the singularity but is computationally inefficient and produces a convolutional truncation ghost. The authors therefore use a least-squares method to model an equivalent autoregressive moving-average (ARMA) filter on the difference operator. The recursive convolution of the ARMA filter with a wavelet has no truncation ghost and an error below 1% of the peak diffraction amplitude. Design and application of the ARMA filter reduces computer (CPU) time by 42% over that repaired with direct convolution. A combination of filter design at a coarse spatial sampling, angular interpolation of filter coefficients to a finer sampling, and recursive application reduces CPU time by 83% over direct convolution or 80% over Fourier convolution, which also has truncation error. >

Truncated asymptotic representation of waves in a one-dimensional elastic medium

A new time‐domain method has been developed for solving for the stress and displacement of normally incident plane waves propagating in a smoothly varying one‐dimensional elastic medium. Both the Young’s modulus E and the density ρ are allowed to vary smoothly with depth. The restriction of geometrical optics, that the wavelength be much less than the material stratification length, is not required in this new method. We truncate the infinite geometrical‐optics asymptotic expansion after n terms (n = 2 in this paper), which imposes a condition on the acoustic impedance I for exact solutions to exist. The resultant expansion is uniform and exact for three general classes of impedance functions. Results are calculated for the case of a medium with a linear velocity gradient (for which there is an exact solution in the frequency domain); the results are compared with a two‐term WKBJ approximation and the new truncated expansion method. Since a linear velocity gradient is not one of the foregoing classes of i...

Phase modulation of acoustic transducers

A comparison of phase modulation and frequency modulation as applied to simple acoustic transducers is presented. We choose the complementary Barker code as the phase modulation code. To obtain optimal results an impulse response deconvolution is required. The final envelopes of the crosscorrelation of the reference signals and the recorded signals demonstrate the usefulness of the complementary Barker code. Whereas the chirp correlation envelope has two significant principal sidelobes, the Barker envelope has no such sidelobes.<<ETX>>

Pulse diffraction by a curved half plane

Abstract Diffraction of a pulsed point source near a hard half-plane cylindrically curved near its edge is analyzed by the geometrical theory of diffraction. Source and receiver are both on the convex side of the curved surface. The solution includes first and second order edge diffracted fields: those of the edge and creeping wave and those of the discontinuity in curvature at the junction between the cylindrical segment and the plane surface. The latter are particularly strong near the reflection boundary, as shown in numerical results for zero offset between a source receiver pair. Creeping waves are calculated across their transition boundary using Fock functions and into the shadow region where they are strong enough to be observed experimentally.

Exact time-domain solutions for acoustic diffraction by a half plane

We derive exact time-domain solutions for scattering of acoustic waves by a half plane by inverse Fourier transforming the frequency-domain integral solutions. The solutions consist of a direct term, a reflected term and two diffraction terms. The diffracting edge induces step function discontinuities in the direct and reflected, terms at two shadow boundries. At each boundary, the associated diffraction term reaches a maximum amplitude of half the geometrical optics term and has a signum function discontinuity so that the total field remains continuous. We evaluate solutions for practical point source configurations by numerically convolving the impulse diffraction responses with a wavelet. We solve the associated problems of convolution with a singular, truncated diffraction operator by analytically derived correction techniques. We produce a zero offset section and compare it to a Kirchhoff integral solution. Our exact diffraction hyperbola exhibits noticeable asymmetry, with higher amplitudes on the reflector side of the edge. Near the apex of the hyperbola the Kirchhoff solution approximates the exact diffraction term symmetric in amplitude about the reflection shadow boundary, but omits the other low amplitude term necessary to ensure continuity at the direct shadow boundary.