Strategies in Adjoint Tomography

Velocity anisotropy caused by fine layering has a strong effect on the travel paths at large vertical offsets in crosshole seismic data. This effect must be considered in seismic waveform tomography, so that the inversion procedure can match the waveforms in real data. In this paper, we propose to properly take into account this anisotropic effect in two stages. First, we invert for the anisotropy parameter simultaneously with the (horizontal) velocity in travel time tomography. Then we incorporate this estimated anisotropy parameter model in the waveform simulation during waveform tomography, to refine the velocity image. When considering this anisotropic effect, far-offset data are properly used in the inversion, then both travel time and waveform tomography may have a better ray coverage, producing a velocity image with a higher resolution.

We argue in this paper for a hierarchical approach for Full Waveform Inversion that begins with the establishment of “starting models” with traveltime tomography, proceeds to Acoustic Waveform Tomography, and will eventually lead on to Anisotropic, Visco-Elastic Waveform Tomography inversions. With each step increasingly accurate physical descriptions are invoked, more of the information content of the data is used, and the final results are correspondingly enhanced. The ultimate goal is “Full” Waveform Inversion, in which the full (anisotropic, 3D, visco-elastic) physics of the earth is incorporated and all parts of the waveform are utilized. Within the framework of Acoustic Waveform Tomography itself, we formulate 2 alternative approaches to the Laplace-Fourier domain formulation of waveform inversion: i) A conventional L2 misfit function, and ii) phase-only misfits derived from the logarithmic wavefield residuals. We apply these approaches to two real 2D data examples: Marine OBS data from the Nankai subduction zone, and land surface seismic data from the Canadian Foothills. We find in both data examples that the phase-only misfit outperforms the conventional L2 approach, and we suggest that this is due to increased ability of the phase-only approach to recover the low-wavenumber components of the model. We also find that a logarithmic phase-amplitude approach that provides a marginal improvement over the phase-only approach. Finally, we use point scattering responses and chequerboard tests to demonstrate the artefacts introduced by the use of an acoustic approach.

Time shift estimation is a key issue in many areas of seismic exploration such as time-lapse studies and traveltime tomography. Automated estimation is useful because it enables applications such as time strain analysis and automated velocity model building. A commonly used automated estimation algorithm is the windowed crosscorrelation. Unfortunately, this method can be inaccurate in areas where time shifts vary significantly over short intervals. Algorithms based on mismatch minimization have been proposed to remedy this problem. All the mentioned methods suffer from cycle skipping in the face of large time shifts. I, therefore, used the dynamic time warping (DTW) algorithm as an alternative method to estimate time shifts. I claimed the time shift estimates produced by DTW are of higher quality than those produced by the previous methods, especially with regard to the cycle-skipping problem. I found that DTW always is able to perfectly restore time shifts applied to traces when the changes are purely temporal. I investigated its accuracy when amplitude changes are present, and found that the algorithm is well suited for time-lapse analysis. Finally, we determined that DTW is resilient against cycle-skipping errors, in the presence of large time shifts and with significant changes in the data, and thus a candidate for use in automated velocity model-building methods, such as waveform tomography or full-waveform inversion.

Magnetic resonance imaging systems usually feature linear and shift-invariant (stationary) transform characteristics. The point spread function or equivalently the modulation transfer function may thus be used for an objective quality assessment of imaging modalities. The recently introduced theory of compressed sensing, however, incorporates nonlinear and nonstationary reconstruction algorithms into the magnetic resonance imaging process which prohibits the usage of the classical point spread function and therefore the according evaluation. In this work, a local point spread function concept was applied to assess the quality of magnetic resonance images which were reconstructed by an iterative soft thresholding algorithm for compressed sensing. The width of the main lobe of the local point spread function was used to perform studies on the spatial and temporal resolution properties of both numerical phantom and in vivo images. The impact of k-space sampling patterns as well as additional sparsifying transforms on the local spatial image resolution was investigated. In addition, the local temporal resolution of image series, which were reconstructed by exploiting spatiotemporal sparsity, was determined. Finally, the dependency of the local resolution on the thresholding parameter of the algorithm was examined. The sampling patterns as well as the additional sparsifying transform showed a distinct impact on the local image resolution of the phantom image. The reconstructions, which were using x-f-space as a sparse transform domain showed slight temporal blurring for dynamic parts of the imaged object. The local image resolution had a dependence on the thresholding parameter, which allowed for optimizing the reconstruction. Local point spread functions enable the evaluation of the local spatial and temporal resolution of images reconstructed with the nonlinear and nonstationary iterative soft thresholding algorithm. By determining the influence of thresholding parameter and sampling pattern chosen on this model-based reconstruction, the method allows selecting appropriate acquisition parameters and thus improving the results.

In order to reduce the RF power deposition of fast spin echo sequences operated at high field strength, the flip angles of the refocusing pulse train are varied from pulse to pulse using a modulated angle refocusing train method. The technique employs high flip angle pulses prior to sampling the center of k-space in order to preserve T(2) contrast, low flip angles after sampling the center of k-space to reduce power and prolong relaxation, and a smooth transition between the high and low flip angle regimes in order to maintain the pseudosteady-state, maximizing signal and avoiding artifact-inducing oscillations. An analytical expression is used to predict and correct for the flip angle dependence of the signal, thus eliminating any deleterious effects of flip angle modulation on the point spread function. Analysis of resolution and SNR were performed in simulation and phantom studies. In human imaging studies, it is shown that RF energy deposition per slice in a single-shot fast spin echo application can be reduced by up to 75%, making the sequence as practical at 3 T as it is has been at 1.5 T.

Application of 2D frequency-domain waveform tomography to a data set from a high-resolution vertical seismic profiling (VSP) experiment at a groundwater contamination site in Hill Air Force Base (HAFB), Utah, reveals a surprisingly complicated shallow substructure with a resolution of approximately 1.5 m. Variance in the waveform misfit function is reduced 69.4% by using an initial velocity model from first-arrival traveltime tomography. The waveform tomography model suggests (1) a low-velocity layer at 1 to 4 m depth, (2) a high-vertical-velocity gradient of 80 m/s/m on average, and (3) severe lateral variations — velocity contrasts as large as about 200 m/s occur in a distance as short as 1.5 m. The model is well correlated with lithologic logs and is interpreted geologically. A Q-value of 20 is estimated for the target area. The extreme lateral and vertical variations of the subsurface compromise many standard seismic processing methods.

GPR tomography is a useful tool for mapping the conductivity and permittivity distributions in the shallow subsurface. By exploiting the full GPR waveforms it is possible to image sub-wavelength features and improve resolution relative to what is possible using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of the final result, therefore limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal resolution and information content analysis. We present here a novel method for computing the sensitivity kernels (Jacobian matrix) based on an FDTD adjoint method. We show that the column sum of absolute values of the Jacobian, often used as a proxy for model resolution, is inadequate, such that a formal resolution analysis should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of the experiment and shows the extent of the unresolved model space.

The goal of tomography is to reconstruct a spatially-varying image function s(x,m), where x is position and m is a finite-length vector of parameters. Many reconstruction methods minimize the total L2 error E ≡ eTe, where individual errors ei quantify misfit between predictions and observations, to quantify goodness of fit. So-called adjoint state methods allow the gradient ∂E/∂mi to be computed extremely efficiently from an adjoint field, facilitating image reconstruction by gradient-descent methods. We examine the structure of the differential equation for the adjoint field under the ray approximation and find that it has the same form as the transport equation, whose solution involves the well-known geometrical spreading function R Consequently, as R is routinely tabulated as part of a ray calculation, no extra work is needed to compute the adjoint field, permitting a rapid calculation of the gradient ∂E/∂mi.

We have witnessed a transit of seismic tomography from ray-based traveltime inversion to wave equation-based waveform inversion during the past two decades. As is widely known, full waveform inversion outperforms traveltime tomography in resolving velocity variations with dimensions comparable and smaller than the dominant wavelength. However, this may not be always true in real practice, mainly due to the presence of unknown data noise, the lack of accurate initial models for the iterative inversion process (including material properties and source mechanisms), and the high demand for computational resources. Further efforts are required to develop techniques for using full waveform contents in seismic imaging studies, especially for the use of high-frequency waveform data (>1 Hz on regional scales). We have attempted to use common-source double-difference traveltime data in wave equation-based adjoint tomography studies of subsurface structures beneath Northeast Japan and Alaska. Because of the high level of waveform similarity, reliable common-source double-difference traveltime data at neighboring seismic stations are measured via cross-correlation approach. Insightful results are obtained. However, it is still computationally prohibitive to model high-frequency data by solving 3-D wave equations, limiting the resolution of seismic images. We admit that there is still a long way to go for the possible wide application of high-frequency full waveform inversion.Traveltime is the most reliable information that can be extracted from raw seismological recordings.  We have developed a new modality of seismic imaging, called adjoint-state traveltime tomography, to unleash the full potential of traveltime in imaging subsurface structures. To avoid potential failure of ray tracing in 3D complex media, isotropic eikonal equation and anisotropic eikonal equations are used to model seismic traveltime field in heterogenous and anisotropic media, and the associated inverse problems are solved by the efficient adjoint state method. No ray tracing is required for the novel adjoint-state traveltime tomography method. Importantly, the sensitivities of traveltime-related objective functions to material parameters can be accurately measured even in complex media. We view adjoint-state traveltime tomography as a new framework for seismic tomography, as it naturally implements various body wave and surface wave tomographic inversions in a very similar way. Good performances of the adjoint-state traveltime tomography method will be reported via various case studies in regions with typically different tectonic settings. It is worth noting that an accompanying software package, TomoATT, is under development.

Multi-robot path planning faces challenges such as conflict avoidance, collaboration, and dynamic environments. This paper proposes a multi-robot path planning algorithm that integrates the improved nutcracker optimization algorithm with the improved dynamic window approach. To address the nutcracker algorithm’s sensitivity to initial conditions and slow convergence, a population initialization strategy is introduced for more diverse initial populations. Additionally, a simplified path node strategy is also designed to shorten paths and reduce steering times. By incorporating a dynamic inertia weight factor , the balance between global exploration and local optimization is improved. To address the limitations of the dynamic window approach, which is unable to avoid dynamic obstacles instantly and is prone to falling into local optimal solutions, the target distance subfunction, the path evaluation subfunction and the deviation from danger zone subfunction are added to the evaluation function. Finally, the two algorithms were fused together and we conducted four experiments to validate the performance of the MANOA, IDWA, and MANOA-IDWA algorithms, as well as the application of MANOA-IDWA in multi-robot path planning. Results show that MANOA-IDWA significantly increases path planning success rates in dynamic environments, producing shorter and smoother paths, thus enhancing the safety and stability of multi-robot operations.

The spatial resolution of EEG/MEG source estimates, often described in terms of source leakage in the context of the inverse problem, poses constraints on the inferences that can be drawn from EEG/MEG source estimation results. Software packages for EEG/MEG data analysis offer a large choice of source estimation methods but few tools to experimental researchers for methods evaluation and comparison. Here, we describe a framework and tools for objective and intuitive resolution analysis of EEG/MEG source estimation based on linear systems analysis, and apply those to the most widely used distributed source estimation methods such as L2-minimum-norm estimation (L2-MNE) and linearly constrained minimum variance (LCMV) beamformers. Within this framework it is possible to define resolution metrics that define meaningful aspects of source estimation results (such as localization accuracy in terms of peak localization error, PLE, and spatial extent in terms of spatial deviation, SD) that are relevant to the task at hand and can easily be visualized. At the core of this framework is the resolution matrix, which describes the potential leakage from and into point sources (point-spread and cross-talk functions, or PSFs and CTFs, respectively). Importantly, for linear methods these functions allow generalizations to multiple sources or complex source distributions. This paper provides a tutorial-style introduction into linear EEG/MEG source estimation and resolution analysis aimed at experimental (rather than methods-oriented) researchers. We used this framework to demonstrate how L2-MNE-type as well as LCMV beamforming methods can be evaluated in practice using software tools that have only recently become available for routine use. Our novel methods comparison includes PLE and SD for a larger number of methods than in similar previous studies, such as unweighted, depth-weighted and normalized L2-MNE methods (including dSPM, sLORETA, eLORETA) and two LCMV beamformers. The results demonstrate that some methods can achieve low and even zero PLE for PSFs. However, their SD as well as both PLE and SD for CTFs are far less optimal for all methods, in particular for deep cortical areas. We hope that our paper will encourage EEG/MEG researchers to apply this approach to their own tasks at hand.

Crosscorrelation is a classical signal-processing technique that plays an important role in exploration and earthquake geophysics. Seismic velocity estimation utilizes the crosscorrelation between observed and predicted seismic records in traveltime tomography. The crosscorrelation between two stations represents the Green’s functions retrieved from ambient noises in passive seismic interferometry. It can be used to estimate the subsurface velocity and amplitude information. The calculation of crosscorrelation usually assumes that the input data are stationary; however, the real seismic data are often non-stationary, due to the presence of multiple wave-modes and background noises. The seismic crosscorrelations often have low signal-to-noise ratio and frequently fail to provide correct information for subsequent processing. To address this problem, we develop a comprehensive technique to reduce contamination and improve the quality of crosscorrelation in the wavelet domain. The new procedure includes the forward wavelet transformation of raw records, the crosscorrelation between wavelet coefficients, single-channel image object detection, multi-channel Kalman-filter object tracking, and inverse wavelet transformation to produce the new crosscorrelation gathers. We effectively remove the unwanted components associated with contaminated wave-modes as the proposed detection and tracking algorithm can accurately extract the target wave-mode. We validate the method for three datasets: a marine streamer survey, a borehole survey, and a broadband dataset from seismology stations. We demonstrate that the proposed method can significantly improve the signal-to-noise ratio of the seismic crosscorrelations, considerably enhancing the quality of the data for subsequent advanced crosscorrelation-based seismic processing.

<p>Southeast Asia is one of the most complex tectonic regions on Earth. This is mainly a result of its location within the triple junction of the Australian, Eurasian and Philippine Sea plates which has created a complicated configuration of active plate tectonic boundaries. Adjoint waveform tomography is especially suitable for imaging such complex regions. By simulating the 3D wavefield, it is possible to directly compare observed and simulated seismograms, thereby taking into account both body and surface waves. The method can account for the effects of anisotropy, anelasticity, wavefront healing, interference and (de)focusing that can hamper other seismological methods.</p><p>To date, sparse instrument coverage in the region has contributed to a heterogeneous path coverage. In this project, we make use of publicly available data as well as our recently deployed networks of broadband seismometers on Borneo and Sulawesi. This, in addition to access to national permanent networks, provides data from over 300 stations which promises a significant improvement in data coverage around the Banda Arc, Borneo and Sulawesi. We employ a geographical weighting scheme to minimise the effect of dense regional arrays and compile a catalogue of 118 well-constrained earthquakes, optimising for coverage, signal-to-noise ratio and data availability. An optimised window selection algorithm allows us to balance amplitude differences and include as much signal as possible while avoiding noisy data.</p><p>Here, we present a seismic waveform tomography for upper mantle structure in Southeast Asia, imaging radially anisotropic S velocity, P velocity and density. We use a gradient-based optimisation scheme (L-BFGS) and adjoint methods to obtain sensitivity kernels as the corresponding gradients. In the first part of the inversion, periods down to 50 s are used to update a 1D initial model, adapting a multi-scale approach in which long periods are inverted for first to avoid cycle skipping. In our long-period results, we observe a strong regional low S-velocity structure with an underlying high-velocity anomaly. The results are consistent with the global <em>S40RTS</em> model. </p>

Most of the optimization algorithm suffers from slow convergence and poor solution accuracy due to nonlinearity characteristics of the problem. This paper proposes a meta-heuristic method, namely the modified Ant Colony Optimization (m-ACO) technique to address these issues. The conventional ant colony optimization algorithm is improved by using multiple random initializations to increase the probability of getting a better start population and hence increase the possibility to achieve near-global optimum. The efficacy of the proposed algorithm is tested on classical benchmark functions and on the PID controllers. The performance of controllers depends on the selection of tuning parameters that are optimized to obtain an optimum solution. The m-ACO technique is used to optimize parameters of PID controller for Coupled Tank System. It is one of the benchmark control problems due to its nonlinear characteristics. The obtained results of the proposed algorithm are compared with the Zeigler Nichols tuned PID controller, and PSO tuned PID controller in terms of transient performances including rise-time, peak overshoot and performance parameters such as Integral Square Error (ISE) and Integral Absolute Error (IAE). The proposed method is also tested for showing effectiveness in set-point tracking and disturbance rejection.

Salp swarm algorithm (SSA) is a well-established population-based optimizer that exhibits strong exploration ability, but slow convergence and poor exploitation capability. In this paper, an endeavour is made to enhance the performance of the basic SSA. The new upgraded version of SSA named as ‘adaptive strategy-based SSA (ABSSA) algorithm’ is proposed in this paper. First, the exploratory scope and food source navigating commands of SSA are enriched using the inertia weight and boosted global best-guided mechanism. Next, a novel velocity clamping strategy is designed to efficiently stabilize the balance between the exploration and exploitation operations. In addition, an adaptive conversion parameter tactic is designed to modify the position update equation to effectively intensify the local exploitation competency and solution accuracy. The effectiveness of the proposed ABSSA algorithm is verified by a series of problems, including 23 classical benchmark functions, 29 complex optimization problems from CEC 2017, and five engineering design tasks. The experimental results show that the developed ABSSA approach performs significantly better than the standard SSA and other competitors. Moreover, ABSSA is implemented to handle path planning and obstacle avoidance (PPOA) tasks in autonomous mobile robots and compared with some swarm intelligent approach-based path planners. The experimental results indicate that the ABSSA-based PPOA method is a reliable path planning algorithm.