High-SNR Staining Algorithm for One-Way Wave Equation-Based Modelling and Imaging

Staining algorithms based on two-way wave equation migration methods have been applied to improve the signal-to-noise ratio (SNR) of poorly illuminated structures such as those in subsalt zones. In regular staining algorithms, when a source wavefield reaches the stained area that is associated with the target structures, a new wavefield called stained wavefield is excited, and this stained wavefield forward extrapolates synchronously with the real source wavefield. The forward-extrapolated stained and real source wavefields are cross-correlated with the backward-extrapolated receiver wavefield, and we obtain the stained and the real reverse time migration (RTM) images. The staining algorithms for RTM can suppress the noise of non-target regions and obtain high SNR images of the target structures. Whereas RTM methods are limited by the low computational efficiency and SNR, by contrast, one-way wave equation migration (OWEM) methods have the advantages of high efficiency and no interference from multiples. Thus, we developed a new staining method based on the generalised screen propagator (GSP) as a case of OWEM methods for subsalt imaging. Furthermore, a new stained wavefield called stained receiver wavefield is proposed here, forming two new staining strategies for seismic imaging, in which forward-propagated source and backward-propagated receiver wavefields can be conveniently selected to be stained at the stained area. Numerical experiments demonstrated that this staining GSP method is more effective in improving the SNR of subsalt structures compared to conventional GSP migration and RTM methods; moreover, these new staining strategies as applied to the OWEM methods can greatly improve the SNR of weakly illuminated structures in subsalt zones, in comparison with regular staining algorithms for one-way methods.     

Q Inversion and Comparison of Influential Factors among Three Methods: CFS,SR, and AA

The goals of this study were to examine factors influencing Q inversion and to provide references for practical application. Three different methods for inverting Q values with VSP data were explored, including centroid frequency shift (CFS), spectral ratio (SR), and amplitude attenuation (AA). Comparison between the CFS and the other two methods was conducted on frequency band widths and low attenuation, wavefield components, interface interference, and thin layers. Results from several sets of VSP modeling data indicated that the CFS method is more stable and accurate for dealing with thin and high Q layers. Frequency band width, especially the presence of high frequencies, influences the inversion effect of all three methods. The wider the band, the better the results. Q inversion from downgoing wavefield was very similar to that of the upgoing wavefield. The CFS method had fewer outliers or skip values from the full wavefield than the other two methods. Moreover, the applications to Q inversion for the set of field VSP data demonstrated that the Q curves from the CFS method coincided with the geological interpretations better than the Q curves of the other methods. Meanwhile, inverse Q filtering shifted the frequency component from 25 Hz to 35 Hz. The results demonstrated that the Q curve is more sensitive to geological horizons than velocity.     

Wave Propagation Simulation Using the CIP Method of Characteristic Equations

We apply the CIP (Cubic Interpolated Profile) scheme to the numerical simulation of the acoustic wave propagation based on characteristic equations.The CIP scheme is based on a concept that both the wavefield and its spatial derivative propagate along the same characteristic curves derived from a hyperbolic differential equation. We describe the derivation of the characteristic equations for the acoustic waves from the basic equations by means of the directional splitting and the diagonalization of the coefficient matrix, and establish geophysical boundary conditions. Since the CIP scheme calculates both the wavefield and its spatial derivatives, it is easy to realize the boundary conditions theoretically. We also show some numerical simulation examples and the CIP can simulate acoustic wave propagation with high stability and less numerical dispersion. The method of characteristics with the CIP scheme is a very powerful technique to deal with the wave propagation in complex geophysical problems.     

An Energy Regularization Method for the Backward Diffusion Problem and Its Applications to Image Deblurring

For the backward diffusion equation, a stable discrete energy regularization algorithm is proposed. Existence and uniqueness of the numerical solution are given. Moreover, the error between the solution of the given backward diffusion equation and the numerical solution via the regularization method can be estimated. Some numerical experiments illustrate the efficiency of the method, and its application in image deblurring.     

Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media

We generalize the existing distorted Born iterative T-matrix (DBIT) method to seismic full-waveform inversion (FWI) based on the scalar wave equation, so that it can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass densities and elastic stiffness tensors. The elastodynamic wave equation for an arbitrary anisotropic heterogeneous medium is represented by an integral equation of the Lippmann-Schwinger type, with a 9-dimensional wave state (displacement-strain) vector. We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory. This allows for domain decomposition and novel variational estimates. The tensorial nonlinear inverse scattering problem is solved iteratively by using an expression for the Fréchet derivatives of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green's functions and wave state vectors that are updated after each iteration. Since the generalized DBIT method is consistent with the Gauss-Newton method, it incorporates approximate Hessian information that is essential for the reduction of multi-parameter cross-talk effects. The DBIT method is implemented efficiently using a variant of the Levenberg-Marquard method, with adaptive selection of the regularization parameter after each iteration. In a series of numerical experiments based on synthetic waveform data for transversely isotropic media with vertical symmetry axes, we obtained a very good match between the true and inverted models when using the traditional Voigt parameterization. This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the use of suitable regularization methods. Since the generalized DBIT method for FWI in anisotropic elastic media is naturally target-oriented, it may be particularly suitable for applications to seismic reservoir characterization and monitoring. However, the theory and method presented here is general.     

An Application of the Level Set Method to Underwater Acoustic Propagation

An algorithm for computing wavefronts, based on the high frequency approximation to the wave equation, is presented. This technique applies the level set method to underwater acoustic wavefront propagation in the time domain. The level set method allows for computation of the acoustic phase function using established numerical techniques to solve a first order transport equation to a desired order of accuracy. Traditional methods for solving the eikonal equation directly on a fixed grid limit one to only the first arrivals, so these approaches are not useful when multi-path propagation is present. Applying the level set model to the problem allows for the time domain computation of the phase function on a fixed grid, without having to restrict to first arrival times. The implementation presented has no restrictions on range dependence or direction of travel, and offers improved efficiency over solving the full wave equation which under the high frequency assumption requires a large number of grid points to resolve the highly oscillatory solutions. Boundary conditions are discussed, and an approach is suggested for producing good results in the presence of boundary reflections. An efficient method to compute the amplitude from the level set method solutions is also presented. Comparisons to analytical solutions are presented where available, and numerical results are validated by comparing results with exact solutions where available, a full wave equation solver, and with wavefronts extracted from ray tracing software.     

Fourier analysis of airflow and transpulmonary pressure signals filtered on-line.

Airflow and transpulmonary pressure curves obtained from a normal man and a dog, during hyperventilation or when breathing spontaneously, were analysed on a digital computer by means of the fast Fourier transform. The same curves were also analysed after passing through an on-line RC filtering algorithm having cutoff frequencies extending from 10 down to 0.1562 Hz. Results show that respiratory parameters can contain a large amount of biological background noise mainly related to cardiovascular motion. The only instance in which the magnitude of fundamental harmonic was not the largest was for the airflow of the dog measured during spontaneous breathing. It was concluded that the cutoff frequency should be adjusted to a value 3-4 times that of the fundamental frequency. More pronounced filtering would cause important distortions of the physiologic signals.     

Source-Independent Amplitude-Semblance Full-Waveform Inversion Using a Hybrid Time- and Frequency-Domain Approach

Full-waveform inversion is a promising tool to produce accurate and high-resolution subsurface models. Conventional full-waveform inversion requires an accurate estimation of the source wavelet, and its computational cost is high. We develop a novel source-independent full-waveform inversion method using a hybrid time- and frequency-domain scheme to avoid the requirement of source wavelet estimation and to reduce the computational cost. We employ an amplitude-semblance objective function to not only effectively remove the source wavelet effect on full-waveform inversion, but also to eliminate the impact of the inconsistency of source wavelets among different shots gathers on full-waveform inversion. To reduce the high computational cost of full-waveform inversion in the time domain, we implement our new algorithm using a hybrid time- and frequency-domain approach. The forward and backward wave propagation operations are conducted in the time domain, while the frequency-domain wavefields are obtained during modeling using the discrete-time Fourier transform. The inversion process is conducted in the frequency domain for selected frequencies. We verify our method using synthetic seismic data for the Marmousi model. The results demonstrate that our novel source-independent full-waveform inversion produces accurate velocity models even if the source signature is incorrect. In addition, our method can significantly reduce the computational time using the hybrid time- and frequency-domain approach compared to the conventional full-waveform inversion in the time domain.     

Numerical Modeling of Anisotropic Elastic-Wave Sensitivity Propagation for Optimal Design of Time-Lapse Seismic Surveys

Reliable subsurface time-lapse seismic monitoring is crucial for many geophysical applications, such as enhanced geothermal system characterization, geologic carbon utilization and storage, and conventional and unconventional oil/gas reservoir characterization, etc. We develop an elastic-wave sensitivity propagation method for optimal design of cost-effective time-lapse seismic surveys considering the fact that most of subsurface geologic layers and fractured reservoirs are anisotropic instead of isotropic. For anisotropic media, we define monitoring criteria using qP- and qS-wave sensitivity energies after decomposing qP- and qS-wave components from the total elastic-wave sensitivity wavefield using a hybrid time- and frequency-domain approach. Geophones should therefore be placed at locations with significant qP- and qS-wave sensitivity energies for cost-effective time-lapse seismic monitoring in an anisotropic geology setting. Our numerical modeling results for a modified anisotropic Hess model demonstrate that, compared with the isotropic case, subsurface anisotropy changes the spatial distributions of elastic-wave sensitivity energies. Consequently, it is necessary to consider subsurface anisotropies when designing the spatial distribution of geophones for cost-effective time-lapse seismic monitoring. This finding suggests that it is essential to use our new anisotropic elastic-wave sensitivity modeling method for optimal design of time-lapse seismic surveys to reliably monitor the changes in subsurface reservoirs, fracture zones or target monitoring regions.     

A reflection scanning acoustic microscope for bone and bone-biomaterials interface studies

A relatively simple scanning acoustic microscope (SAM) that operates in the reflection mode has been constructed. The system uses a 20 MHz spherically focused transducer, acting both as transmitter and as detector, to obtain acoustic impedance information on a thin surface layer at a maximum resolution of approximately 100 micron. The specimen is mounted on an X-Y driving system (precision, 5 micron) under computer control in order to scan a grid of 256 x 256 points across areas ranging from 6.5 to 1300 mm2. An algorithm is used to reference the data against standards; specially developed software provides for pseudo-color mapping, three-dimensional images, zooming to 16 x magnification, contouring, and single line profiles of the data. The system has been used to determine inhomogeneities in surface acoustic properties of mineralized tissues and implant materials, in many cases as a complement to using ultrasonic wave propagation techniques to measure the bulk anisotropic properties.     

Primate Pleuroesophageal Tissue Barrier Frequency Response and Esophageal Pressure Waveform Bandwidth in Health and Acute Lung Injury

Background: Dynamic intraesophageal pressure (Pes) is used to estimate intrapleural pressure (Ppl) to calculate lung compliance and resistance. This study investigated the nonhuman primate Ppl-Pes tissue barrier frequency response and the dynamic response requirements of Pes manometers.

Methods: In healthy monkeys and monkeys with acute lung injury undergoing ventilation, simultaneous Ppl and Pes were measured directly to determine the Ppl-Pes tissue barrier amplitude frequency response, using the swept-sine wave technique. The bandwidths of physiologic Pes waveforms acquired during conventional mechanical ventilation were calculated using digital low-pass signal filtering.

Results: The Ppl-Pes tissue barrier is amplitude-uniform within the bandwidth of conventional Pes waveforms in healthy and acute lung injury lungs, and does not significantly attenuate Ppl-Pes signal transmission between 1 and 40 Hz. At Pes frequencies higher than conventional clinical regions of interest the Ppl-Pes barrier resonates significantly, is pressure amplitude dependent at low-pressure offsets, and is significantly altered by acute lung injury.

Allowing for 5% or less Pes waveform error, the maximum Pes bandwidths during conventional ventilation were 1.9 Hz and 3.4 Hz for physiologic and extreme-case waveforms in healthy lungs and 4.6 Hz and 8.5 Hz during acute lung injury.     

Higher-Order Rytov Approximation for Large-Scale and Strong Perturbation Media

In the field of geophysics, although the first-order Rytov approximation is widely used, the higher-order approximation is seldom discussed. From both theoretical analysis and numerical tests, the accumulated phase error introduced in the first-order Rytov approximation cannot be neglected in the presence of strong velocity perturbation. In this paper, we are focused on improving the phase accuracy of forward scattered wavefield, especially for the large-scale and strong velocity perturbation case. We develop an equivalent source method which can update the imaginary part of the complex phase iteratively, and the higher-order scattered wavefield can be approximated by multiplying the incident wavefield by the exponent of the imaginary part of the complex phase. Although the convergence of the proposed method has not been proved mathematically, numerical examples demonstrate that our method can produce an improved accuracy for traveltime (phase) prediction, even for strong perturbation media. However, due to the neglect of the real part of the complex phase, the amplitude change of the scattered wavefield cannot be recovered. Furthermore, in the presence of multi-arrivals phenomenon, the equivalent scattering source should be handled carefully due to the multi-directions of the wavefield. Further investigations should be done to improve the applicability of the proposed method.     

Design and optimization of a novel fast distributed Kalman consensus filtering algorithm

A new type of fast distributed Kalman consensus filtering algorithm based on local information feedback is presented to tackle filtering problems in wireless sensor networks. First, this fast filtering issues are transformed into a stochastic stability problem of the dynamic estimation errors, which can be solved by Lyapunov's second method and matrix theory. Then, two sufficient conditions about the proportional-like feedback (double gains regulation) method and incremental Proportional-Integral-Derivative (PID) feedback method for the asymptotical stability of the systems are presented, respectively. Moreover, to achieve a faster convergence rate, a novel optimal method is given by combing a genetic algorithm and incremental PID. Finally, an illustrative example is presented to give a comparison of the convergence speed between the three filtering algorithms in the same condition, and verify the effectiveness and advantage of the proposed theoretical results in this article.     

A New Coupled Complex Boundary Method for Bioluminescence Tomography

In this paper, we introduce and study a new method for solving inverse source problems, through a working model that arises in bioluminescence tomography (BLT). In the BLT problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal's body surface. The BLT problem possesses strong ill-posedness and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter for trade off between the accuracy and stability of approximate solutions. The new method is based on a combination of the boundary condition and the boundary measurement in a parameter-dependent single complex Robin boundary condition, followed by the Tikhonov regularization. By properly adjusting the parameter in the Robin boundary condition, we achieve two important properties for our new method: first, the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy; second, the convergence order of the regularized solutions reaches one with respect to the noise level. Then, the finite element method is used to compute numerical solutions and a new finite element error estimate is derived for discrete solutions. These results improve related results found in the existing literature. Several numerical examples are provided to illustrate the theoretical results.     

Concepts in the Direct Waveform Inversion (DWI) Using Explicit Time-Space Causality

The Direct Waveform Inversion (DWI) is a recently proposed waveform inversion idea that has the potential to simultaneously address several existing challenges in many full waveform inversion (FWI) schemes. A key ingredient in DWI is the explicit use of the time-space causality property of the wavefield in the inversion which allows us to convert the global nonlinear optimization problem in FWI, without information loss, into local linear inversions that can be readily solved. DWI is a recursive scheme which sequentially inverts for the subsurface model in a shallow-to-deep fashion. Therefore, there is no need for a global initial velocity model to implement DWI. DWI is unconditionally convergent when the reflection traveltime from the boundary of inverted model is beyond the finite recording time in seismic data. In order for DWI to work, DWI must use the full seismic wavefield including interbed and free surface multiples and it combines seismic migration and velocity model inversion into one process. We illustrate the concepts in DWI using 1D and 2D models.     

Truncated $L_1$ Regularized Linear Regression: Theory and Algorithm

Truncated $L_1$ regularization proposed by Fan in [5], is an approximation to the $L_0$ regularization in high-dimensional sparse models. In this work, we prove the non-asymptotic error bound for the global optimal solution to the truncated $L_1$ regularized linear regression problem and study the support recovery property. Moreover, a primal dual active set algorithm (PDAS) for variable estimation and selection is proposed. Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm (PDASC). Data-driven parameter selection rules such as cross validation, BIC or voting method can be applied to select a proper regularization parameter. The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set (bcTCGA).     

Underconnected, but how? A survey of functional connectivity MRI studies in autism spectrum disorders

Growing consensus suggests that autism spectrum disorders (ASD) are associated with atypical brain networks, thus shifting the focus to the study of connectivity. Many functional connectivity studies have reported underconnectivity in ASD, but results in others have been divergent. We conducted a survey of 32 functional connectivity magnetic resonance imaging studies of ASD for numerous methodological variables to distinguish studies supporting general underconnectivity (GU) from those not consistent with this hypothesis (NGU). Distinguishing patterns were apparent for several data analysis choices. The study types differed significantly with respect to low-pass filtering, task regression, and whole-brain field of view. GU studies were more likely to examine task-driven time series in regions of interest, without the use of low-pass filtering. Conversely, NGU studies mostly applied task regression (for removal of activation effects) and low-pass filtering, testing for correlations across the whole brain. Results thus suggest that underconnectivity findings may be contingent on specific methodological choices. Whereas underconnectivity reflects reduced efficiency of within-network communication in ASD, diffusely increased functional connectivity can be attributed to impaired experience-driven mechanisms (e.g., synaptic pruning). Both GU and NGU findings reflect important aspects of network dysfunction associated with sociocommunicative, cognitive, and sensorimotor impairments in ASD.     

Partially observed linear quadratic control problem with delay via backward separation method

In this paper, we study a partially observed linear quadratic optimal control problem derived by stochastic differential delay equations. Combining backward separation method with stochastic filtering, we obtain optimal feedback regulators in some special cases. Some filtering results for anticipated backward stochastic differential equations are also developed by expressing the solutions of the anticipated backward stochastic differential equations as some Itô's processes. Copyright © 2016 John Wiley & Sons, Ltd.     

Primate pleuroesophageal tissue barrier frequency response and esophageal pressure waveform bandwidth in health and acute lung injury

BACKGROUND: Dynamic intraesophageal pressure (Pes) is used to estimate intrapleural pressure (Ppl) to calculate lung compliance and resistance. This study investigated the nonhuman primate Ppl-Pes tissue barrier frequency response and the dynamic response requirements of Pes manometers. METHODS: In healthy monkeys and monkeys with acute lung injury undergoing ventilation, simultaneous Ppl and Pes were measured directly to determine the Ppl-Pes tissue barrier amplitude frequency response, using the swept-sine wave technique. The bandwidths of physiologic Pes waveforms acquired during conventional mechanical ventilation were calculated using digital low-pass signal filtering. RESULTS: The Ppl-Pes tissue barrier is amplitude-uniform within the bandwidth of conventional Pes waveforms in healthy and acute lung injury lungs, and does not significantly attenuate Ppl-Pes signal transmission between 1 and 40 Hz. At Pes frequencies higher than conventional clinical regions of interest the Ppl-Pes barrier resonates significantly, is pressure amplitude dependent at low-pressure offsets, and is significantly altered by acute lung injury. Allowing for 5% or less Pes waveform error, the maximum Pes bandwidths during conventional ventilation were 1.9 Hz and 3.4 Hz for physiologic and extreme-case waveforms in healthy lungs and 4.6 Hz and 8.5 Hz during acute lung injury. CONCLUSIONS: In monkeys, the Ppl-Pes tissue barrier has a frequency response suitable for Ppl estimation during low-frequency mechanical ventilation, and Pes manometers should have a minimum uniform frequency response up to 8.5 Hz. However, the Ppl-Pes tissue barrier adversely affects the accurate estimation of dynamic Ppl at high frequencies, with varied airway pressure amplitudes and offsets, such as the Ppl encountered during high-frequency oscillatory ventilation.