We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high- and low-frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state-of-the-art schemes.

Distributed subsurface imaging is of high relevance for autonomous seismic surveys by multi-agent networks as envisioned for future planetary missions. The goal is to achieve a cooperative reconstruction of a subsurface image at each agent by relying on data exchange among the agents. To this end, distributed full waveform inversion for high-resolution imaging has been proposed. However, full waveform inversion always requires an initial model of the subsurface. To provide each agent in the network with such a model, we propose a distributed traveltime tomography. To this end, we integrate a distributed kernel-based regression of traveltime residuals into traveltime tomography. By that, each agent computes an approximation of all time residuals in the network and can perform a traveltime tomography to obtain a subsurface image locally. We conduct numerical evaluations for a synthetic subsurface model and the SEG salt model. The results show that each receiver indeed achieves a subsurface image that is close to the global result even for a low network connectivity.

Imaging the subsurface of extra-terrestrial bodies and planets has gained significant attention in recent space exploration missions. Multi-agent systems that autonomously perform subsurface imaging have been proposed. There, agents collaborate to image the subsurface by leveraging their wireless connections, enabling each agent to obtain an estimate of the subsurface image. However, traditional subsurface imaging techniques rely on a single entity for data collection and inversion, making them centralized schemes that limit direct availability of subsurface images at the agents. In this article, we propose the joint use of distributed seismic imaging techniques based on traveltime tomography and full waveform inversion, namely, the distributed traveltime tomography (D-TOMO) and the adapt-then-combine full waveform inversion (ATC-FWI). Combined in a sequential manner these techniques allow each agent to infer high-resolution subsurface images by exchanging data with their neighboring agents starting from a simple initial subsurface model. Unlike existing decentralized seismic imaging methods, our proposed scheme is fully distributed and provides flexibility without the need of anchor nodes or a full mesh topology. We demonstrate that ATC-FWI can recover high-frequency components based on a low-resolution subsurface image provided by D-TOMO in the initial stage. To assess the imaging performance, we employ a synthetic model, the SEG/EAGE salt model as well as real data from field measurements conducted over a tunnel.

Swarm exploration by multi-agent systems relies on stable inter-agent communication. However, so far both exploration and communication have been mainly considered separately despite their strong inter-dependency in such systems. In this paper, we present the first steps towards a framework that unifies both of these realms by a “tight” integration. We propose to make exploration “communication-aware” and communication “exploration-aware” by using tools of probabilistic learning and semantic communication, thus enabling the coordination of knowledge and action in multi-agent systems. We anticipate that by a “tight” integration of the communication chain, the exploration strategy will balance the inference objective of the swarm with exploration-tailored, i.e., semantic, inter-agent communication. Thus, by such a semantic communication design, communication efficiency in terms of latency, required data rate, energy, and complexity may be improved. With this in mind, the research proposed in this work addresses challenges in the development of future distributed sensing and data processing platforms—sensor networks or mobile robotic swarms consisting of multiple agents—that can collect, communicate, and process spatially distributed sensor data.

In this article, we describe in detail three seismic measurement campaigns based on refraction methods that we conducted at different sites in Bavaria, Germany. The measured data is published as an open data set. The particularity of this data set lies in its available ground truth information about each measurement site. Acquiring seismic data from sites with ground truth information is important for validation of seismic inversion algorithms. Since near-surface seismic field data with ground truth information is rather limited, we anticipate this data set to be a valuable contribution to the research community. For the measurements, three sites have been selected: (1) a gravel pit with a ground water layer, (2) a site above a highway tunnel and (3) a surface over underground tubes. The measurements have been conducted using line arrays of geophones, the Geode Seismograph from Geometrics Inc. and hammer strikes as seismic source. To obtain inversion results a travel time tomography based on first-arrivals within the software SeisImager is used. The inversion results show that we are able to image the ground water layer in the gravel pit, the highway tunnel and partly features of underground tubes. Furthermore, the results coincide with available ground truth information about the measurement sites. This paper summarizes the measurement campaigns and the respective data sets obtained through these campaigns. The data have been published by the authors as an open data set under the license CC BY 4.0 on figshare to make it available to the research community for validation of seismic data processing and inversion techniques.

This work discusses a variational Bayesian learning approach towards decentralized blind deconvolution of seismic signals within a sensor network. Blind seismic deconvolution is cast into a probabilistic framework based on Sparse Bayesian learning developed for blind image deconvolution. The posterior distribution of the signals of interest is then approximated using a variational Bayesian method. Depending on a particular form of selected variational factors, the scheme is shown to generalize the state-of-the-art distributed seismic blind deconvolution algorithm. The algorithm operates by repeatedly alternating between two stages: (i) estimation of seismic source wavelet and (ii) reflectivity estimation. The wavelet is computed in a distributed fashion using Alternating Direction Method of Multipliers. Based on this estimate each sensor then locally obtains a sparse reflectivity estimate. Numerical evaluation with synthetic seismic data shows that the proposed method outperforms existing deconvolution algorithms in the high signal-to-noise ratio (SNR) regime. In the low SNR regime a higher sensitivity of sparse Bayesian learning regarding model mismatches in the estimated source wavelet is observed. Also, processing of seismic data generated with an acoustic wave equation shows that the proposed method is able to recover the original reflectivities more accurately, with more distinct support of the reflectivities, as compared to existing methods despite present model mismatches. The algorithm is also applied to the estimation of real seismic data, and shows improved performance as compared to a state-of-the-art estimation method.