Simultaneous Sources Research Articles

NeRSI: Neural Implicit Representations for 5D Seismic Data Interpolation

Due to challenging field operations and resource constraints, seismic data acquisition often requires coping with missing traces. Interpolation algorithms are crucial for reconstructing these missing traces to enable improved subsurface analysis and interpretation. While deep learning has made exciting advances in seismic reconstruction, its focus has predominantly been on 2D and 3D datasets with relatively low rates of missing data. Five-dimensional (5D) seismic data reconstruction entails considering simultaneous sources and receivers deployed in areal arrays to solve the reconstruction problem. The latter offers greater data redundancy, which can be leveraged to enhance interpolation quality. Traditional 5D deep learning interpolation methods rely heavily on synthetic training pairs, posing challenges when applied to real-world data. This necessitates transfer learning techniques, which can be cumbersome. Addressing this, we introduce a self-supervised, coordinate-based deep interpolation algorithm that obviates the need for labeled data. Employing a multi-layer perceptron (MLP) network can effectively encode the continuous seismic wavefield inherent in 5D data. Once trained, the MLP can infer missing trace amplitudes from their coordinates. We contribute to boosting the MLP, enabling it to generate seismic profiles rather than single-point predictions. This enhancement significantly strengthens the model’s performance and efficiency. Moreover, we apply nuclear norm regularization to the output profiles, improving the reconstruction quality. The effectiveness of our algorithm is supported by both synthetic and field data experiments, demonstrating its superior reconstruction capabilities.

A mixed domain deblending approach for simultaneous source data based on deep learning

The simultaneous source acquisition technology breaks the limitations of traditional seismic survey, which allows more than one source to fire almost at the same time. When the survey time is fixed, simultaneous source acquisition can increase the number of sources, while when the number of sources is fixed, this technique can greatly reduce the survey time. At present, the great advantages of this high-efficiency acquisition technology have received wide attention from academia and industry, and researchers have proposed a series of deblending methods and obtained good results. In recent years, the rapid development of deep learning provides a new solution for deblending, and it has obvious advantages in computational time compared to traditional methods when processing large-scale seismic data. We proposed a novel iterative deblending method based on deep learning, which integrates the advantages of seismic data processing in different domains. In the proposed method, by selecting the appropriate combination of domains, the separation quality is significantly improved compared to the deblended results in a single domain. The effectiveness of the proposed method is verified by deblending the synthetic and field data, and the better performance of the proposed method are demonstrated by comparing it with the multilevel median filter method and conventional deep learning-based methods.

Synthesis of NIR/SWIR Absorbing InSb Nanocrystals Using Indium(I) Halide and Aminostibine Precursors

AbstractColloidal InSb quantum dots (QDs) are a potential alternative to toxic Pb‐ and Hg‐chalcogenide QDs for covering the technologically important near‐infrared/shortwave infrared (NIR/SWIR) spectral range. However, appropriate Sb precursors are scarce and obtaining narrow size distributions is challenging. Tris(dimethylamido)antimony (Sb(NMe2)3) is an appealing choice due to its commercial availability and non‐pyrophoric character but implies the reduction of antimony from the +3 to the required –3 state. In reported works, strong reducing agents such as lithium triethylborohydride are used, which lead to the fast co‐reduction of both Sb3+ and In3+. The downsides of this approach are reproducibility issues and the risk of forming metal nanoparticles due to the different reduction kinetics of Sb3+ and In3+. Here, indium(I) halides are explored as simultaneous indium source and mild reducing agent for the antimony precursor. The wavelength of the excitonic absorption peak of the phase‐pure InSb QDs obtained with this approach can be tuned from 630 to 1890 nm, which corresponds to a size range of ≈2–7 nm. The synthesis can also be conducted in a heat‐up manner, which facilitates the scale‐up and paves the way for the use of InSb QDs in applications such as NIR/SWIR photodetectors, cameras, biological imaging, and telecommunications.

The advantage of running a direct expansion CO2 heat pump with solar-and-air simultaneous heat sources: experimental and numerical investigation

Dual-source solar-air heat pumps represent a promising solution for overcoming the limitations associated with single-source utilization, thereby enhancing heat pump performance. However, running the heat pump by alternatively employing the more advantageous source requires the integration of a controller capable of continuously monitoring and predicting the heat pump's performance in response to dynamic environmental and operational variables. Even so, a selective alternate operation does not allow to get the maximum possible performance from the use of the two heat sources. A different approach to address this challenge is the simultaneous utilization of the two sources, by properly combining two evaporators in the CO2 circuit. This paper presents an experimental investigation of a dual-source heat pump using CO2 as refrigerant, which can operate in three different evaporation modes: air-mode (using a finned-coil evaporator), solar-mode (using a photovoltaic-thermal PV-T evaporator), and simultaneous-mode (using both the evaporators simultaneously). The novel solution presented here does not require to split the refrigerant flow rate between the two evaporators and at the same time it solves the problem of possible maldistribution at the inlet of the evaporators. Experimental data indicate that the heat pump operating in simultaneous-mode allows to increase the evaporation pressure and the coefficient of performance compared to operation in air-mode or solar-mode. The measurements have been employed for validating a model of the system, capable of predicting steady-state and dynamic performance under various environmental and operational conditions. Simulation results show that the simultaneous-mode operation can be outperformed by the solar-mode only at high irradiance and low air temperature, when the evaporation temperature gets higher than the air temperature. Finally, the impact of the number of PV-T collectors and solar irradiance on the heat pump performance has been simulated and discussed. On this regard, the simultaneous use of the two heat sources adds more flexibility to the system and its design, because even the availability of a small solar area can contribute enhancing the performance over the mere air source heat pump.

Simultaneous organic aerosol source apportionment at two Antarctic sites reveals large-scale and ecoregion-specific components

Abstract. Antarctica and the Southern Ocean (SO) are the most pristine areas of the globe and represent ideal places to investigate aerosol–climate interactions in an unperturbed atmosphere. In this study, we present submicrometer aerosol (PM1) source apportionment for two sample sets collected in parallel at the British Antarctic Survey stations of Signy and Halley during the austral summer of 2018–2019. Water-soluble organic matter (WSOM) is a major aerosol component at both sites (37 % and 29 % of water-soluble PM1, on average, at Signy and Halley, respectively). Remarkable differences between pelagic (open-ocean) and sympagic (influenced by sea ice) air mass histories and related aerosol sources are found. The application of factor analysis techniques to series of spectra obtained by means of proton-nuclear magnetic resonance (H-NMR) spectroscopy on the samples allows the identification of five organic aerosol (OA) sources: two primary organic aerosol (POA) types, characterized by sugars, polyols, and degradation products of lipids and associated with open-ocean and sympagic/coastal waters, respectively; two secondary organic aerosol (SOA) types, one enriched in methanesulfonic acid (MSA) and dimethylamine (DMA) and associated with pelagic waters and the other characterized by trimethylamine (TMA) and linked to sympagic environments; and a fifth component of unclear origin, possibly associated with the atmospheric aging of primary emissions. Overall, our results strongly indicate that the emissions from sympagic and pelagic ecosystems affect the variability in the submicrometer aerosol composition in the study area, with atmospheric circulation establishing marked latitudinal gradients only for some of the aerosol components (e.g., the sympagic components) while distributing the others (e.g., pelagic and/or aged components) both in maritime and inner Antarctic regions.

Simultaneous MEG and EEG source imaging of electrophysiological activity in response to acute transcranial photobiomodulation.

Transcranial photobiomodulation (tPBM) is a non-invasive neuromodulation technique that improves human cognition. The effects of tPBM of the right forehead on neurophysiological activity have been previously investigated using EEG in sensor space. However, the spatial resolution of these studies is limited. Magnetoencephalography (MEG) is known to facilitate a higher spatial resolution of brain source images. This study aimed to image post-tPBM effects in brain space based on both MEG and EEG measurements across the entire human brain. MEG and EEG scans were concurrently acquired for 6 min before and after 8-min of tPBM delivered using a 1,064-nm laser on the right forehead of 25 healthy participants. Group-level changes in both the MEG and EEG power spectral density with respect to the baseline (pre-tPBM) were quantified and averaged within each frequency band in the sensor space. Constrained modeling was used to generate MEG and EEG source images of post-tPBM, followed by cluster-based permutation analysis for family wise error correction (p < 0.05). The 8-min tPBM enabled significant increases in alpha (8-12 Hz) and beta (13-30 Hz) powers across multiple cortical regions, as confirmed by MEG and EEG source images. Moreover, tPBM-enhanced oscillations in the beta band were located not only near the stimulation site but also in remote cerebral regions, including the frontal, parietal, and occipital regions, particularly on the ipsilateral side. MEG and EEG results shown in this study demonstrated that tPBM modulates neurophysiological activity locally and in distant cortical areas. The EEG topographies reported in this study were consistent with previous observations. This study is the first to present MEG and EEG evidence of the electrophysiological effects of tPBM in the brain space, supporting the potential utility of tPBM in treating neurological diseases through the modulation of brain oscillations.

Least-squares reverse time migration of simultaneous sources with deep-learning-based denoising

Least-squares reverse time migration (LSRTM) is currently one of the most advanced migration imaging techniques in the field of geophysics. It uses least-squares inversion to fit the observed data, resulting in high-resolution imaging results with more accurate amplitudes and better illumination compensation than conventional reverse time migration (RTM). However, noise in the observed data and the Born approximation forward operator can result in high-wavenumber artifacts in the final imaging results. Moreover, iteratively solving LSRTM leads to one or two orders of computational cost higher than conventional RTM, making it challenging to apply extensively in industrial applications. Simultaneous source acquisition technology can reduce the computational cost of LSRTM by reducing the number of wavefield simulations. However, this technique also can cause high-wavenumber crosstalk artifacts in the migration results. To effectively remove the high-wavenumber artifacts caused by these issues, simultaneous source and deep learning are combined to speed up LSRTM as well as suppress high-wavenumber artifacts. A deep residual neural network (DR-Unet) is trained with synthetic samples, which are generated by adding field noise to synthesized noise-free migration images. Then, the trained DR-Unet is applied on the gradient of LSRTM to remove high-wavenumber artifacts in each iteration. Compared to directly applying DR-Unet denoising to LSRTM results, embedding DR-Unet denoising into the inversion process can better preserve weak reflectors and improve denoising effects. Finally, the proposed LSRTM method is tested on two synthetic data sets and a land data set. The tests demonstrate that the proposed method can effectively remove high-wavenumber artifacts, improve imaging results, and accelerate convergence speed.

Free-surface multiple attenuation and seismic deghosting for blended data using convolutional neural networks

Simultaneous source acquisition has become common over the past few decades for marine seismic surveys because of the increased efficiency of seismic acquisition by limiting the time, reducing the cost, and having less environmental impact than conventional single-source (or unblended) acquisition surveys. For simultaneous source acquisition, seismic sources at different locations are fired with time delays, and the recorded data are referred to as the blended data. The air-water interface (or free surface) creates strong multiples and ghost reflections for blended seismic data. The multiples and/or ghost reflections caused by a source in the blended data overlap with the primary reflections of another source, thus creating a strong interference between the primary and multiple events of different sources. We develop a convolutional neural network (CNN) method to attenuate free-surface multiples and remove ghost reflections simultaneously from the blended seismic data. The CNN-based solution that we develop operates on single traces and is not sensitive to the missing near-offset traces, missing traces, and irregular/sparse acquisition parameters (e.g., for ocean-bottom node acquisition and time-lapse monitoring studies). We illustrate the efficacy of our free-surface multiple attenuation and seismic deghosting method by presenting synthetic and field data applications. The numerical experiments demonstrate that our CNN-based approach for simultaneously attenuating free-surface multiples and removing ghost reflections can be applied to the blended data without the deblending step. Although the interference of primaries and multiples from different shots in the blended data makes free-surface multiple attenuation harder than the unblended data, we determine that our CNN-based method effectively attenuates free-surface multiples in the blended synthetic and field data even when the delay time for the blending is different in the training data than in the data to which the CNN is applied.

Evolutionary Games‐Assisted Synchronization Metasurface for Simultaneous Multisource Invisibility Cloaking

AbstractThe realization of a metasurface cloak for the simultaneous invisibility of multiple sources presents a long‐standing scientific challenge. Ideally, for the establishment of a simultaneous multisource invisibility cloak, the metasurface must provide a wide phase coverage and angular stability in a single architecture, especially for broadband, wide‐angle, and even omnidirectional scenarios. However, achieving this goal has proven to be elusive thus far. Current approaches for implementing metasurface‐based invisibility cloak involve both active and passive metasurface. These approaches often rely on phase‐compensation mechanisms, which inevitably encounter issues related to limited incidence angles or narrow working bands. Here, a novel paradigm of synchronization metasurface optimized through an evolution‐optimization strategy, enabling the realization of simultaneous multisource invisibility cloaking, is proposed. The underlying physics of the synchronization metasurface relies on an evolution‐optimization strategy (an evolutionary game algorithm), which is used to get rid of the entanglement between incident directions, frequencies, and metasurface phase gradients. Consequently, the synchronization metasurface is capable of manipulating simultaneous incoming waves at any angle over a wide range (cloak). In experimental validation, the synchronization metasurface demonstrates an impressive capability to cloak both single and simultaneous double sources in any direction, highly resembling background fields.

Robust multidimensional reconstruction via group sparsity with Radon operators

Seismic data processing, specifically tasks like denoising and interpolation, often hinges on sparse solutions of linear systems. Group sparsity plays an essential role in this context by enhancing sparse inversion. It introduces more refined constraints, which preserve the inherent relationships within seismic data. To this end, we propose a robust orthogonal matching pursuit algorithm, combined with Radon operators in the frequency-slowness [Formula: see text] domain, to tackle the strong group sparsity problem. This approach is vital for interpolating seismic data and attenuating erratic noise simultaneously. Our algorithm takes advantage of group sparsity by selecting the dominant slowness group in each iteration and fitting Radon coefficients with a robust [Formula: see text] norm using the alternating direction method of multipliers (ADMM) solver. Its ability to resist erratic noise, along with its superior performance in applications such as simultaneous source deblending and reconstruction of noisy onshore data sets, underscores the importance of group sparsity. Synthetic and real comparative analyses further demonstrate that strong group sparsity inversion consistently outperforms corresponding traditional methods without the group sparsity constraint. These comparisons emphasize the necessity of integrating group sparsity in these applications, thereby indicating its indispensable role in optimizing seismic data processing.

The Impact of Age-Related Hearing Loss on Working Memory among Older Individuals: An Event-Related Potential Study

Introduction: Age-related hearing loss (ARHL) may affect working memory (WM), which impacts problem-solving, decision-making, language comprehension, and learning. Limited research exists on how ARHL affects WM using N-back tasks, but studying this is crucial for understanding neural markers and associated cognitive processes. Our study explores the impact of ARHL on WM using behavioral and electrophysiological measures and how it correlates with speech-in-noise scores in older individuals with ARHL. Method: The study involved two groups, each with 20 participants aged 60–80. Group 1 had individuals with mild to moderate sensorineural hearing loss, while Group 2 had age- and education-matched controls with normal or near-normal hearing. Participants underwent audiological assessments and completed cognitive tests, including simple reaction time and N-back tests. During the performance of cognitive tasks, a simultaneous electroencephalography was recorded. Data analysis included behavioral and event-related potentials, source estimation, and functional connectivity analysis. Results: The study revealed significantly poor accuracy, longer reaction time, and smaller P300 amplitude among individuals with ARHL, even after controlling for general slowing. Individuals with ARHL experience compromised neural activity, particularly in the temporal and parietal regions, which are vital for cognition and WM. Furthermore, individuals with ARHL exhibited poor communication between the superior temporal gyrus and insulae regions among the brain regions mediating WM during the 1-back task. Also, the study found a strong correlation between hearing measures and WM outcomes. Conclusion: The study findings suggest that individuals with ARHL have impaired WM compared to those with normal hearing. This indicates a potential link between ARHL and cognitive decline, which could significantly affect daily life and quality of life. The widely used WM test with simultaneous EEG recording and source estimation analysis would further validate the usefulness of the study in assessing WM in this population.

Simultaneous Source Localization and Formation via a Distributed Sign Gradient-Free Algorithm

This paper develops a distributed sign gradient-free algorithm for simultaneous source localization and formation of a multi-robot system. A distinguished feature of the algorithm is that it takes into account robots' measure noise as well as ternary communication, which significantly reduces the communication cost of the overall network. Considering the presence of noise, the algorithm is designed to be gradient-free. In addition, an inherent connection is established between the selection of control parameters and the convergence property of the sign gradient-free algorithm, as well as signal strength, noisy intensity, formation radius, and the number of informed robots.

Neural-Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.

AWED: Asymmetric Wavelet Encoder–Decoder Framework for Simultaneous Gas Distribution Mapping and Gas Source Localization

AWED: Asymmetric Wavelet Encoder–Decoder Framework for Simultaneous Gas Distribution Mapping and Gas Source Localization

Exploring Background Noise With a Large‐N Infrasound Array: Waterfalls, Thunderstorms, and Earthquakes

AbstractAmbient infrasound noise contains an abundance of information that is typically overlooked due to limitations of typical infrasound arrays. To evaluate the ability of large‐N infrasound arrays to identify weak signals hidden in background noise, we examine data from a 22‐element array in central Idaho, USA, spanning 58 days using a standard beamforming method. Our results include nearly continuous detections of diverse weak signals from infrasonic radiators, sometimes at surprising distances. We observe infrasound from both local (8 km) and distant (195 km) waterfalls. Thunderstorms and earthquakes are also notable sources, with distant thunderstorm infrasound observed from ∼800 to 900 km away. Our findings show that large‐N infrasound arrays can detect very weak signals below instrument and environmental noise floors, including from multiple simultaneous sources, enabling new infrasound monitoring applications and helping map the composition of background noise wavefields.

A hybrid WUDT-NAFnet for simultaneous source data deblending

Simultaneous source technology, which reduces seismic survey time and improves the quality of seismic data by firing more than one source with a narrow time interval, is compromised by the massive blended interference. Therefore, deblending algorithms have been developed to separate this interference. Recently, deep learning (DL) has been proved its great potential in suppressing the interference. The most popular DL method employs neural network as a filter to attenuate the blended noise in an iterative estimation and subtraction framework (IESF). However, there are still amplitude distortion and blended noise residual problems, especially when dealing with weak signal submerged in strong interference. To address these problems, we propose a hybrid WUDT-NAFnet, which contains two sub-networks. The first network is a wavelet based U-shape deblending transformer network (WUDTnet), incorporated into IESF as a robust regularization term to iteratively separate the blended interference. The second network is a nonlinear activate free network (NAFnet) designed to recover the event amplitude and further suppress the weak noise residual in IESF. With the hybrid network, the blended noise can be separated purposefully and accurately. Examples using synthetic and field seismic data demonstrate that the WUDT-NAFnet outperforms traditional curvelet transform (CT) based method and the deblending transformer (DT) model in terms of deblending. Additionally, for field applications, the data augmentation method of bicubic interpolation is applied to mitigate the feature difference between synthetic and field data. Consequently, the trained network exhibits strong signal preservation ability in numerical field example without requiring additional training.

Simultaneous source separation and noise reduction with structure-oriented space-varying alpha-trimmed mean filter

Median filters are often used in simultaneous source data to remove sudden noise disturbances. Nonetheless, the median filter has a poor ability to process random noise, which can affect its performance in seismic data processing. This paper introduces a novel filtering method, a structure-oriented space-varying alpha-trimmed mean filter, which is an improvement of median filtering, and can deal with random noise better. The proposed filter's window length can be adaptively adjusted based on geological conditions, enabling the effective removal of spiky noise during simultaneous source acquisition and common random noise in geological exploration. This paper introduces the main differences between different types of median filtering methods and provides an overview of the principles and steps involved in our proposed approach. Our method's effectiveness is evaluated through its application to both simple synthetic examples and field data, alongside a comparative analysis against other existing approaches. The results of this research demonstrate that the approach we proposed here can efficiently make spike-like noise and random noise disappear while simultaneously maintaining vital signal characteristics.

A Convolutional Neural Network for Beamforming and Image Reconstruction in Passive Cavitation Imaging.

Convolutional neural networks (CNNs), initially developed for image processing applications, have recently received significant attention within the field of medical ultrasound imaging. In this study, passive cavitation imaging/mapping (PCI/PAM), which is used to map cavitation sources based on the correlation of signals across an array of receivers, is evaluated. Traditional reconstruction techniques in PCI, such as delay-and-sum, yield high spatial resolution at the cost of a substantial computational time. This results from the resource-intensive process of determining sensor weights for individual pixels in these methodologies. Consequently, the use of conventional algorithms for image reconstruction does not meet the speed requirements that are essential for real-time monitoring. Here, we show that a three-dimensional (3D) convolutional network can learn the image reconstruction algorithm for a 16×16 element matrix probe with a receive frequency ranging from 256 kHz up to 1.0 MHz. The network was trained and evaluated using simulated data representing point sources, resulting in the successful reconstruction of volumetric images with high sensitivity, especially for single isolated sources (100% in the test set). As the number of simultaneous sources increased, the network's ability to detect weaker intensity sources diminished, although it always correctly identified the main lobe. Notably, however, network inference was remarkably fast, completing the task in approximately 178 s for a dataset comprising 650 frames of 413 volume images with signal duration of 20μs. This processing speed is roughly thirty times faster than a parallelized implementation of the traditional time exposure acoustics algorithm on the same GPU device. This would open a new door for PCI application in the real-time monitoring of ultrasound ablation.

Deep learning for source localization and seabed classification under dynamic oceanographic environments using explosive sound signals

A deep-learning approach is proposed for simultaneous source localization and seabed classification of underwater signals generated by SUS (Signal, Underwater Sound) MK64 explosives. The charges were deployed in two separate shallow water acoustic experiments on the New England Mudpatch region in 2017 (SBCEX17) and 2022 (SBCEX22) conducted under different oceanographic conditions. The proposed approach uses a multitask learning (MTL) methodology, and convolutional neural networks (CNNs) trained on the spectrogram representation of SUS signals in the 10–199 Hz frequency band where the time-frequency modal dispersion curves exhibit distinct patterns. CNNs were trained on simulated data generated using the normal modes model, ORCA. This synthetic dataset is composed of several sound speed profiles measured in the water column in both experiments and representative seabeds ranging from muddy to sandy sediments. CNNs were tested on the signals measured in the two experiments where the source localization achieved a low mean squared error (0.35–0.8 km), and the seabed classification closely matched existing inversion results in the Mudpatch area. Notably, our method effectively handled oceanographic variations, showcasing the utilization of modal dispersion for training deep learning algorithms. [Work supported by ONR Grant N00014-21-1-2760.]

Machine Learning–Based Source Identification in Sewer Networks

Motivated by the valuable epidemiological information it reveals, wastewater surveillance has received significant attention in recent years. Furthermore, monitoring the water quality in sewer systems has been shown to provide useful information to support wastewater treatment operations. Yet, a critical need still exists for developing novel approaches for rapid and efficient source identification of chemical and biological species of interest in sewer systems. A limited number of source identification approaches have been proposed in previous literature, and the majority of these approaches employed various simplifying assumptions that limit their usage in real-life applications. In this study, a machine learning–based simulation-optimization framework was developed to determine the characteristics (i.e., concentration and loading pattern) of multiple simultaneous injection sources in sewer systems. The simulation was conducted using a surrogate model in the form of a multilayer perceptron neural network, which was trained using simulation results derived from the Storm Water Management Model (SWMM). The simulation model was then coupled with a genetic algorithm to reveal the characteristics of multiple sources that reproduce the concentration patterns observed at one or more monitoring locations in the sewer system. The proposed framework was applied to a range of injection scenarios and was able to identify the characteristics of multiple simultaneous injection sources under different conditions. The results showed that the residence time plays a significant role in the identifiability of the injection source location. The proposed framework is applicable to a wide number of source identification applications, including contamination source identification and wastewater-based epidemiology.