Akaike Bayesian Information Criterion Research Articles

Characterizing the spatial correlation of coseismic slip distributions: A data driven Bayesian approach

Summary The spatial correlation of coseismic slip is a necessary input for generating stochastic seismic rupture models, which are commonly employed in seismic and tsunami hazard assessments. To date, the spatial correlation of individual earthquakes is characterized using finite fault models by finding the combination of parameters of a von Kármán autocorrelation function that best fits the observed autocorrelation function of the finite fault model. However, because a priori spatial correlation conditions (i.e., not in the data) are generally applied in finite fault model generation, the results obtained using this method may be biased. Additionally, robust uncertainty estimates for spatial correlations of coseismic slip are generally not performed. Considering these limitations in the classic method, here, a method is developed based on a Bayesian formulation of Finite Fault Inversion (FFI) with positivity constraints. This method allows for characterizing the spatial correlation of coseismic slip and its uncertainties for an earthquake by using samples of coseismic slip from a posterior probability density function (PDF). Furthermore, a Bayesian model selection criterion called Akaike Bayesian Information Criterion (ABIC) is applied to objectively choose between different prior spatial correlation schemes before computing the posterior, to reduce subjectivity due to this prior condition. The ABIC is calculated using an approximate analytical expression of Bayesian evidence. The method is applied to simulated P-waves, demonstrating that model selection allows for objectively estimating the most suitable prior spatial correlation scheme in FFI. Additionally, the target spatial correlation of coseismic slip is accurately recovered using samples from the posterior PDF, as well as their uncertainties. Moreover, in the simulated experiment, it is shown that a non-robust choice of the prior spatial correlation scheme can significantly bias the estimated spatial correlations of coseismic slip. We apply our method to observed P-waves from the 2015, Illapel earthquake (Mw = 8.3), finding that the spatial correlation of coseismic slip of this earthquake is better described by a von Kármán ACF, with mean correlation lengths of around 47 km and Hurst parameter of 0.58. We conclude that using our method reduces biases associated with prior spatial correlation conditions and allows for robust estimation of spatial correlations of coseismic slip and their uncertainties.

Spatial Heterogeneity of b Values in Northeastern Tibetan Plateau and Its Interpretation.

The northeastern margin of the Tibetan Plateau (NE Tibetan Plateau) exhibits active geological structures and has experienced multiple strong earthquakes, with M ≥ 7, throughout history. Particularly noteworthy is the 1920 M81/2 earthquake in the Haiyuan region that occurred a century ago and is documented as one of the deadliest earthquakes. Consequently, analyzing seismic risks in the northeastern margin of the Tibetan Plateau holds significant importance. The b value, a crucial parameter for seismic activity, plays a pivotal role in seismic hazard analyses. This study calculates the spatial b values in this region based on earthquake catalogs since 1970. The study area encompasses several major active faults, and due to variations in b values across different fault types, traditional grid-search methods may introduce significant errors in calculating the spatial b value within complex fault systems. To address this, we employed the hierarchical space-time point-process (HIST-PPM) method proposed by Ogata. This method avoids partitioning earthquake samples, optimizes parameters using Akaike's Bayesian Information Criterion (ABIC) with entropy maximization, and theoretically allows for a higher spatial resolution and more accurate b value calculations. The results indicate a high spatial heterogeneity in b values within the study area. The northwestern and southeastern regions exhibit higher b values. Along the Haiyuan fault zone, the central rupture zone of the Haiyuan earthquake has relatively higher b values than other regions of this fault zone, which is possibly related to the sufficient release of stress during the main rupture of the Haiyuan earthquake. The b values vary from high in the west to low in the east along the Zhongwei fault. On the West Qinling fault zone, the epicenter of the recent Minxian-Zhangxian earthquake is associated with a low b value. In general, regions with low b values correspond well to areas with moderate-strong seismic events in the past 50 years. The spatial differences in b values may reflect variances in seismic hazards among fault zones and regions within the same fault zone.

Present‐day Upper‐crustal Strain Rate Field in Southeastern Tibet and its Geodynamic Implications: Constraints from GPS Measurements with ABIC Method

AbstractThe Earth's surface kinematics and deformation are fundamental to understanding crustal evolution. An effective research approach is to estimate regional motion field and deformation fields based on modern geodetic networks. If the discrete observed velocity field is obtained, the velocity related fields, such as dilatation rate and maximum shear strain rate, can be estimated by applying varied mathematical approaches. This study applied Akaike's Bayesian Information Criterion (ABIC) method to calculate strain rate fields constrained by GPS observations in the southeast Tibetan Plateau. Comparison with results derived from other three methods revealed that our ABIC‐derived strain rate fields were more precise. The maximum shear strain rate highlighted the Xianshuihe–Xiaojiang fault system as the main boundary for the outward migration of material in southeastern Tibet, indicating rotation of eastern Tibet material around the eastern Himalaya rather than whole extrusion along a fixed channel. Additionally, distinct dilatation rate patterns in the northeast and southwest regions of the fault system were observed. The northeast region, represented by the Longmenshan area, exhibited negative dilatational anomalies; while the southwest region, represented by the Jinsha River area north of 29°N, displayed positive dilatational anomalies. This indicates compression in the former and extension in the latter. Combined with deep geophysical observations, we believe that the upper and lower crusts of the Jinsha River area north of 29°N are in an entire expanding state, probably caused by the escape‐drag effect of material. The presence of a large, low‐viscosity region south of 29°N may not enable the entire escape of the crust, but instead result in a differential escape of the lower crust faster than the upper crust.

Improvement of Seafloor Positioning Through Correction of Sound Speed Profile Temporal Variation

Dear Editor, This letter proposes a high-precision seafloor transponder positioning method based on the correction of sound speed profile (SSP) temporal variation. In the proposed method, the ocean sound speed error is modeled as the temporal variation of a background SSP, and the linearized expression of the acoustic travel time with respect to the sound speed coefficient is derived based on the ray acoustic model. Moreover, the proposed method introduces the constraint of acoustic ranging observations between seafloor transponders and determines the weights of travel time and ranging observations using Akaike's Bayesian information criterion (ABIC) to reduce the positioning error caused by the correlation between sound speed and position parameters. The experimental results in the South China Sea show that the proposed method performs better than the global navigation satellite system-acoustic ranging combined positioning solver (GARPOS) [1], in terms of rigid distance errors and long baseline positioning accuracy.

Source process of two Mw 6.9 aftershocks of the 2015 Mw 8.3 Illapel earthquake

The rupture of the September 16, 2015, Mw 8.3 Illapel earthquake extended over 200 km length along strike, where the southern portion of the rupture area is controlled tectonically by the collision of the Juan Fernandez Ridge at ∼32.5°S. On November 11th, two large aftershocks occurred in less than an hour, at shallow depths and epicenters closely located. Both events occurred beyond, but nearby, the northern limit of the Illapel rupture. We inverted kinematic rupture models by joint inversion of strong-motion and teleseismic body waves datasets. The Akaike's Bayesian Information Criterion (ABIC) was used to estimate the relative weighting between datasets, as well as the weighting of spatial and temporal constraints. The rupture of the first event propagated updip from the hypocenter, and later in a bilateral mode, with large slip to the south. The slip solution yields a total seismic moment of 4.44 × 1019 N m (Mw 7.0), and peak-slip of 0.82 m. The epicenter of the second event relocates 15 km southwest with respect to the first one. The rupture of the second event propagated mainly southwards and updip to the trench, re-rupturing an area already broken by the first event. The estimated seismic moment is 3.11 × 1019 N m (Mw 6.9), with a maximum slip of 0.59 m. The source durations from their respective moment-rate functions are 35 s, in both models. The spatial slip distribution retrieved for the two events suggests that the upper portion of the megathrust slipped, a region that is usually thought to behave aseismically, controlled by velocity-strengthening friction. We also relocated the earthquake catalog using a double-difference algorithm. The spatial distribution of seismicity shows clusters that are analyzed in different groups, and the most remarkable feature being a strip running parallel - and close by - to the trench region with very low seismicity. The majority of regional moment tensor solutions are thrust faulting mechanisms, and given the centroid depths retrieved, these events are consistent with interplate seismicity.

Joint inversion of GNSS and GRACE/GFO data for terrestrial water storage changes in the Yangtze River Basin

SUMMARYSatellite geodetic technologies, such as the Global Navigation Satellite System (GNSS), Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO), have complementary advantages in inferring terrestrial water storage (TWS) changes at regional and basin scales. We introduced a joint inversion strategy to infer TWS changes using GNSS- and GRACE/GFO-derived vertical displacements based on Green's function theory in the Yangtze River Basin (YRB) from January 2011 to December 2020. Additionally, we investigated the performance of variance component estimation (VCE) and Akaike's Bayesian Information Criterion (ABIC) to determine the optimal relative weights of different observation data. The performance of our joint inversion strategy was verified through a closed-loop simulation and multi-source hydrometeorological data [i.e. the time derivative of TWS changes (${\rm d}S/{\rm d}t$) from precipitation (P), evapotranspiration (ET) and run-off (R) based on the water balance equation, called P-ET-R]. The closed-loop simulation shows that the TWS changes from joint inversion have better consistencies with the synthetic signals than those of GNSS- and GRACE-only estimates, and the corresponding root mean square error (RMSE) decreased 1.43−6.28 mm and correlation coefficient (CC) increased 3−10 per cent. The ABIC was more suitable for the joint inversion of measured GRACE/GFO and GNSS data for TWS changes in the YRB. Analysis from the measured data shows that the spatial patterns and seasonal characteristics in TWS changes derived from GNSS, GRACE/GFO and their joint inversion are in good agreement in the YRB. The contribution of GNSS observations to the joint inversion in the upstream of the YRB is greater than that of GRACE/GFO due to the relatively densely distributed GNSS stations, but the opposite is true in the downstream. Furthermore, the joint inversion results have better agreements with P and P-ET-R compared to GNSS- and GRACE/GFO-only estimates in the upstream, and the corresponding CCs increased 5−7 per cent (for P) and 2−5 per cent (for P-ET-R), respectively, which further demonstrates the effectiveness of our joint inversion strategy. Our estimation strategy provides a new insight for joint inversion of GNSS and GRACE/GFO data to obtain more reliable TWS changes.

Applicability evaluation of Akaike’s Bayesian information criterion to covariance modeling in the cross-section adjustment method

The applicability of Akaike’s Bayesian Information Criterion (ABIC) to the covariance modeling in the cross-section adjustment method has been investigated. In the conventional cross-section adjustment method, the covariance matrices are assumed to be true. However, this assumption is not always appropriate. To improve the reliability of the cross-section adjustment method, the estimation of the covariance model using the metric ABIC has been introduced, and the performance of ABIC has been investigated through simple numerical experiments. This paper derives the formula to efficiently evaluate ABIC which is represented by a lower rank matrix to enable numerical experiments with large samples in a realistic computation time. From the results of the numerical experiments, it has been confirmed that ABIC tends to select a covariance model with fewer hyperparameters and a smaller variance for the estimation error. However, it has also been found that this desirable property of ABIC will be lost when the structure of the covariance model is far from the true one.

Anelastic deformation in the lower crust and its implications for tectonic dynamics in Kyushu, Southwest Japan

Most of the seismicity in inland Kyushu, southwest Japan occur in the localized intraplate shear zones which are Beppu-Shimabara Graben (BSG) and left-lateral shear zone (LSZ). One of the largest fault systems in Japan (Median Tectonic Line—MTL), and subduction zone of the Philippine Sea Plate also exist near Kyushu. These suggest that the island arc, such as Kyushu has a complex deformation process. This study estimated the anelastic strain rate in the lower crust and the interplate coupling rate via inversion analysis using Global Navigation Satellite System data to elucidate the seismotectonics. Deformation in the lower crust and interplate coupling were modeled by cuboid volumetric sources and a back slip model, respectively. To stabilize the solution, a L2 regularization constraint was applied to the anelastic strain rate. Further, constraints on direction and smoothing to the slip deficit rate were applied. These strength of the constraints were determined via the minimum value of the Akaike Bayesian information criterion. The analyses showed that the anelastic strain rate of the BSG and LSZ was ∼0.6 ×10−6 yr−1, and BSG was related to MTL activity. The findings also suggest that this anelastic deformation in the lower crust created a stress concentration zone in the upper crust of BSG and LSZ, with a stress change rate of ∼6–10 kPa·yr−1. The value is consistent with the stress drop and recurrence interval of regional earthquakes, suggesting that the seismicity around BSG and LSZ is strongly influenced by anelastic deformation in the lower crust. It is also suggested that BSG and LSZ development is influenced by slab rollback, and a subducting ridge. Lastly, a comparison between the deviatoric stress field estimated using focal mechanisms and the anelastic strain rate suggests the existence of a shear zone consisting of weak faults south of BSG.

A New Method Applied for the Determination of Relative Weight Ratios Under the TensorFlow Platform When Estimating Coseismic Slip Distribution

AbstractWhen estimating a coseismic slip distribution with multiple observation types, the relative weight ratios (the contribution ratios of all kinds of actual observations in the joint inversion, which should be positive by default) and regularization parameter critically impact the inversion accuracy. In this paper, we propose a new method for determining the relative weights of multiple observations of jointing inversion slip distributions. This method regards the observations and the relative weight ratios as the training data sets and training parameters, respectively; in addition, the constructed function was optimized by the gradient descent method and the exponential decay learning rate method under the TensorFlow platform (GDED). We compared the GDED method with the Helmert variance component estimation method (HVCE) and Akaike's Bayesian information criterion method (ABIC) by designing eight simulation experiments. These simulations included changing the errors and resolutions of the observations, the grid size, the strike angle and the dip angle of the fault, the moment magnitudes of earthquakes, the number of observation types, and the complexity of subduction‐zone earthquakes. We analyzed and discussed the characteristics of the above three methods in determining the relative weight ratios during the joint inversion process. The results of these simulation experiments showed that the GDED method and the ABIC method perform much better than the HVCE method when negative variance occurs in the HVCE method, while the accuracies of the slip distributions produced by the three methods were similar when no negative variance occurred; the GDED method can be used to prevent the occurrence of negative variance compared to the HVCE method and is more time efficient than the ABIC method. Furthermore, we applied these methods to invert the source parameters of the 2015 Mw 8.3 Illapel earthquake (in Chile), and the inversion results showed that the slip of the Illapel earthquake was mainly distributed at depths of approximately 10–50 km. The maximum slip of the Illapel earthquake was approximately 7.9 m, distributed 50–70 km northwest of the epicenter at depths of approximately 10–20 km.

Tectonic stress fields inferred from long-term CMT data ranging over different periods

SUMMARYWe have developed an inversion method for estimating 3-D tectonic stress fields from centroid moment tensor (CMT) data of seismic events. To obtain reliable inversion analysis results, we need to use as much data as possible, ranging over different periods. In this study, we improved the previously developed CMT data inversion method to incorporate preceding inversion analysis results into the present analysis as direct prior information about the stress field. The spatial distribution of seismic events and/or their focal mechanisms in a region would change from one period to another, reflecting temporal stress changes there. In the improved inversion method, in addition to the hyperparameter controlling the roughness of stress fields, we introduced another hyperparameter that controls the relative weight of direct prior information to the observed data to be analysed. The relative weights of direct and indirect prior information to the observed data are appropriately determined by using Akaike's Bayesian Information Criterion. We applied the improved inversion method to the observed CMT data of seismic events of 24 yr (1997−2020) in northeast Japan, where the Tohoku-oki megathrust event (Mw 9.0) occurred on 11 March 2011 at the North American–Pacific Plate boundary. To investigate temporal changes in tectonic stress orientation, we divided the target period into the inter-, pre- and post-seismic periods of the megathrust event: P1 (January 1997−January 2007), P2 (February 2007−February 2011), and P3 (March 2011−December 2020). According to successive inversion analysis results for P1 and P2, we confirmed that the tectonic stress orientation was stable for 14 yr before the megathrust event. On the other hand, successive inversion analysis results for P2 and P3 indicated a possibility that the 2011 megathrust event caused significant changes in tectonic stress orientation in three regions. However, two of them were negative in the quantitative evaluation of the reliability of detected temporal changes. In conclusion, the stress orientation change in the region off Fukushima and Ibaraki, the southern margin of the main rupture area of the megathrust event, seems to be real.

Plate‐Locking, Uncertainty Estimation and Spatial Correlations Revealed With a Bayesian Model Selection Method: Application to the Central Chile Subduction Zone

AbstractInversions of geodetic data are regularly used to estimate interseismic locking in subduction zones. However, the ill‐posed nature of these problems motivates us to include prior information, physically consistent with processes of the subduction seismic cycle. To deal with model instabilities, we present an inversion method to estimate both plate‐locking and model uncertainties by inverting Global Navigation Satellite System derived velocities based on a Bayesian model selection scheme. Our method allows us to impose positivity constraints via a multivariate folded‐normal distribution, with a specified covariance matrix. Model spatial correlations are explored and ranked to find models that best explain the observed data and for a better understanding of locking models. This approach searches for hyperparameters of the prior joint multivariate probability density function (PDF) of model parameters that minimize the Akaike Bayesian Information Criterion (ABIC). To validate our approach, we invert synthetic displacements from analytic models, yielding satisfactory results. We then apply the method to estimate the plate‐locking in Central Chile (28°–39°S) and its relation to the coseismic slip distribution of earthquakes with magnitudes Mw > 8.0, on the subduction zone since 2010. We also search among different prior PDFs for a single ductile‐fragile limit depth. Our results confirms a spatial correlation between locked asperities and the 2010 Mw 8.8 Maule and 2015 Mw 8.3 Illapel earthquake rupture zones. The robustness of our locking model shows potential to improve future seismic and tsunami hazard estimations.

Simultaneous calibration of instrument scale factor and drift rate in network adjustment for continental-scale gravity survey campaign

SUMMARY The scale factor of each relative gravimeter must be calibrated both before and after the fieldwork of a terrestrial gravity survey, to reduce uncertainties and ensure high precision. Conventionally, such calibration is a time-consuming process performed following well-established baselines. We propose a new Bayesian method to estimate the scale factor in a hybrid gravity network that includes several absolute gravity observation stations. In this approach, the scale factor is estimated as a hyperparameter using the Akaike Bayesian information criterion and using known absolute gravity stations in the network or/and calibrated instruments as constraints. Testing the sensitivity of the gravity values and the residuals of the gravity difference between two successive stations to the change of the scale factor demonstrates the robustness of this method. We also test the sensitivity of the estimated scale factor in the presence of Gaussian noise and the non-linear instrumental drift rate. Moreover, if the maximum absolute gravity interval is greater than 60 per cent of the range of gravity values in the network, or if the known scale factors of calibrated gravimeters are well calibrated, this approach can provide reasonable estimates of the daily drift rate and the unknown scale factors, where the latter has an error of <3 × 10−5. We apply this approach to real gravity campaign data from Yunnan in China and use a cross-validation method to compare estimated gravity values and corresponding gravity values obtained from absolute gravity observations at the same stations, to validate how the proposed method improves estimation accuracy of the gravity value at each station.

Consistent estimation of strain-rate fields from GNSS velocity data using basis function expansion with ABIC

Present day crustal displacement rates can be accurately observed at stations of global navigation satellite system (GNSS), and crustal deformation has been investigated by estimating strain-rate fields from discrete GNSS data. For this purpose, a modified least-square inversion method was proposed by Shen et al. (J Geophys Res 101:27957–27980, 1996). This method offers a simple formulation for simultaneously estimating smooth velocity and strain-rate fields from GNSS data, and it has contributed to clarify crustal deformation fields in many regions all over the world. However, we notice three theoretical points to be examined when we apply the method: mathematical inconsistency between estimated velocity and strain-rate fields, difficulty in objectively determining the optimal value of a hyperparameter that controls smoothness, and inappropriate estimation of uncertainty. In this study, we propose a method of basis function expansion with Akaike’s Bayesian information criterion (ABIC), which overcomes the above difficulties. Application of the two methods to GNSS data in Japan reveals that the inconsistency in the method of Shen et al. is generally insignificant, but could be clear in regions with sparser observation stations such as in islet areas. The method of basis function expansion with ABIC shows a significantly better performance than the method of Shen et al. in terms of the trade-off curve between the residual of fitting and the roughness of velocity field. The estimated strain-rate field with the basis function expansion clearly exhibits a low strain-rate zone in the forearc from the southern Tohoku district to central Japan. We also find that the Ou Backbone Range has several contractive spots around active volcanoes and that these locations well correspond to the subsidence areas detected by InSAR after the 2011 Tohoku-oki earthquake. Thus, the method of basis function expansion with ABIC would serve as an effective tool for estimating strain-rate fields from GNSS data.

Crustal strain-rate fields estimated from GNSS data with a Bayesian approach and its correlation to seismic activity in Mainland China

We propose a new Bayesian approach to estimate continuous crustal strain-rate fields from spatially discrete displacement-rate data, based on Global Navigation Satellite System (GNSS) observations, under the prior constraint on spatial flatness of the strain-rate fields. The optimal values of the hyperparameters in the model of strain-rate fields are determined by using Akaike's Bayesian Information Criterion. A methodological merit of this approach is that, by introducing a two-layer Delaunay tessellation technique, the time-consuming computation of strain rates can be omitted through the model estimation process. We apply the Bayesian approach to GNSS displacement-rate data in Mainland China to obtain a unique GNSS velocity field for sub-regions with different tectonic backgrounds. We also examine the correlation between the estimated strain-rate fields and seismic activity by using the Molchan Error Diagram. The results show that the rate of maximum shear strain is positively correlated with the occurrence of earthquakes, indicating the strain rate can be used to augment probabilistic earthquake models for background seismicity forecasting.

Bayesian estimation of scale factor for CG-5 relative gravimeter

The terrestrial time-variable microgravity survey is an important means to monitor geodynamic processes underground. The Scintrex CG-5 relative gravimeter, which is the mainstream instrument for terrestrial relative gravity measurement at present, its scale factor (SF) is an important factor affecting the quality of the observation data. Unlike the conventional gravity adjustment procedure, this study takes account of the nonlinear drift rate of the CG-5 gravimeter, depending on the known absolute gravity (AG) in the network, and the scale factor is considered as one of the hyper-parameters to be estimated by means of Akaike’s Bayesian information Criterion (ABIC). In order to quantify the errors caused by the bias of scale factor, we applied this new approach to process actual gravity survey campaign data in Yunnan gravity network from 2018 to 2020, then analyzed the residuals of gravity differences (GD) between station pairs and the difference of GD between two relative gravimeters (CG5 #1169 and CG5 #1170). The cross-validation of the absolute gravity (AG) from the quasi-synchronous observation in the network is also used in the paper. It has shown that this new approach is effective to improve the accuracy of scale factor and adjustment results.

A new look at Akaike’s Bayesian information criterion for inverse ill-posed problems

Akaike’s Bayesian information criterion (ABIC) has been widely used in inverse ill-posed problems. Little has been done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution of measurements for ABIC under the assumption of normal distributions and show that the principle of ABIC is to statistically estimate the variances of measurements and prior data by maximizing the marginal distribution of measurements. The determination of the regularization parameter with ABIC is essentially equivalent to estimating the relative weighting between measurements and prior data. We prove that ABIC theoretically would produce a biased estimate of the variance of measurements. Since the prior mean is generally unknown but arbitrarily treated as zero in inverse ill-posed problems, ABIC is shown to fail to produce any reasonable estimate for the prior variance. Although ABIC is constructed under the Bayesian framework, it essentially plays more or less the same role as biased regularization from the frequentist’s point of view. ABIC error evaluation cannot be performed under the Bayesian framework but should be more appropriately done with the frequentist’s standpoint in terms of mean squared errors. ABIC is sensitive to prior distributions. In the case of non-informative prior distribution, ABIC leads to the conventional weighted least squares (LS) estimate of parameters and cannot be used to solve inverse ill-posed problems. It is not linked to the regularization parameter but only straightforwardly produces an unbiased estimator for the noise level of measurements, which is only applicable numerically for well-posed problems but not for inverse ill-posed problems. Numerical simulated examples are used to demonstrate the statistical performances of ABIC.

Comparative study of exponential smoothing models and Box-Jenkins ARIMA model of partitioned data of daily stock prices of the CRDB Bank in Tanzania

Data mining techniques and other analytical techniques have played a significant role in analysing data from different sources. Data from stock market consist of high volatility and hence it needs a special care to fit a model for forecasting future stock prices values. In the stock market, investors trade to get positive returns through buying at a lower price and selling at a higher price. However, not all investors get positive returns on their investment in stock market because of large amount of risk involved in the stock market due to vast fluctuation in the stock market prices. This study is conducted to compare and select the best model among autoregressive integrated moving average (ARIMA), single exponential smoothed model (SES), double exponential smoothed model (DES), and Damped trend linear exponential smoothed model. The modelling process was preceded by analysing the time series which revealed the presence of non-stationarity. The resultant models were found as ARIMA(1,1,2), Simple Exponential Smoothing (SES) and Double exponential smoothing (DES) whose parameters’ estimates were also found to be statistically significant. Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used to select the best model among all the three fitted models. The performance of the fitted model is analyzed and the market behavior for future forecast is studied. ARIMA(1,1,2) is selected as the best model for daily stock forecasting for the CRDB bank in Tanzania.

Source characteristics of the March 16, 2014 Mw 6.7 earthquake and its implications for the Mw 8.2 Pisagua mainshock

The March 16, 2014 Mw 6.7 earthquake played an important role in the complex seismic sequence leading to the nucleation of the April 1st, 2014 Mw 8.2 Pisagua earthquake in northern Chile. The Mw 6.7, an upper plate reverse faulting event with nodal planes highly rotated counterclockwise with respect to the strike of the megathrust at its location, is analyzed. For each nodal plane of the regional W-phase centroid moment tensor solution, the spatiotemporal slip distribution is inverted using near-field records. The optimal space and time smoothing constraints are determined objectively based on the Akaike's Bayesian Information Criterion. We analyze seismicity on the region affected by the Mw 6.7 and Mw 8.2 Pisagua mainshock, with accurate hypocenter locations obtained using a 3D heterogeneous medium. We also performed regional moment tensor inversion of events (M≥4.0) occurred before the Mw 8.2. Our results suggest the sub-vertical fault plane dipping southward (dip∼70°) as being the causative fault of the March 16 Mw 6.7 earthquake. The rupture propagated to the northwest, lasted 15s, and yielded a total seismic moment of 1.36×1019Nm (Mw 6.7). Estimated slip is characterized by total rupture length of ∼22km, and suggest shallow slip distributed between ∼ 3km, down to 17km depth. A comparison between coastal tide gauge records and forward tsunami modeling show similarity of the time series, thus supporting the plausibility of our estimated slip models. Our interpretation suggests that the rupture of the Mw 6.7 intraplate could be explained by stress accommodation between two segments along-dip with different mechanical properties at the interplate boundary, and inside the upper plate.

Akaike's Bayesian Information Criterion for the Joint Inversion of Terrestrial Water Storage Using GPS Vertical Displacements, GRACE and GLDAS in Southwest China.

Global navigation satellite systems (GNSS) techniques, such as GPS, can be used to accurately record vertical crustal movements induced by seasonal terrestrial water storage (TWS) variations. Conversely, the TWS data could be inverted from GPS-observed vertical displacement based on the well-known elastic loading theory through the Tikhonov regularization (TR) or the Helmert variance component estimation (HVCE). To complement a potential non-uniform spatial distribution of GPS sites and to improve the quality of inversion procedure, herein we proposed in this study a novel approach for the TWS inversion by jointly supplementing GPS vertical crustal displacements with minimum usage of external TWS-derived displacements serving as pseudo GPS sites, such as from satellite gravimetry (e.g., Gravity Recovery and Climate Experiment, GRACE) or from hydrological models (e.g., Global Land Data Assimilation System, GLDAS), to constrain the inversion. In addition, Akaike’s Bayesian Information Criterion (ABIC) was employed during the inversion, while comparing with TR and HVCE to demonstrate the feasibility of our approach. Despite the deterioration of the model fitness, our results revealed that the introduction of GRACE or GLDAS data as constraints during the joint inversion effectively reduced the uncertainty and bias by 42% and 41% on average, respectively, with significant improvements in the spatial boundary of our study area. In general, the ABIC with GRACE or GLDAS data constraints displayed an optimal performance in terms of model fitness and inversion performance, compared to those of other GPS-inferred TWS methodologies reported in published studies.

Shallow intraplate seismicity related to the Illapel 2015 Mw 8.4 earthquake: Implications from the seismic source

The September 16, 2015, Mw 8.4 Illapel, Chile earthquake is the first large event occurring in north-central Chile after the 1943 earthquake, filling a known seismic gap in the region. The earthquake took place in a complex tectonic region, nearby an area where transition from erosive to accretionary margin occurs due to the collision of Juan Fernandez Ridge (JFR) along the Chilean margin. We inverted the kinematic rupture process of the 2015 Mw 8.4 Illapel earthquake from the joint inversion of teleseismic body waves and near-field data. The relative weighting between datasets and the weighting of spatial/temporal constraints are objectively estimated by applying the Akaike's Bayesian Information Criterion. The coseismic slip model yields a total seismic moment of 4.92 × 1021 Nm occurred over ~120 s. The rupture shows both downdip and updip propagation with slip extending along the thrust interface from ~50 km depth to shallow near-trench depths (<15 km), with maximum slip of ~9 m located at shallow depths, where low average rupture speeds ~1.8–2 km/s are estimated. Outer-rise events, triggered within the oceanic Nazca plate after the mainshock, did not penetrate into the mantle and are related to preexisting faults due to both bending of Nazca plate and JFR uplift, which promotes a tensional stress regime in the surrounding area. This seismicity was triggered by static stress transfer from near-trench slip revealed by our source rupture modelling, suggesting outer-rise seismicity as a proxy for near-trench coseismic slip. Crustal seismicity within continental South American plate is observed prior to, and after, the mainshock, mainly related to extensional faulting within eroded and fractured wedge due to tectonic processes along erosive margins. We also show evidence of shallow seismicity after the mainshock associated with a long-lived crustal fault, which can represent a high seismic hazard for La Serena-Coquimbo conurbation.