Optimal feedback control of two-photon fluorescence in Coumarin 515 based on genetic algorithm

An optimal feedback control of two-photon fluorescence in the Coumarin 515 ethanol solution excited by shaping femtosecond laser pulses based on genetic algorithm is demonstrated experimentally. The two-photon fluorescence intensity can be enhanced by similar to 20%. Second harmonic generation frequency-resolved optical gating traces indicate that the optimal laser pulses are positive chirp, which are in favor of the effective population transfer of two-photon transitions. The dependence of the two-photon fluorescence signal on the laser pulse chirp is investigated to validate the theoretical model for the effective population transfer of two-photon transitions. The experimental results appear the potential applications in nonlinear spectroscopy and molecular physics. (c) 2005 Elsevier B.V. All rights reserved.

Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

Measurement of small vibration amplitudes of a rough surface by an interferometer with a self-pumped phase-conjugate mirror

The application of a Michelson interferometer with a self-pumped phase-conjugate mirror to measure small vibration amplitudes of a rough surface is described. The distorted wave front of the light that is diffusely reflected from the rough surface is restored by phase conjugation to provide an interference signal with a high signal-to-noise ratio. The vibration amplitudes of a stainless-steel sample are measured with a precision of similar to 5 nm. (C) 2000 Optical Society of America OCIS codes: 120.3180, 190.5040, 120.7280.

A Multiwavelength Study of the Intracluster Medium and the Characterization of the Multiwavelength Sub/millimeter Inductance Camera

The first part of this thesis combines Bolocam observations of the thermal Sunyaev-Zel’dovich (SZ) effect at 140 GHz with X-ray observations from Chandra, strong lensing data from the Hubble Space Telescope (HST), and weak lensing data from HST and Subaru to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive, dynamically relaxed galaxy clusters. For five of the six clusters, the full multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The multiwavelength analysis yields considerably better constraints on the total mass and concentration compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulent and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95% confidence, where r500c refers to radius at which the average enclosed density is 500 times the critical density of the Universe. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for the clusters in this sample.

The second part of this thesis focuses on the characterization of the Multiwavelength Sub/millimeter Inductance Camera (MUSIC), a photometric imaging camera that was commissioned at the Caltech Submillimeter Observatory (CSO) in 2012. MUSIC is designed to have a 14 arcminute, diffraction-limited field of view populated with 576 spatial pixels that are simultaneously sensitive to four bands at 150, 220, 290, and 350 GHz. It is well-suited for studies of dusty star forming galaxies, galaxy clusters via the SZ Effect, and galactic star formation. MUSIC employs a number of novel detector technologies: broadband phased-arrays of slot dipole antennas for beam formation, on-chip lumped element filters for band definition, and Microwave Kinetic Inductance Detectors (MKIDs) for transduction of incoming light to electric signal. MKIDs are superconducting micro-resonators coupled to a feedline. Incoming light breaks apart Cooper pairs in the superconductor, causing a change in the quality factor and frequency of the resonator. This is read out as amplitude and phase modulation of a microwave probe signal centered on the resonant frequency. By tuning each resonator to a slightly different frequency and sending out a superposition of probe signals, hundreds of detectors can be read out on a single feedline. This natural capability for large scale, frequency domain multiplexing combined with relatively simple fabrication makes MKIDs a promising low temperature detector for future kilopixel sub/millimeter instruments. There is also considerable interest in using MKIDs for optical through near-infrared spectrophotometry due to their fast microsecond response time and modest energy resolution. In order to optimize the MKID design to obtain suitable performance for any particular application, it is critical to have a well-understood physical model for the detectors and the sources of noise to which they are susceptible. MUSIC has collected many hours of on-sky data with over 1000 MKIDs. This work studies the performance of the detectors in the context of one such physical model. Chapter 2 describes the theoretical model for the responsivity and noise of MKIDs. Chapter 3 outlines the set of measurements used to calibrate this model for the MUSIC detectors. Chapter 4 presents the resulting estimates of the spectral response, optical efficiency, and on-sky loading. The measured detector response to Uranus is compared to the calibrated model prediction in order to determine how well the model describes the propagation of signal through the full instrument. Chapter 5 examines the noise present in the detector timestreams during recent science observations. Noise due to fluctuations in atmospheric emission dominate at long timescales (less than 0.5 Hz). Fluctuations in the amplitude and phase of the microwave probe signal due to the readout electronics contribute significant 1/f and drift-type noise at shorter timescales. The atmospheric noise is removed by creating a template for the fluctuations in atmospheric emission from weighted averages of the detector timestreams. The electronics noise is removed by using probe signals centered off-resonance to construct templates for the amplitude and phase fluctuations. The algorithms that perform the atmospheric and electronic noise removal are described. After removal, we find good agreement between the observed residual noise and our expectation for intrinsic detector noise over a significant fraction of the signal bandwidth.

Rhythm generation in monkey motor cortex explored using pyramidal tract stimulation.

We investigated whether stimulation of the pyramidal tract (PT) could reset the phase of 15-30 Hz beta oscillations observed in the macaque motor cortex. We recorded local field potentials (LFPs) and multiple single-unit activity from two conscious macaque monkeys performing a precision grip task. EMG activity was also recorded from the second animal. Single PT stimuli were delivered during the hold period of the task, when oscillations in the LFP were most prominent. Stimulus-triggered averaging of the LFP showed a phase-locked oscillatory response to PT stimulation. Frequency domain analysis revealed two components within the response: a 15-30 Hz component, which represented resetting of on-going beta rhythms, and a lower frequency 10 Hz response. Only the higher frequency could be observed in the EMG activity, at stronger stimulus intensities than were required for resetting the cortical rhythm. Stimulation of the PT during movement elicited a greatly reduced oscillatory response. Analysis of single-unit discharge confirmed that PT stimulation was capable of resetting periodic activity in motor cortex. The firing patterns of pyramidal tract neurones (PTNs) and unidentified neurones exhibited successive cycles of suppression and facilitation, time locked to the stimulus. We conclude that PTN activity directly influences the generation of the 15-30 Hz rhythm. These PTNs facilitate EMG activity in upper limb muscles, contributing to corticomuscular coherence at this same frequency. Since the earliest oscillatory effect observed following stimulation was a suppression of firing, we speculate that inhibitory feedback may be the key mechanism generating such oscillations in the motor cortex.

Dynamical behavior of damped driven coupled single electron simple harmonic oscillators

Coherent coupling between a large number of qubits is the goal for scalable approaches to solid state quantum information processing. Prototype systems can be characterized by spectroscopic techniques. Here, we use pulsed-continuous wave microwave spectroscopy to study the behavior of electrons trapped at defects within the gate dielectric of a sol-gel-based high-k silicon MOSFET. Disorder leads to a wide distribution in trap properties, allowing more than 1000 traps to be individually addressed in a single transistor within the accessible frequency domain. Their dynamical behavior is explored by pulsing the microwave excitation over a range of times comparable to the phase coherence time and the lifetime of the electron in the trap. Trap occupancy is limited to a single electron, which can be manipulated by resonant microwave excitation and the resulting change in trap occupancy is detected by the change in the channel current of the transistor. The trap behavior is described by a classical damped driven simple harmonic oscillator model, with the phase coherence, lifetime and coupling strength parameters derived from a continuous wave (CW) measurement only. For pulse times shorter than the phase coherence time, the energy exchange between traps, due to the coupling, strongly modulates the observed drain current change. This effect could be exploited for 2-qubit gate operation. The very large number of resonances observed in this system would allow a complex multi-qubit quantum mechanical circuit to be realized by this mechanism using only a single transistor.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

A differential recursive scheme for suppression of Peak to average power ratio for OFDM

A differential recursive scheme for suppression of Peak to average power ratio (PAPR) for Orthogonal frequency division multiplexing (OFDM) signal is proposed in this thesis. The pseudo-randomized modulating vector for the subcarrier series is differentially phase-encoded between successive components in frequency domain first, and recursion manipulates several samples of Inverse fast Fourier transformation (IFFT) output in time domain. Theoretical analysis and experimental result exhibit advantage of differential recursive scheme over direct output scheme in PAPR suppression. And the overall block diagram of the scheme is also given.

Two-photon asymmetric color-locking second-order stochastic correlation of attosecond polarization beats

Based on the phase-conjugation polarization interference between two two-photon processes, we theoretically investigated the attosecond scale asymmetry sum-frequency polarization beat in four-level system (FASPB). The field correlation has weak influence on the FASPB signal when the laser has narrow bandwidth. Conversely, when the laser has broadband linewidth, the FASPB signal shows resonance-nonresonance cross correlation. The two-photon signal exhibits hybrid radiation-matter detuning terahertz; damping oscillation, i.e., when the laser frequency is off resonance from the two-photon transition, the signal exhibits damping oscillation and the profile of the two-photon self-correlation signal also exhibits zero time-delay asymmetry of the maxima. We have also investigated the asymmetry of attosecond polarization beat caused by the shift of the two-photon self-correlation zero time-delay phenomenon, in which the maxima of the two two-photon signals are shifted from zero time-delay point to opposite directions. As an attosecond ultrafast modulation process, FASPB can be intrinsically extended to any level-summation systems of two dipolar forbidden excited states.

Characteristics of low-frequency components of the near-bottom current in the Chinese Pioneer Area

Two deep-sea moorings were deployed respectively in the east area and the west area of Chinese Pioneer Area (CPA) in the tropic east Pacific to monitor the regional deep-sea dynamics below 600 meters above bottom (mab) from July 1997 to Oct. 1999. Results of statistics, spectral estimate and correlation analysis of the low-passed velocity data show that time scales of low-frequency components of the near-bottom currents are 25similar to120 days, in which 51-day period dominates the lower band of the frequency domain. Topographic features have obvious effect on low-frequency currents below 50 mab; modulations of the bottom-intensified sheared mean flow to the low-frequency currents are the dynamic mechanism of the frequency shift that occurs in both the east-area and the west-area.

Fourier有限差分法深度偏移与正演模拟

With the development of seismic exploration, the target becomes more and more complex, which leads to a higher demand for the accuracy and efficiency in 3D exploration. Fourier finite-difference (FFD) method is one of the most valuable methods in complex structure exploration, which keeps the ability of finite-differenc method in dealing with laterally varing media and inherits the predominance of the phase-screen method in stablility and efficiency. In this thesis, the accuracy of the FFD operator is highly improved by using simulated annealing algorithm. This method takes the extrapolation step and band width into account, which is more suitable to various band width and discrete scale than the commonely-used optimized method based on velocity contrast alone. In this thesis, the FFD method is extended to viscoacoustic modeling. Based on one-way wave equation, the presented method is implemented in frequency domain; thus, it is more efficient than two-way methods, and is more convenient than time domain methods in handling attenuation and dispersion effects. The proposed method can handle large velocity contrast and has a high efficiency, which is helpful to further research on earth absorption and seismic resolution. Starting from the frequency dispersion of the acoustic VTI wave equation, this thesis extends the FFD migration method to the acoustic VTI media. Compared with the convetional FFD method, the presented method has a similar computational efficiency, and keeps the abilities of dealing with large velocity contrasts and steep dips. The numerical experiments based on the SEG salt model show that the presented method is a practical migration method for complex acoustical VTI media, because it can handle both large velocity contrasts and large anisotropy variations, and its accuracy is relatively high even in strong anisotropic media. In 3D case, the two-way splitting technique of FFD operator causes artificial azimuthal anisotropy. These artifacts become apparent with increasing dip angles and velocity contrasts, which prevent the application of the FFD method in 3D complex media. The current methods proposed to reduce the azimuthal anisotropy significantly increase the computational cost. In this thesis, the alternating-direction-implicit plus interpolation scheme is incorporated into the 3D FFD method to reduce the azimuthal anisotropy. By subtly utilizing the Fourier based scheme of the FFD method, the improved fast algorithm takes approximately no extra computation time. The resulting operator keeps both the accuracy and the efficiency of the FFD method, which is helpful to the inhancements of both the accuracy and the efficiency for prestack depth migration. The general comparison is presented between the FFD operator and the generalized-screen operator, which is valuable to choose the suitable method in practice. The percentage relative error curves and migration impulse responses show that the generalized-screen operator is much sensiutive to the velocity contrasts than the FFD operator. The FFD operator can handle various velocity contrasts, while the generalized-screen operator can only handle some range of the velocity contrasts. Both in large and weak velocity contrasts, the higher order term of the generalized-screen operator has little effect on improving accuracy. The FFD operator is more suitable to large velocity contrasts, while the generalized-screen operator is more suitable to middle velocity contrasts. Both the one-way implicit finite-difference migration and the two-way explicit finite-differenc modeling have been implemented, and then they are compared with the corresponding FFD methods respectively. This work gives a reference to the choosen of proper method. The FFD migration is illustrated to be more attractive in accuracy, efficiency and frequency dispertion than the widely-used implicit finite-difference migration. The FFD modeling can handle relatively coarse grids than the commonly-used explicit finite-differenc modeling, thus it is much faster in 3D modeling, especially for large-scale complex media.

基于匹配追踪方法的地震信号时频分析研究

Seismic signal is a typical non-stationary signal, whose frequency is continuously changing with time and is determined by the bandwidth of seismic source and the absorption characteristic of the media underground. The most interesting target of seismic signal’s processing and explaining is to know about the local frequency’s abrupt changing with the time, since this kind of abrupt changing is indicating the changing of the physical attributes of the media underground. As to the seismic signal’s instantaneous attributes taken from time-frequency domain, the key target is to search a effective, non-negative and fast algorithm time-frequency distribution, and transform the seismic signal into this time-frequency domain to get its instantaneous power spectrum density, and then use the process of weighted adding and average etc. to get the instantaneous attributes of seismic signal. Time-frequency analysis as a powerful tool to deal with time variant non-stationary signal is becoming a hot researching spot of modern signal processing, and also is an important method to make seismic signal’s attributes analysis. This kind of method provides joint distribution message about time domain and frequency domain, and it clearly plots the correlation of signal’s frequency changing with the time. The spectrum decomposition technique makes seismic signal’s resolving rate reach its theoretical level, and by the method of all frequency scanning and imaging the three dimensional seismic data in frequency domain, it improves and promotes the resolving abilities of seismic signal vs. geological abnormal objects. Matching pursuits method is an important way to realize signal’s self-adaptive decomposition. Its main thought is that any signal can be expressed by a series of time-frequency atoms’ linear composition. By decomposition the signal within an over completed library, the time-frequency atoms which stand for the signal itself are selected neatly and self-adaptively according to the signal’s characteristics. This method has excellent sparse decomposition characteristics, and is widely used in signal de-noising, signal coding and pattern recognizing processing and is also adaptive to seismic signal’s decomposition and attributes analysis. This paper takes matching pursuits method as the key research object. As introducing the principle and implementation techniques of matching pursuits method systematically, it researches deeply the pivotal problems of atom type’s selection, the atom dictionary’s discrete, and the most matching atom’s searching algorithm, and at the same time, applying this matching pursuits method into seismic signal’s processing by picking-up correlative instantaneous messages from time-frequency analysis and spectrum decomposition to the seismic signal. Based on the research of the theory and its correlative model examination of the adaptively signal decomposition with matching pursuit method, this paper proposes a fast optimal matching time-frequency atom’s searching algorithm aimed at seismic signal’s decomposition by frequency-dominated pursuit method and this makes the MP method pertinence to seismic signal’s processing. Upon the research of optimal Gabor atom’s fast searching and matching algorithm, this paper proposes global optimal searching method using Simulated Annealing Algorithm, Genetic Algorithm and composed Simulated Annealing and Genetic Algorithm, so as to provide another way to implement fast matching pursuit method. At the same time, aimed at the characteristics of seismic signal, this paper proposes a fast matching atom’s searching algorithm by means of designating the max energy points of complex seismic signal, searching for the most optimal atom in the neighbor area of these points according to its instantaneous frequency and instantaneous phase, and this promotes the calculating efficiency of seismic signal’s matching pursuit algorithm. According to these methods proposed above, this paper implements them by programmed calculation, compares them with some open algorithm and proves this paper’s conclusions. It also testifies the active results of various methods by the processing of actual signals. The problems need to be solved further and the aftertime researching targets are as follows: continuously seeking for more efficient fast matching pursuit algorithm and expanding its application range, and also study the actual usage of matching pursuit method.

复杂介质边界元法数值模拟研究

A major impetus to study the rough surface and complex structure in near surface model is because accuracy of seismic observation and geophysical prospecting can be improved. Wave theory study about fluid-satuated porous media has important significance for some scientific problems, such as explore underground resources, study of earth's internal structure, and structure response of multi-phase porous soil under dynamic and seismic effect. Seismic wave numerical modeling is one of the effective methods which understand seismic propagation rules in complex media. As a numerical simulation method, boundary element methods had been widely used in seismic wave field study. This paper mainly studies randomly rough surface scattering which used some approximation solutions based on boundary element method. In addition, I developed a boundary element solution for fluid saturated porous media. In this paper, we used boundary element methods which based on integral expression of wave equation to study the free rough surface scattering effects of Kirchhoff approximation method, Perturbation approximation method, Rytov approximation method and Born series approximation method. Gaussian spectrum model of randomly rough surfaces was chosen as the benchmark model. The approximation methods result were compared with exact results which obtained by boundary element methods, we study that the above approximation methods were applicable how rough surfaces and it is founded that this depends on and ( here is the wavenumber of the incident field, is the RMS height and is the surface correlation length ). In general, Kirchhoff approximation which ignores multiple scatterings between any two surface points has been considered valid for the large-scale roughness components. Perturbation theory based on Taylor series expansion is valid for the small-scale roughness components, as and are .Tests with the Gaussian topographies show that the Rytov approximation methods improves the Kirchhoff approximation in both amplitude and phase but at the cost of an extra treatment of transformation for the wave fields. The realistic methods for the multiscale surfaces come with the Born series approximation and the second-order Born series approximation might be sufficient to guarantee the accuracy of randomly rough surfaces. It could be an appropriate choice that a complex rough surface can be divided into large-, medium-, and small-scale roughness components with their scattering features be studied by the Kirchhoff or Rytov phase approximations, the Born series approximation, and the perturbation theory, respectively. For this purpose, it is important to select appropriate parameters that separate these different scale roughness components to guarantee the divided surfaces satisfy the physical assumptions of the used approximations, respectively. In addition, in this paper, the boundary element methods are used for solving the porous elastic wave propagation and carry out the numerical simulation. Based on the fluid-saturated porous model, this paper analyses and presents the dynamic equation of elastic wave propagation and boundary integral equation formulation of fluid saturated porous media in frequency domain. The fundamental solutions of the elastic wave equations are obtained according to the similarity between thermoelasticity and poroelasticity. At last, the numerical simulation of the elastic wave propagation in the two-phase isotropic media is carried out by using the boundary element method. The results show that a slow quasi P-wave can be seen in both solid and fluid wave-field synthetic seismograms. The boundary element method is effective and feasible.

粘弹性介质中的地震波传播与波形反演研究

The real earth is far away from an ideal elastic ball. The movement of structures or fluid and scattering of thin-layer would inevitably affect seismic wave propagation, which is demonstrated mainly as energy nongeometrical attenuation. Today, most of theoretical researches and applications take the assumption that all media studied are fully elastic. Ignoring the viscoelastic property would, in some circumstances, lead to amplitude and phase distortion, which will indirectly affect extraction of traveltime and waveform we use in imaging and inversion. In order to investigate the response of seismic wave propagation and improve the imaging and inversion quality in complex media, we need not only consider into attenuation of the real media but also implement it by means of efficient numerical methods and imaging techniques. As for numerical modeling, most widely used methods, such as finite difference, finite element and pseudospectral algorithms, have difficulty in dealing with problem of simultaneously improving accuracy and efficiency in computation. To partially overcome this difficulty, this paper devises a matrix differentiator method and an optimal convolutional differentiator method based on staggered-grid Fourier pseudospectral differentiation, and a staggered-grid optimal Shannon singular kernel convolutional differentiator by function distribution theory, which then are used to study seismic wave propagation in viscoelastic media. Results through comparisons and accuracy analysis demonstrate that optimal convolutional differentiator methods can solve well the incompatibility between accuracy and efficiency, and are almost twice more accurate than the same-length finite difference. They can efficiently reduce dispersion and provide high-precision waveform data. On the basis of frequency-domain wavefield modeling, we discuss how to directly solve linear equations and point out that when compared to the time-domain methods, frequency-domain methods would be more convenient to handle the multi-source problem and be much easier to incorporate medium attenuation. We also prove the equivalence of the time- and frequency-domain methods by using numerical tests when assumptions with non-relaxation modulus and quality factor are made, and analyze the reason that causes waveform difference. In frequency-domain waveform inversion, experiments have been conducted with transmission, crosshole and reflection data. By using the relation between media scales and characteristic frequencies, we analyze the capacity of the frequency-domain sequential inversion method in anti-noising and dealing with non-uniqueness of nonlinear optimization. In crosshole experiments, we find the main sources of inversion error and figure out how incorrect quality factor would affect inverted results. When dealing with surface reflection data, several frequencies have been chosen with optimal frequency selection strategy, with which we use to carry out sequential and simultaneous inversions to verify how important low frequency data are to the inverted results and the functionality of simultaneous inversion in anti-noising. Finally, I come with some conclusions about the whole work I have done in this dissertation and discuss detailly the existing and would-be problems in it. I also point out the possible directions and theories we should go and deepen, which, to some extent, would provide a helpful reference to researchers who are interested in seismic wave propagation and imaging in complex media.