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Successful estimation of airgun‐array signatures from near‐field measurements depends on the accuracy of poorly controlled model parameters such as the effective sea surface reflection coefficient and source depth. We propose a method for prediction of robust source signatures, which are insensitive to fluctuations of the latter parameters. The method uses vertical pairs of near‐field hydrophones to measure near‐field pressure and its vertical gradient, combination of which eliminates sea surface reflections from the near‐field data. This excludes the uncertainty related to the fluctuating sea state and source depth from the process of inversion of the near‐field data for source signature. The method explicitly separates the recorded near‐field pressure into its up and down going components, which allows one to measure the effective frequency‐ and angle‐dependent sea surface reflection coefficient right at the source, as well as to estimate the actual source depth. Tests on synthetic and field data demonstrate robust performance of the method.

The imaging of steep salt boundaries has received much attention with the advent of improved wider azimuth acquisition designs and advanced imaging techniques such as reverse time migration (RTM), for example. However, despite these advancements in capability, there are cases in which the salt boundary is either poorly illuminated or completely absent in the migrated image. To provide a solution to this problem, we have developed two RTM methods for imaging salt boundaries, which use transmitted wavefields. In the first technique, downgoing waves, typically recorded in walkaway vertical seismic profile surveys, are used to image the salt flank via the generation of aplanatic isochrones. This image can be generated in the absence of an explicit interpretation of the salt flank using dual migration velocity models, as demonstrated on a 3D walkaway field data set from the Gulf of Mexico. In the second technique, we extend the basic theory to include imaging of upgoing source wavefields, which are transmitted at the base salt from below, as acquired by a surface acquisition geometry. This technique has similarities to the prism-imaging method, yet it uses transmitted instead of reflected waves at the salt boundary. Downgoing and upgoing methods are shown to satisfactorily generate an image of the salt flank; however, transmission imaging can create artifacts if reflection arrivals are included in the migration or the acquisition geometry is limited in extent. Increased wavelet stretch is also observed due to the higher transmission coefficient. An important benefit of these methods is that transmission imaging produces an opposite depth shift to errors in the velocity model compared with imaging of reflections. When combined with conventional seismic reflection surveys, this behavior can be used to provide a constraint on the accuracy of the salt and/or subsalt velocities.

Subsalt imaging in the Gulf of Mexico often suffers from illumination problems where various steep geologic features are not captured with conventional imaging techniques due to the lack of a direct wave path from the source to the steep reflector and back to the receiver. The exact geometry of these invisible salt flanks or salt welds is of great interest to interpreters during salt model building and prospect mapping. This paper discusses a suite of technologies that uses prism waves for imaging geologic interfaces with reverse time migration (RTM). Prism wave RTM imaging represents an example of imaging with multiples, Due to its specific geometric setup, it is often complementary to traditional RTMs. Specifically, the prism wave reflections can illuminate steep features that are invisible otherwise. Furthermore, by utilizing prism wave RTM in “reverse,” one can specify the steep event as the input prism wave generator (often a well-constrained salt boundary) and obtain an alternative (and perhaps cleaner) image of the sediment geometries next to this input event. In the industry, a lot of resources are spent on trying to improve illumination for the geologic features of interest by acquiring additional seismic surveys. With prism wave imaging, one can instead leverage the seismic signal that has already been recorded. We believe that even with moderate prism wave illumination uplift, the interpretive value gained can be quite large. To give the reader a glimpse of what is possible, we present several real data examples highlighting the utility of prism waves in interpretation.

Coherent states in imaginary time are used to represent the Boltzmann operator in terms of a classical chain of N coupled beads. The resulting representation is similar to the path integral molecular dynamics (PIMD) approach, except for additional nearest-neighbor coupling terms in the effective Hamiltonian. Each time step of the molecular dynamics evolution of the effective classical system provides appropriately thermalized Gaussians that can be used as distribution functions to sample initial conditions for real-time semiclassical initial value representation (IVR) methods. The approach is illustrated with numerical calculations of thermal expectation values and canonical time correlation functions for several one-dimensional quantum systems.

The second paper of the series discusses the effect of thermal noise o the stretching vibraional dynamics of symmetric triatomic ABA molecules. In particular, noise-induced transitions between symmetric and antisymmetric normal-mode vibrations are discussed, in the context of symmetry breaking of vibrational dynamics. The statistics of symmetry breaking transitions and the average lifetimes of normal modes of different symmetries are derived analytically and compared with direct numerical simulations. The average lifetimes of symmetric and antisymmetric normal modes are found to be inversely proportional to bath friction strength and depend on the dimensionless parameter κ which is the combination of bath temperature, bond anharmonicity and bond–bond coupling strength. Antisymmetric normal mode depends weakly on κ and is always stable. Symmetric normal mode depends significantly on κ and becomes unstable at κ = 1 . Higher temperatures destabilize symmetric normal mode and therefore decrease the ratio of symmetric-to-antisymmetric normal mode populations contrary to intuitive expectation.

The dissipative vibrational dynamics of a symmetric triatomic ABA molecule is extensively studied in a series of three papers. The momentum-dependent rotor model is used to describe the dynamical behavior of an ABA molecule with a single 1:1 nonlinear resonant coupling. Four characteristic modes, including symmetric normal modes, asymmetric normal modes, local modes, and quasi-local modes, are identified at different energy regimes. Under the influence of thermal noise, an ABA molecule switches between the four distinct modes intermittently along its dynamic trajectory, resulting in blinking of vibrational bond energy. The statistics of these dynamic transitions (i.e., "vibrational blinking") is obtained from numerical integration of stochastic equations in this paper and will be analyzed within the theoretical framework of noise-induced symmetry breaking and activated barrier crossing in the next two papers. This study demonstrates the rich dynamic behavior of a highly nonlinear system in a dissipative environment and is instructive for understanding the stability and stochasticity of energy localization in complex systems ranging from polyatomic molecules to nanostructures and micromechanical oscillators.

The paper discusses the effect of quantum chaos on photon-echo signals of two-electronic-state molecular systems. The temporal profile of photon-echo signals is shown to reveal key information about nuclear dynamics on the excited electronic state surface. Specifically, the suppression of echo signals at a particular value of the delay time tau1 between the first and second excitation pulses is demonstrated as a signature of quantum level statistics that corresponds to the classically chaotic nuclear motion in the excited electronic state surface.

© 2015 AIP Publishing LLC. Generalized nonlinear response theory is presented for stochastic dynamical systems. Experiments in which multiple measurements of dynamical quantities are used along with multiple perturbations of parameters of dynamical systems are described by generalized response functions (GRFs). These constitute a new type of multidimensional measures of stochastic dynamics either in the time or the frequency domains. Closed expressions for GRFs in stochastic dynamical systems are derived and compared with numerical non-equilibrium simulations. Several types of perturbations are considered: impulsive and periodic perturbations of temperature and impulsive perturbations of coordinates. The present approach can be used to study various types of stochastic processes ranging from single-molecule conformational dynamics to chemical kinetics of finite-size reactors such as biocells.

The semiclassical expression for the momentum autocorrelation function of a particle in a one-dimensional box is analyzed. The classical autocorrelation function is shown to be the first term of the semiclassical series. Systematical inclusion of all the terms restores quantum recurrence of the momentum autocorrelation function.

Primary H/D kinetic isotope effects for the [1,5] hydrogen shift reaction in 13-atomic 1,3-pentadiene and [1,7] hydrogen shift reaction in 23-atomic 7-methylocta-1,3,5-triene are calculated using the semiclassical instanton approach. All 33 and 63 internal degrees of freedom, respectively, are treated quantum mechanically with multidimensional tunneling automatically accounted for by the instanton approach. Reactive potential energy surfaces are calculated on-the-fly using mPW1K/6-31+G(d,p) and mPWB1K/6-31+G(d,p) electronic structure methods. The calculated kinetic isotope effects agree well with the previously reported experimental measurements. The analytical expressions of the semiclassical instanton approach allow one to determine quantitative contributions of various physical mechanisms to the calculated kinetic isotope effects. Multidimensional tunneling is found to play important role in both studied hydrogen shift reactions.

A theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuation-dissipation relations for steady-state chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided. © 2014 AIP Publishing LLC.

A new class of experiments is proposed which involve multiple measurements combined with multiple perturbations of a nonlinear classical complex system. A family of multipoint n + m − 1 dimensional measures R(n,m) that provide complimentary information on complex systems is obtained by combining m non linear stimuli and n measurements. They represent the combined effect of causal response and noncausal spontaneous fluctuations. The proposed signals can be measured either in the frequency domain or in the time domain. Generalized fluctuation-dissipation relations which hold in the nonlinear regime restrict the number of independent techniques. Two dimensional correlation plots derived from such measurements can reveal various types of couplings among collective modes.

The quantum-classical correspondence in the presence of dissipation is studied. The semiclassical expression for the linear response function of an anharmonic system is expressed in a series containing classical stability matrix elements, which can diverge due to the chaotic behavior of stochastic trajectories. The presence of dissipation in most cases removes the divergence of higher-order correction terms, thus suppressing quantum effects and making the system more classical. The regime of system-bath coupling, which makes quantum dynamics completely classical, is obtained in terms of friction, temperature, and anharmonicity. Special cases when bath coupling may lead to enhancement of quantum effects are discussed.

@Introduction.—Response theory predicts the response of a physical system to an external disturbance perturbatively and forms the theoretical basis of describing many experimental measurements. It was first pointed out by van Kampen that even a weak perturbation leads to the failure of classical nonequilibrium perturbation theory at sufficiently long times [1]. Despite this argument, the application of linear response theory does not lead to practical difficulties because phase-space averaging over the initial density matrix with Boltzmann distribution cancels the divergence at long times. Yet, thermal distribution may not remove the divergence of nonlinear response functions. The purpose of this Letter is to study the divergence of classical response functions of quasiperiodic systems. The analytical treatment of the behavior of the classical response function has not been studied except for a few exactly solvable anharmonic systems such as quartic [2] and Morse [3,4] oscillators, showing that in some cases classical response functions diverge at long times. However, the divergent behavior in the general case of systems with regular dynamics has not been systematically investigated. The proof of the divergence has important implications for the conceptual development of quantumclassical correspondence in response theory and can be established by employing the methods of Fourier expansion and asymptotic decomposition. The response function is well defined quantum mechanically in eigenstate space and is expressed by a set of nested commutators � � @

The correspondence principle between the quantum commutator $[\stackrel{^}{A},\stackrel{^}{B}]$ and the classical Poisson brackets $\ensuremath{\iota}\ensuremath{\hbar}{A,B}$ is examined in the context of response theory. The classical response function is obtained as the leading term of the $\ensuremath{\hbar}$ expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase without bound at long times as a result of ignoring divergent higher-order contributions. Systematical inclusion of higher-order contributions improves the accuracy of the $\ensuremath{\hbar}$ expansion at finite times. Resummation of all the higher-order terms establishes the classical-quantum correspondence $⟨v+n|\stackrel{^}{\ensuremath{\alpha}}(t)|v⟩\ensuremath{\leftrightarrow}{\ensuremath{\alpha}}_{n}{e}^{\ensuremath{\iota}n\ensuremath{\omega}t}{|}_{{J}_{v}+n\ensuremath{\hbar}/2}$. The time interval of the validity of the simple classical limit $[\stackrel{^}{A}(t),\stackrel{^}{B}(0)]\ensuremath{\rightarrow}\ensuremath{\iota}\ensuremath{\hbar}{A(t),B(0)}$ is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.

Time-divergence in linear and nonlinear classical response functions can be removed by taking a phase-space average within the quantized uncertainty volume O(hn) around the microcanonical energy surface. For a quasiperiodic system, the replacement of the microcanonical distribution density in the classical response function with the quantized uniform distribution density results in agreement of quantum and classical expressions through Heisenberg's correspondence principle: each matrix element (u/alpha(t)/v) corresponds to the (u-v)th Fourier component of alpha(t) evaluated along the classical trajectory with mean action (Ju+Jv)/2. Numerical calculations for one- and two-dimensional systems show good agreement between quantum and classical results. The generalization to the case of N degrees of freedom is made. Thus, phase-space averaging within the quantized uncertainty volume provides a useful way to establish the classical-quantum correspondence for the linear and nonlinear response functions of a quasiperiodic system.

The semiclassical instanton approach to the calculation of reaction rate constants at arbitrary temperatures in multiatomic systems is combined with high-level ab initio calculations of reactive potential energy surface (PES). The number of required ab initio calculations weakly depends on system size and allows on-the-fly evaluations of PES with high accuracy. The approach can be efficiently parallelized and provides a practical way of calculating quantum reaction rate constants with account of nuclear quantum effects such as multidimensional tunneling and zero point energies, which are rigorously incorporated in the theory. An algorithm for the search of instanton trajectories is explained. Application of the approach is illustrated for H + H(2) → H(2) + H and D + D(2) → D(2) + D bimolecular reactions in the wide temperature range with on-the-fly evaluation of PES at the ab initio full configuration interaction (FCI), coupled-cluster single double (CCSD), and single and double excitation configuration interaction (CISD) levels.

The semiclassical instanton approach discussed by Kryvohuz [J. Chem. Phys. 134, 114103 (2011)10.1063/1.3565425] is applied to calculate kinetic H/D isotope effect (KIE) of intramolecular hydrogen transfer in cis-1,3-pentadiene. All 33 vibrational degrees of freedom are treated quantum mechanically with semiclassical approximation. Nuclear quantum effects such as tunneling under the barrier and zero-point energy are automatically incorporated in the theory, and are shown to be responsible for the observed appreciable kinetic isotope effect in cis-1,3-pentadiene. Over the barrier passage is also automatically included. Numerical calculations are performed on an empirical valence bond potential energy surface and compared with the previous experimental and theoretical studies. An estimation of heavy-atom ^(12)C/^(13)C KIE in the same system is also provided and the factors contributing to it are discussed.

The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5–2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K.

A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top triatomic molecules observed numerically in classical molecular dynamics simulations of ozone. The Coriolis coupling is shown to result in an effective diffusive energy exchange between the rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the K-component of the rotational angular momentum that governs the diffusion.

A theory that describes the non-RRKM (non-Rice-Ramsperger-Kassel-Marcus) effects in the lifetime statistics of activated ozone molecules is derived. The non-RRKM effects are shown to originate due to the diffusive energy exchange between vibrational and rotational degrees of freedom in ozone molecule. The lifetime statistics is found to be intramolecular diffusion controlled at long times. The theoretical results are in good agreement with the direct MD simulations of lifetime statistics.