scholarly journals Grid-search event location with non-Gaussian error models

2006 ◽  
Vol 158 (1) ◽  
pp. 55-66 ◽  
Author(s):  
William Rodi
Keyword(s):  
Grid Search ◽  
Error Models ◽  
Event Location ◽  
Non Gaussian

scholarly journals Alignment Error Models and Ensemble-Based Data Assimilation

2005 ◽  
Vol 133 (6) ◽  
pp. 1687-1709 ◽  
Author(s):  
W. Gregory Lawson ◽  
James A. Hansen
Keyword(s):  
Minimum Variance ◽  
Error Model ◽  
Alignment Error ◽  
Error Models ◽  
Wide Range ◽  
Estimation Problems ◽  
Estimation Scheme ◽  
Non Gaussian ◽  
The Individual ◽  
Alignment Errors

Abstract The concept of alternative error models is suggested as a means to redefine estimation problems with non-Gaussian additive errors so that familiar and near-optimal Gaussian-based methods may still be applied successfully. The specific example of a mixed error model including both alignment errors and additive errors is examined. Using the specific form of a soliton, an analytical solution to the Korteweg–de Vries equation, the total (additive) errors of states following the mixed error model are demonstrably non-Gaussian for large enough alignment errors, and an ensemble of such states is handled poorly by a traditional ensemble Kalman filter, even if position observations are included. Consideration of the mixed error model itself naturally suggests a two-step approach to state estimation where the alignment errors are corrected first, followed by application of an estimation scheme to the remaining additive errors, the first step aimed at removing most of the non-Gaussianity so the second step can proceed successfully. Taking an ensemble approach for the soliton states in a perfect-model scenario, this two-step approach shows a great improvement over traditional methods in a wide range of observational densities, observing frequencies, and observational accuracies. In cases where the two-step approach is not successful, it is often attributable to the first step not having sufficiently removed the non-Gaussianity, indicating the problem strictly requires an estimation scheme that does not make Gaussian assumptions. However, in these cases a convenient approximation to the two-step approach is available, which trades obtaining a minimum variance estimate ensemble mean for more physically sound updates of the individual ensemble members.

Generalized neural network trained with a small amount of base samples: Application to event detection and phase picking in downhole microseismic monitoring

Geophysics ◽  
2021 ◽  
pp. 1-66
Author(s):  
Xiong Zhang ◽  
Huihui Chen ◽  
Wei Zhang ◽  
Xiao Tian ◽  
Fangdong Chu
Keyword(s):  
Neural Network ◽  
Event Detection ◽  
Data Augmentation ◽  
Microseismic Monitoring ◽  
Grid Search ◽  
Multiple Receivers ◽  
Prediction Function ◽  
The Neural Network ◽  
Event Location ◽  
Trained Neural Network

The deep learning method has been successfully applied to many geophysical problems to extract features from seismic big data. However, some applications may not have sufficient available data to directly train a generalized neural network. We apply data augmentation on a significantly small number of samples to train a generalized neural network for microseismic event detection and phase picking, which could be used in different project settings and areas. We use the U-Net architecture consisting of 2D convolutional layers to create the prediction function, and map the waveforms recorded by using multiple receivers to the P/S arrival time labels; thus, the neural network can learn the P/S moveout features from multiple receivers. The training set is generated by simulating various realizations of the data based on ten original samples from the beginning of a hydraulic fracturing stage. The trained neural network is then used to detect the events and pick the P/S phases from the continuous data for different stages and projects. A grid search from a precalculated traveltime table is performed to determine the event location after an event is detected. We build a real-time event detection and location workflow without human intervention by combining the neural network and grid search method, and apply the workflow to a different stage from the training events and a completely independent project that the neural network has not encountered. The results show that microseismic events are successfully detected and located, and the picking performance of the neural network is superior to that of a traditional auto regression picker.

scholarly journals A likelihood framework for deterministic hydrological models and the importance of non-stationary autocorrelation

2019 ◽  
Vol 23 (4) ◽  
pp. 2147-2172 ◽  
Author(s):  
Lorenz Ammann ◽  
Fabrizio Fenicia ◽  
Peter Reichert
Keyword(s):  
Temporal Resolution ◽  
Realistic Model ◽  
Model Parameters ◽  
Hydrological Models ◽  
Correlated Errors ◽  
State Variables ◽  
Widespread Application ◽  
Error Models ◽  
Joint Inference ◽  
Non Gaussian

Abstract. The widespread application of deterministic hydrological models in research and practice calls for suitable methods to describe their uncertainty. The errors of those models are often heteroscedastic, non-Gaussian and correlated due to the memory effect of errors in state variables. Still, residual error models are usually highly simplified, often neglecting some of the mentioned characteristics. This is partly because general approaches to account for all of those characteristics are lacking, and partly because the benefits of more complex error models in terms of achieving better predictions are unclear. For example, the joint inference of autocorrelation of errors and hydrological model parameters has been shown to lead to poor predictions. This study presents a framework for likelihood functions for deterministic hydrological models that considers correlated errors and allows for an arbitrary probability distribution of observed streamflow. The choice of this distribution reflects prior knowledge about non-normality of the errors. The framework was used to evaluate increasingly complex error models with data of varying temporal resolution (daily to hourly) in two catchments. We found that (1) the joint inference of hydrological and error model parameters leads to poor predictions when conventional error models with stationary correlation are used, which confirms previous studies; (2) the quality of these predictions worsens with higher temporal resolution of the data; (3) accounting for a non-stationary autocorrelation of the errors, i.e. allowing it to vary between wet and dry periods, largely alleviates the observed problems; and (4) accounting for autocorrelation leads to more realistic model output, as shown by signatures such as the flashiness index. Overall, this study contributes to a better description of residual errors of deterministic hydrological models.

STATEMENT OF THE PROBLEM ON SYNTHESIS OF OPTIMAL EVALUATION OF SIGNAL PARAMETERS IN NON-GAUSSIAN NOISE

2012 ◽  
Vol 71 (17) ◽  
pp. 1541-1555
Author(s):  
V. A. Baranov ◽  
S. V. Baranov ◽  
A. V. Nozdrachev ◽  
A. A. Rogov
Keyword(s):  
Gaussian Noise ◽  
Signal Parameters ◽  
Non Gaussian ◽  
Optimal Evaluation
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