ALBERT

Description: This paper presents direct-seismogram inversion (DSI) for receiver-side structure which treats the source signal incident from below (the effective source–time function—STF) as a vector of unknown parameters in a Bayesian framework. As a result, the DSI method developed here does not require deconvolution by observed seismogram components as typically applied in receiver-function inversion and avoids the problematic issue of choosing subjective tuning parameters in this deconvolution. This results in more meaningful inversion results and uncertainty estimation compared to classic receiver-function inversion. A rigorous derivation is presented of the likelihood function required for unbiased inversion results. The STF is efficiently inferred by a maximum-likelihood closed-form expression that does not require deconvolution by noisy waveforms. Rather, deconvolution is only by predicted impulse responses for the unknown environment (considered to be a 1-D, horizontally stratified medium). For a given realization of the parameter vector which describes the medium below the station, data predictions are computed as the convolution of the impulse response and the maximum-likelihood source estimate for that medium. Therefore, the assumption of a Gaussian pulse with specified parameters, typical for the prediction of receiver functions, is not required. Directly inverting seismogram components has important consequences for the noise on the data. Since the signal processing does not require filtering and deconvolution, data errors are less correlated and more straightforward to model than those for receiver functions. This results in better inversion results (parameter values and uncertainties), since assumptions made in the derivation of the likelihood function are more likely to be met by the inversion process. The DSI method is demonstrated for simulated waveforms and then applied to data for station Hyderabad on the Indian craton. The measured data are inverted with both the new DSI and traditional receiver-function inversion. All inversions are carried out for a trans-dimensional model that treats the number of layers in the model as unknown. Results for DSI are consistent with previous studies for the same location. The DSI has clear advantages in trans-dimensional inversion. Uncertainty estimates appear more realistic (larger) in both model complexity (number of layers) and in terms of seismic velocity profiles. Receiver-function inversion results in more complex profiles (highly-layered structure) and suggests unreasonably small uncertainties. This effect is likely also significant when the parametrization is considered to be fixed but exacerbated for the trans-dimensional model: If hierarchical errors are poorly estimated, trans-dimensional models overestimate the structure which produces unfavourable results for the receiver-function inversion.

Description: Ultra-low velocity zones (ULVZs) are small-scale structures in the Earth's lowermost mantle inferred from the analysis of seismological observations. These structures exhibit a strong decrease in compressional ( P )-wave velocity, shear ( S )-wave velocity, and an increase in density. Quantifying the elastic properties of ULVZs is crucial for understanding their physical origin, which has been hypothesized either as partial melting, iron enrichment, or a combination of the two. Possible disambiguation of these hypotheses can lead to a better understanding of the dynamic processes of the lowermost mantle, such as, percolation, stirring and thermochemical convection. To date, ULVZs have been predominantly studied by forward waveform modelling of seismic waves that sample the core–mantle boundary region. However, ULVZ parameters (i.e. velocity, density, and vertical and lateral extent) obtained through forward modelling are poorly constrained because inferring Earth structure from seismic observations is a non-linear inverse problem with inherent non-uniqueness. To address these issues, we developed a trans-dimensional hierarchical Bayesian inversion that enables rigorous estimation of ULVZ parameter values and their uncertainties, including the effects of model selection. The model selection includes treating the number of layers and the vertical extent of the ULVZ as unknowns. The posterior probability density (solution to the inverse problem) of the ULVZ parameters is estimated by reversible jump Markov chain Monte Carlo sampling that employs parallel tempering to improve efficiency/convergence. First, we apply our method to study the resolution of complex ULVZ structure (including gradually varying structure) by probabilistically inverting simulated noisy waveforms. Then, two data sets sampling the CMB beneath the Philippine and Tasman Seas are considered in the inversion. Our results indicate that both ULVZs are more complex than previously suggested. For the Philippine Sea data, we find a strong decrease in S -wave velocity, which indicates the presence of iron-rich material, albeit this result is accompanied with larger parameter uncertainties than in a previous study. For the Tasman Sea data, our analysis yields a well-constrained S -wave velocity that gradually decreases with depth. We conclude that this ULVZ represents a partial melt of iron-enriched material with higher melt content near its bottom.

Description: Screening and isolation of a new Bacillus subtilis strain and production of its proteases for leather unhairing are described. B. subtilis strain BLBc 11 was isolated from the aerobic sludge of a tannery. Optimization of enzyme production by this bacterium was carried out using the Plackett-Burman and central composite design. Unhairing and inter-fibrillary removal capabilities were evaluated by scanning electron microscopy and determination of proteoglycans and glycosaminoglycans. Crude enzymatic extracts of B. subtilis BLBc 11 cultures were applied for the unhairing process of hides with excellent results, suggesting that this safe enzymatic preparation can replace the toxic chemicals commonly used in this process. The applicability of unpurified proteolytic extracts from microorganisms isolated from tannery sludge for unhairing of hides was investigated. The Bacillus subtilis BLBc 11 strain turned out to be an excellent producer of such enzymes with hide unhairing capabilities. This safe enzymatic preparation can replace the toxic chemicals commonly used in this process.

Description: Screening and isolation of a new Bacillus subtilis strain and production of its proteases for leather unhairing are described. B. subtilis strain BLBc 11 was isolated from the aerobic sludge of a tannery. Optimization of enzyme production by this bacterium was carried out using the Plackett-Burman and central composite design. Unhairing and inter-fibrillary removal capabilities were evaluated by scanning electron microscopy and determination of proteoglycans and glycosaminoglycans. Crude enzymatic extracts of B. subtilis BLBc 11 cultures were applied for the unhairing process of hides with excellent results, suggesting that this safe enzymatic preparation can replace the toxic chemicals commonly used in this process. The applicability of unpurified proteolytic extracts from microorganisms isolated from tannery sludge for unhairing of hides was investigated. The Bacillus subtilis BLBc 11 strain turned out to be an excellent producer of such enzymes with hide unhairing capabilities. This safe enzymatic preparation can replace the toxic chemicals commonly used in this process.

Description: This paper develops a probabilistic Bayesian approach to the problem of inferring the spatiotemporal evolution of earthquake rupture on a fault surface from seismic data with rigorous uncertainty estimation. To date, uncertainties of rupture parameters are poorly understood, and the effect of choices such as fault discretization on uncertainties has not been studied. We show that model choice is fundamentally linked to uncertainty estimation and can have profound effects on results. The approach developed here is based on a trans-dimensional self-parametrization of the fault, avoids regularization constraints and provides rigorous uncertainty estimation that accounts for model-selection ambiguity associated with the fault discretization. In particular, the fault is parametrized using self-adapting irregular grids which intrinsically match the local resolving power of the data and provide parsimonious solutions requiring few parameters to capture complex rupture characteristics. Rupture causality is ensured by parametrizing rupture-onset time by a rupture-velocity field and obtaining first rupture times from the eikonal equation. The Bayesian sampling of the parameter space is implemented on a computer cluster with a highly efficient parallel tempering algorithm. The inversion is applied to simulated and observed W-phase waveforms from the 2010 Maule (Chile) earthquake. Simulation results show that our approach avoids both over- and underparametrization to ensure unbiased inversion results with uncertainty estimates that are consistent with data information. The simulation results also show the ability of W-phase data to resolve the spatial variability of slip magnitude and rake angles. In addition, sensitivity to spatially dependent rupture velocities exists for kinematic slip models. Application to the observed data indicates that residual errors are highly correlated and likely dominated by theory error, necessitating the iterative estimation of a non-stationary data covariance matrix. The moment magnitude for the Maule earthquake is estimated to be ~8.9, with slip concentrated in two zones updip of and north and south of the hypocentre, respectively. While this aspect of the slip distribution is similar to previous studies, we show that the slip maximum in the southern zone is poorly resolved compared to the northern zone. Both slip maxima are higher than reported in previous studies, which we speculate may be due to the lack of bias caused by the regularization used in other studies.

Description: 〈span〉〈div〉SUMMARY〈/div〉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, 〈span〉M〈/span〉〈sub〉w〈/sub〉 = 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.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉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 which 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 non-linear 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 dataset we consider, uncertainty is low at the shallow portion of the fault and increase with depth. In addition, a simulation with a large station azimuthal gap of 180〈sup〉〈span〉o〈/span〉〈/sup〉 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 down dip, mainly in a oblique direction, which is poorly resolved compared to the main slip patch and may be an artifact. 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.〈/span〉

Description: 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.

Description: We have applied probabilistic inversion using a transdimensional hierarchical model to ocean-acoustic reflection measurements to recover shallow sediment structure including sound-velocity dispersion, frequency-dependent attenuation, and their uncertainties. Parameter and uncertainty inferences were obtained from Markov-chain simulations using the Metropolis-Hastings algorithm for transdimensional models where the number of sediment layers is unknown. Transdimensional algorithms often exhibit slow convergence that is greatly exacerbated by computationally intensive data predictions. Advances were made to improve the performance of Markov-chain simulation and data prediction. Chain-mixing across dimensions was addressed using a tempered sequence of interacting Markov chains, which substantially improves convergence rates. The acoustic recordings were processed to give seabed reflection coefficients as a function of frequency, grazing angle, and integration time (penetration depth). Such reflection-coefficient data cannot be generally described by plane-wave theory. Therefore, data were predicted using plane-wave decomposition and solving the Sommerfeld integral to compute spherical-wave reflection coefficients. This computationally intensive forward model was implemented massively in parallel using the compute unified device architecture on an inexpensive graphics processing unit, which substantially increases performance and allows transdimensional uncertainty estimation for complex layered seabeds. Velocity- and attenuation-frequency dependence were modeled using Buckingham’s viscous grain-shearing theory, which predicts frequency dependence similar to that of Biot’s theory at low frequencies but due to different physical causes. The algorithm was applied at two experiment sites off the coast of Sicily that exhibit different degrees of sediment complexity. The rigorous uncertainty estimation allows inferences that can distinguish between friction- and viscous-loss mechanisms in complex layered media. Results at both sites indicated dispersive sediments at some depths where the variability of velocity and attenuation as a function of frequency clearly exceeds the estimated uncertainties.

Description: Direct stacks of teleseismic waveforms recorded at a station have been used as an alternative to receiver functions for the retrieval of crustal 1D S -wave velocity models through inversion. Although they generally feature lower signal-to-noise ratios, their use has recently gained some attention because they do not rely on deconvolution. Avoiding deconvolution in waveform processing is a significant advantage for probabilistic (Bayesian) inversion methods that rely on a realistic assumption about the statistical distribution of waveform noise. However, the preservation of the effective source time function (STF) in the waveform data poses new challenges in the data processing. In this short note, we show that the simple technique that has been applied to directly stack waveforms to date lacks precision, because waveforms with emergent onsets or more complicated STFs are often stacked out of phase, which leads to artifacts in the stacked trace. We introduce a new cross-correlation-based stacking technique that avoids phase errors by stacking groups of mutually coherent traces and creating stacks for each of these families of traces. This separates the dataset into groups of events with similar STFs, which can be inverted jointly or separately. Electronic Supplement: Figure of stacks for four additional global stations.