Highly efficient Bayesian joint inversion for receiver-based data and its application to lithospheric structure beneath the southern Korean Peninsula

With the deployment of extensive seismic arrays, systematic and efficient parameter and uncertainty estimation is of increasing importance and can provide reliable, regional models for crustal and upper-mantle structure.We present an efficient Bayesian method for the joint inversion of surface-wave dispersion and receiver-function data that combines trans-dimensional (trans-D) model selection in an optimization phase with subsequent rigorous parameter uncertainty estimation. Parameter and uncertainty estimation depend strongly on the chosen parametrization such that meaningful regional comparison requires quantitative model selection that can be carried out efficiently at several sites. While significant progress has been made for model selection (e.g. trans-D inference) at individual sites, the lack of efficiency can prohibit application to large data volumes or cause questionable results due to lack of convergence. Studies that address large numbers of data sets have mostly ignored model selection in favour of more efficient/simple estimation techniques (i.e. focusing on uncertainty estimation but employing ad-hoc model choices). Our approach consists of a two-phase inversion that combines trans-D optimization to select the most probable parametrization with subsequent Bayesian sampling for uncertainty estimation given that parametrization. The trans-D optimization is implemented here by replacing the likelihood function with the Bayesian information criterion (BIC). The BIC provides constraints on model complexity that facilitate the search for an optimal parametrization. Parallel tempering (PT) is applied as an optimization algorithm. After optimization, the optimal model choice is identified by the minimum BIC value from all PT chains. Uncertainty estimation is then carried out in fixed dimension. Data errors are estimated as part of the inference problem by a combination of empirical and hierarchical estimation. Data covariance matrices are estimated from data residuals (the difference between prediction and observation) and periodically updated. In addition, a scaling factor for the covariance matrix magnitude is estimated as part of the inversion. The inversion is applied to both simulated and observed data that consist of phase- and group-velocity dispersion curves (Rayleigh wave), and receiver functions. The simulation results show that model complexity and important features are well estimated by the fixed dimensional posterior probability density. Observed data for stations in different tectonic regions of the southern Korean Peninsula are considered. The results are consistent with published results, but important features are better constrained than in previous regularized inversions and are more consistent across the stations. For example, resolution of crustal and Moho interfaces, and absolute values and gradients of velocities in lower crust and upper mantle are better constrained

Probabilistic two dimensional joint water-column and seabed inversion

This paper develops a probabilistic two-dimensional (2D) inversion for geoacoustic seabed and water-column parameters in a strongly range-dependent environment. Range-dependent environments in shelf and shelf-break regions are of increasing importance t

Efficient Bayesian uncertainty estimation in linear finite fault inversion with positivity constraints by employing a log-normal prior

Obtaining slip distributions for earthquakes results in an ill-posed inverse problem. While this implies that only limited and uncertain information can be recovered from the data, inferences are typically made based only on a single regularized model. Here, we develop an inversion approach that can quantify uncertainties in a Bayesian probabilistic framework for the finite fault inversion (FFI) problem. The approach is suitably efficient for rapid source characterization and includes positivity constraints for model parameters, a common practice in FFI, via coordinate transformation to logarithmic space. The resulting inverse problem is nonlinear and the most probable solution can be obtained by iterative linearization. In addition, model uncertainties are quantified by approximating the posterior probability distribution by a Gaussian distribution in logarithmic space. This procedure is straightforward since an analytic expression for the Hessian of the objective function is obtained. In addition to positivity, we apply smoothness regularization to the model in logarithmic space. Simulations based on surface wave data show that smoothing in logarithmic space penalizes abrupt slip changes less than smoothing in linear space. Even so, the main slip features of models that are smooth in linear space are recovered well with logarithmic smoothing. Our synthetic experiments also show that, for the data set we consider, uncertainty is low at the shallow portion of the fault and increases with depth. In addition, a simulation with a large station azimuthal gap of 180° significantly increases the slip uncertainties. Further, the marginal posterior probabilities obtained from our approximate method are compared with numerical Markov Chain Monte Carlo sampling. We conclude that the Gaussian approximation is reasonable and meaningful inferences can be obtained from it. Finally, we apply the new approach to observed surface wave records from the great Illapel earthquake (Chile, 2015, Mw = 8.3). The location and amplitude of our inferred peak slip is consistent with other published solutions but the spatial slip distribution is more compact, likely because of the logarithmic regularization. We also find a minor slip patch downdip, mainly in an oblique direction, which is poorly resolved compared to the main slip patch and may be an artefact. We conclude that quantifying uncertainties of finite slip models is crucial for their meaningful interpretation, and therefore rapid uncertainty quantification can be critical if such models are to be used for emergency response

Time reverse imaging for far-field tsunami forecasting: 2011 Tohoku earthquake case study

This paper describes a new method for forecasting far-field tsunamis by combining aspects of least squares tsunami source inversion (LSQ) with time reverse imaging (TRI). This method has the same source representation as LSQ but uses TRI to estimate initial sea surface displacement. We apply this method to the 2011 Japan tsunami, and the results show that the method produces tsunami waveforms of excellent agreement with observed waveforms at both near- and far-field stations not used in the source estimation. The spatial distribution of cumulative sea surface displacement agrees well with other models obtained in more sophisticated inversions, but resolve source kinematics are not well resolved. The method has potential for application in tsunami warning systems, as it is computationally efficient and can be used to estimate the initial source model by applying precomputed Green's functions in order to provide more accurate and realistic tsunami predictions

Meso-Scale Seabed Quantification with Geoacoustic Inversion

Abstract Knowledge of sub-seabed geoacoustic properties, for example depth dependent sound speed and porosity, is of importance for a variety of applications. Here, we present a semi-automated geoacoustic inversion method for autonomous underwater vehicle data that objectively adapts model inference to seabed structure. Through parallelized trans-dimensional Bayesian inference, we infer seabed properties along a 12 km survey track on the scale of about 10 cm and 50 m in the vertical and horizontal, respectively. The inferred seabed properties include sound speed, attenuation, density, and porosity as a function of depth from acoustic reflection coefficient data. Parameter uncertainties are quantified, and the seabed properties agree closely with core samples at two control points and the layering structure with an independent sub-bottom seismic survey. Recovering high resolution seabed properties over large areas is shown to be feasible, which could become an important tool for marine industries, navies and oceanic research organizations

Strain-based forward modeling and inversion of seismic moment tensors using distributed acoustic sensing (DAS) observations

This study used a waveform inversion of distributed acoustic sensing (DAS) data, acquired in two horizontal monitoring wells, to estimate the moment tensor (MT) of two induced microearthquakes. An analytical forward model was developed to simulate far-field tangential strain generated by an MT source in a homogeneous and anisotropic medium, averaged over the gauge length along a fiber of arbitrary orientation. To prepare the data for inversion, secondary scattered waves were removed from the field observations, using f-k filtering and time-windowing. The modeled and observed primary arrivals were aligned using a cut-and-paste approach. The MT parameters were inverted via a least-squares approach, and their uncertainties were determined through bootstrap analysis. Using simulated data with additive noise derived from the field data and the same fiber configuration as the monitoring wells, the inversion method adequately resolved the MT. Despite the assumption of Gaussian noise, which underlies the least-squares inversion approach, the method was robust in the presence of heavy-tailed noise observed in field data. When the inversion was applied to field data, independent inversion results using P-waves, S-waves, and both waves together yielded results that were consistent between the two events and for different wave types. The agreement of the inversion results for two events resulting from the same stress field illustrated the reliability of the method. The uncertainties of the MT parameters were small enough to make the inversion method useful for geophysical interpretation. The variance reduction obtained from the data predicted for the most probable MT was satisfying, even though the polarity of the P-waves was not always correctly reproduced

Trans-Dimensional Geoacoustic Inversion of Wind-Driven Ambient Noise

This letter applies trans-dimensional Bayesian geoacoustic inversion to quantify the uncertainty due to model selection when inverting bottom-loss data derived from wind-driven ambient-noise measurements. A partition model is used to represent the seabed, in which the number of layers, their thicknesses, and acoustic parameters are unknowns to be determined from the data. Exploration of the parameter space is implemented using the Metropolis–Hastings algorithm with parallel tempering, whereas jumps between parameterizations are controlled by a reversible-jump Markov chain Monte Carlo algorithm. Sediment uncertainty profiles from inversion of simulated and experimental data are presented

A multi-centric dataset on patient-individual pathological lymph node involvement in head and neck squamous cell carcinoma

DATASET We provide a dataset on lymph node metastases in 968 patients with newly diagnosed head and neck squamous cell carcinoma (HNSCC). All patients received neck dissection and we report the number of metastatic versus investigated lymph nodes per lymph node level (LNL) for every individual patient. Additionally, clinicopathological factors including T-category, primary tumor subsite (ICD-O-3 code), age, and sex are reported for all patients. The data is provided as three datasets: Dataset 1 contains 373 HNSCC patients treated at Centre Léon Bérard (CLB), France, with primary tumor location in the oral cavity, oropharynx, hypopharynx, and larynx. Dataset 2 contains 332 HNSCC patients treated at the Inselspital, Bern University Hospital (ISB), Switzerland with primary tumor location in the oral cavity, oropharynx, hypopharynx, and larynx. For these patients, additional information is provided including lateralization of the primary tumor, size and location of the largest metastases, and clinical involvement based on computed tomography (CT), magnetic resonance imaging (MRI), and/or 18FDG-positron emission tomography (PET/CT) imaging. Dataset 3 consists of 263 oropharyngeal SCC patients underlying a previous publication by Bauwens et al. [1], which were treated at CLB. For these patients, additional information including HPV status, lateralization of the primary tumor and clinically diagnosed lymph node involvement is provided. REUSE POTENTIAL The data may be used to quantify the probability of occult lymph node metastases in each LNL, depending on an individual patient's characteristics of the primary tumor and the location of clinically diagnosed lymph node metastases. As such, the data may contribute to further personalize the elective treatment of the neck for HNSCC patients, i.e. definition of the elective clinical target volume (CTV-N) in radiotherapy (RT) and the extent of neck dissection (ND) in surgery. There exists only one similar publicly available dataset that reports clinical involvement per LNL in 287 oropharyngeal SCC patients [2]. The data presented in this article substantially extends the available data, it additionally includes pathologically assessed involvement per LNL, and it provides data for multiple subsites in the head and neck region

Modelling the lymphatic metastatic progression pathways of OPSCC from multi-institutional datasets.

The elective clinical target volume (CTV-N) in oropharyngeal squamous cell carcinoma (OPSCC) is currently based mostly on the prevalence of lymph node metastases in different lymph node levels (LNLs) for a given primary tumor location. We present a probabilistic model for ipsilateral lymphatic spread that can quantify the microscopic nodal involvement risk based on an individual patient's T-category and clinical involvement of LNLs at diagnosis. We extend a previously published hidden Markov model (HMM), which models the LNLs (I, II, III, IV, V, and VII) as hidden binary random variables (RVs). Each represents a patient's true state of lymphatic involvement. Clinical involvement at diagnosis represents the observed binary RVs linked to the true state via sensitivity and specificity. The primary tumor and the hidden RVs are connected in a graph. Each edge represents the conditional probability of metastatic spread per abstract time-step, given disease at the edge's starting node. To learn these probabilities, we draw Markov chain Monte Carlo samples from the likelihood of a dataset (686 OPSCC patients) from three institutions. We compute the model evidence using thermodynamic integration for different graphs to determine which describes the data best.The graph maximizing the model evidence connects the tumor to each LNL and the LNLs I through V in order. It predicts the risk of occult disease in level IV is below 5% if level III is clinically negative, and that the risk of occult disease in level V is below 5% except for advanced T-category (T3 and T4) patients with clinical involvement of levels II, III, and IV. The provided statistical model of nodal involvement in OPSCC patients trained on multi-institutional data may guide the design of clinical trials on volume-deescalated treatment of OPSCC and contribute to more personal guidelines on elective nodal treatment