Arrival-time picking uncertainty: Theoretical estimations and their application to microseismic data

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. U65-U76
Author(s):  
Ivan Abakumov ◽  
Aurelian Roeser ◽  
Serge A. Shapiro
Keyword(s):  
Seismic Waves ◽  
Arrival Time ◽  
Signal To Noise Ratio ◽  
Estimation Error ◽  
Additive White Gaussian Noise ◽  
Accurate Determination ◽  
Microseismic Monitoring ◽  
High Signal ◽  
Arrival Times ◽  
Velocity Models

Traveltime-based methods depend on the accurate determination of the arrival times of seismic waves. They further benefit from information on the uncertainty with which the arrival times are determined. Among other applications, arrival-time uncertainties are used to weight data in inversion algorithms and to define the resolution of reconstructed velocity models. The most physically meaningful approaches for the estimation of arrival-time uncertainties are based on probabilistic formulations. The two approaches for the assessment of the lower bound of arrival-time uncertainties, the Cramér–Rao Bound (CRB) and the Ziv–Zakai Bound (ZZB), have been reviewed. The CRB determines the minimum-achievable estimation error under the assumption of a high signal-to-noise ratio (S/N) but underestimates said error for small S/N. The ZZB provides a better result for noisy data because it utilizes a priori information. The CRB and ZZB require knowledge of the spectral variance of the signal, which often is hard to determine in seismic experiments. Furthermore, both bounds assume additive white Gaussian noise (AWGN), which does not hold for seismic data. To overcome these problems, alternative expressions have been proposed, which yield comparable estimates as CRB and ZZB but are solely based on the S/N and the dominant period in the data. Moreover, a recipe to correct the S/N and account for the difference between the seismic noise and AWGN has been provided. For a case study of downhole microseismic monitoring, it is determined that the new expressions provide station-dependent arrival-time uncertainties, which are used as weights to improve source location uncertainties.

Assisted traveltime picking of crosshole GPR data

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. J35-J48 ◽  
Author(s):  
Bernard Giroux ◽  
Abderrezak Bouchedda ◽  
Michel Chouteau
Keyword(s):  
Time Window ◽  
Signal To Noise Ratio ◽  
Real Data ◽  
Information Criterion ◽  
High Signal ◽  
Data Sets ◽  
Signal To Noise ◽  
Arrival Times ◽  
Common Time ◽  
Waveform Similarity

We introduce two new traveltime picking schemes developed specifically for crosshole ground-penetrating radar (GPR) applications. The main objective is to automate, at least partially, the traveltime picking procedure and to provide first-arrival times that are closer in quality to those of manual picking approaches. The first scheme is an adaptation of a method based on cross-correlation of radar traces collated in gathers according to their associated transmitter-receiver angle. A detector is added to isolate the first cycle of the radar wave and to suppress secon-dary arrivals that might be mistaken for first arrivals. To improve the accuracy of the arrival times obtained from the crosscorrelation lags, a time-rescaling scheme is implemented to resize the radar wavelets to a common time-window length. The second method is based on the Akaike information criterion(AIC) and continuous wavelet transform (CWT). It is not tied to the restrictive criterion of waveform similarity that underlies crosscorrelation approaches, which is not guaranteed for traces sorted in common ray-angle gathers. It has the advantage of being automated fully. Performances of the new algorithms are tested with synthetic and real data. In all tests, the approach that adds first-cycle isolation to the original crosscorrelation scheme improves the results. In contrast, the time-rescaling approach brings limited benefits, except when strong dispersion is present in the data. In addition, the performance of crosscorrelation picking schemes degrades for data sets with disparate waveforms despite the high signal-to-noise ratio of the data. In general, the AIC-CWT approach is more versatile and performs well on all data sets. Only with data showing low signal-to-noise ratios is the AIC-CWT superseded by the modified crosscorrelation picker.

scholarly journals Upper Bound on the Bit Error Probability of Systematic Binary Linear Codes via Their Weight Spectra

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jia Liu ◽  
Mingyu Zhang ◽  
Chaoyong Wang ◽  
Rongjun Chen ◽  
Xiaofeng An ◽  
...  
Keyword(s):  
Upper Bound ◽  
Error Probability ◽  
Linear Codes ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
High Signal ◽  
Binary Linear Codes ◽  
Enumerating Function ◽  
Bit Error Probability ◽  
Better Than

In this paper, upper bound on the probability of maximum a posteriori (MAP) decoding error for systematic binary linear codes over additive white Gaussian noise (AWGN) channels is proposed. The proposed bound on the bit error probability is derived with the framework of Gallager’s first bounding technique (GFBT), where the Gallager region is defined to be an irregular high-dimensional geometry by using a list decoding algorithm. The proposed bound on the bit error probability requires only the knowledge of weight spectra, which is helpful when the input-output weight enumerating function (IOWEF) is not available. Numerical results show that the proposed bound on the bit error probability matches well with the maximum-likelihood (ML) decoding simulation approach especially in the high signal-to-noise ratio (SNR) region, which is better than the recently proposed Ma bound.

scholarly journals A benchmark case study for seismic event relative location

2020 ◽  
Vol 223 (2) ◽  
pp. 1313-1326
Author(s):  
S J Gibbons ◽  
T Kværna ◽  
T Tiira ◽  
E Kozlovskaya
Keyword(s):  
Time Delay ◽  
Signal To Noise Ratio ◽  
Source Region ◽  
Ground Truth ◽  
Double Difference ◽  
High Signal ◽  
Relative Location ◽  
Data Set ◽  
Velocity Models ◽  
Event Location

Summary ‘Precision seismology’ encompasses a set of methods which use differential measurements of time-delays to estimate the relative locations of earthquakes and explosions. Delay-times estimated from signal correlations often allow far more accurate estimates of one event location relative to another than is possible using classical hypocentre determination techniques. Many different algorithms and software implementations have been developed and different assumptions and procedures can often result in significant variability between different relative event location estimates. We present a Ground Truth (GT) dataset of 55 military surface explosions in northern Finland in 2007 that all took place within 300 m of each other. The explosions were recorded with a high signal-to-noise ratio to distances of about 2°, and the exceptional waveform similarity between the signals from the different explosions allows for accurate correlation-based time-delay measurements. With exact coordinates for the explosions, we are able to assess the fidelity of relative location estimates made using any location algorithm or implementation. Applying double-difference calculations using two different 1-D velocity models for the region results in hypocentre-to-hypocentre distances which are too short and it is clear that the wavefield leaving the source region is more complicated than predicted by the models. Using the GT event coordinates, we are able to measure the slowness vectors associated with each outgoing ray from the source region. We demonstrate that, had such corrections been available, a significant improvement in the relative location estimates would have resulted. In practice we would of course need to solve for event hypocentres and slowness corrections simultaneously, and significant work will be needed to upgrade relative location algorithms to accommodate uncertainty in the form of the outgoing wavefield. We present this data set, together with GT coordinates, raw waveforms for all events on six regional stations, and tables of time-delay measurements, as a reference benchmark by which relative location algorithms and software can be evaluated.

A COMPARITIVE STUDY OF W-CDMA CELL SEARCH DESIGNS

2005 ◽  
Vol 14 (01) ◽  
pp. 129-135 ◽  
Author(s):  
SANAT KAMAL BAHL ◽  
JIM PLUSQUELLIC ◽  
JOSEPH THOMAS
Keyword(s):  
Cyclic Codes ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Base Station ◽  
Acquisition Time ◽  
High Signal ◽  
Cell Search ◽  
Field Programmable ◽  
Search Designs ◽  
Search Design

In this letter an Improved Cell Search Design using cyclic codes (Improved CSD) is compared with the 3GPP Cell Search Design using comma free codes (3GPP-comma free CSD) in terms of (1) hardware utilization on a field programmable gate array and (2) acquisition time measures for different probabilities of false alarm rates. Our results indicate that for an additive white Gaussian noise channel in a high signal-to-noise ratio the Improved CSD achieves faster synchronization with the base station and has lower hardware utilization when compared with the 3GPP-comma free CSD scheme under the same design constraints.

scholarly journals A review and appraisal of arrival-time picking methods for downhole microseismic data

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. KS71-KS91 ◽  
Author(s):  
Jubran Akram ◽  
David W. Eaton
Keyword(s):  
Arrival Time ◽  
Hybrid Methods ◽  
Optimal Parameter ◽  
Signal To Noise Ratio ◽  
Information Criterion ◽  
High Signal ◽  
Data Set ◽  
Single Level ◽  
Microseismic Data ◽  
Arrival Time Picking

We have evaluated arrival-time picking algorithms for downhole microseismic data. The picking algorithms that we considered may be classified as window-based single-level methods (e.g., energy-ratio [ER] methods), nonwindow-based single-level methods (e.g., Akaike information criterion), multilevel- or array-based methods (e.g., crosscorrelation approaches), and hybrid methods that combine a number of single-level methods (e.g., Akazawa’s method). We have determined the key parameters for each algorithm and developed recommendations for optimal parameter selection based on our analysis and experience. We evaluated the performance of these algorithms with the use of field examples from a downhole microseismic data set recorded in western Canada as well as with pseudo-synthetic microseismic data generated by adding 100 realizations of Gaussian noise to high signal-to-noise ratio microseismic waveforms. ER-based algorithms were found to be more efficient in terms of computational speed and were therefore recommended for real-time microseismic data processing. Based on the performance on pseudo-synthetic and field data sets, we found statistical, hybrid, and multilevel crosscorrelation methods to be more efficient in terms of accuracy and precision. Pick errors for S-waves are reduced significantly when data are preconditioned by applying a transformation into ray-centered coordinates.

A Seismic Event Relative Location Benchmark Case Study

2020 ◽  
Author(s):  
Tormod Kvaerna ◽  
Steven J. Gibbons ◽  
Timo Tiira ◽  
Elena Kozlovskaya
Keyword(s):  
Time Delay ◽  
Signal To Noise Ratio ◽  
Source Region ◽  
Ground Truth ◽  
Double Difference ◽  
High Signal ◽  
Relative Location ◽  
Hypocenter Determination ◽  
Velocity Models ◽  
Event Location

<p>"Precision seismology'' encompasses a set of methods which use differential measurements of time-delays to estimate the relative locations of earthquakes and explosions.  Delay-times estimated from signal correlations often allow far more accurate estimates of one event location relative to another than is possible using classical hypocenter determination techniques.  Many different algorithms and software implementations have been developed and different assumptions and procedures can often result in significant variability between different relative event location estimates.  We present a Ground Truth (GT) database of 55 military surface explosions in northern Finland in 2007 that all took place within 300 meters of each other.  The explosions were recorded with a high signal-to-noise ratio to distances of about 2 degrees, and the exceptional waveform similarity between the signals from the different explosions allows for accurate correlation-based time-delay measurements.  With exact coordinates for the explosions, we can assess the fidelity of relative location estimates made using any location algorithm or implementation.  Applying double-difference calculations using two different 1-d velocity models for the region results in hypocenter-to-hypocenter distances which are too short and the wavefield leaving the source region is more complicated than predicted by the models.  Using the GT event coordinates, we can measure the slowness vectors associated with each outgoing ray from the source region. We demonstrate that, had such corrections been available, a significant improvement in the relative location estimates would have resulted.  In practice we would of course need to solve for event hypocenters and slowness corrections simultaneously, and significant work will be needed to upgrade relative location algorithms to accommodate uncertainty in the form of the outgoing wavefield.  We present this dataset, together with GT coordinates, raw waveforms for all events on six regional stations, and tables of time-delay measurements, as a reference benchmark by which relative location algorithms and software can be evaluated.</p>

scholarly journals Recent Helioseismological Results from Space: Solar p-mode Oscillations from IPHIR on the PHOBOS Mission

1990 ◽  
Vol 121 ◽  
pp. 279-288
Author(s):  
C. Fröhlich ◽  
T. Toutain ◽  
R.M. Bonnet ◽  
A.V. Bruns ◽  
J.P. Delaboudinière ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Accurate Determination ◽  
Spectral Irradiance ◽  
High Signal ◽  
Line Shapes ◽  
Solar Spectral Irradiance ◽  
Evaluation Of Data ◽  
Very High ◽  
Better Than

AbstractIPHIR (Interplanetary Helioseismology by IRradiance measurements) is a solar irradiance experiment on the USSR planetary mission PHOBOS to Mars and its satellite Phobos. The experiment was built by an international consortium including PMOD/WRC, LPSP, SSD/ESA, KrAO and CRIP. The sensor is a three channel sunphotometer (SPM) which measures the solar spectral irradiance at 335, 500 and 865 nm with a precision of better than 1 part-per-million (ppm). It is the first experiment dedicated to the investigation of solar oscillations from space. The results presented here are from a first evaluation of data gathered during 160 days of the cruise phase of PHOBOS II, launched on July, 12th 1988. The long uninterrupted observation produces a spectrum of the solar p-mode oscillations in the 5-minute range with a very high signal-to-noise ratio, which allows an accurate determination of frequencies and line shapes of these modes.

scholarly journals Earthquake relocation in the wester termination of the North Aegean Trough

2018 ◽  
Vol 40 (3) ◽  
pp. 1091
Author(s):  
Ch. K. Karamanos ◽  
G. V. Karakostas ◽  
E. E. Papadimitriou ◽  
M. Sachpazi
Keyword(s):  
Time Delays ◽  
Seismic Waves ◽  
S Wave ◽  
Data Set ◽  
Arrival Times ◽  
Velocity Models ◽  
The North ◽  
North Aegean ◽  
Focal Parameters ◽  
Hypocentral Location

The area of North Aegean Trough exhibits complex tectonic characteristics as a consequence of the presence of complicated active structures. Exploitation of accurately determined earthquake data considerably contributes in the investigation of these structures and such accuracy is seeking through certain procedures. The determination of focal parameters of earthquakes that occurred in this area during 1964-2003 was performed by collecting all the available data for Ρ and S arrivals. After selecting the best solutions from an initial hypocentral location, 739 earthquakes were found that fulfilled certain criteria for the accuracy and used for further processing. The study area was divided in 16 sub regions and by the use of the HYPOINVERSE computer program, the travel time curves were constructed, and were used to define the velocity models for each one of them. For each sub region the time delays were calculated and used as time corrections in the arrival times of the seismic waves. The Vp/Vs ratio, necessary for S—wave velocity models, was calculated with two different methods and was found equal to 1.76. The velocity models and the time delays were used to relocate the events of the whole data set. The relocation resulted in significant improvement of the accuracy in the focal parameters determination.

scholarly journals Comparison of Terrestrial and Lunar Time Scales by Giant Pulsar Impulses

2021 ◽  
Vol 65 (11) ◽  
pp. 1136-1144
Author(s):  
A. E. Rodin ◽  
V. V. Oreshko ◽  
V. A. Fedorova
Keyword(s):  
Time Scales ◽  
Cross Correlation ◽  
Arrival Time ◽  
Signal To Noise Ratio ◽  
High Signal ◽  
The Moon ◽  
Recording Equipment ◽  
Giant Pulses ◽  
Cross Correlation Analysis ◽  
Pulse Arrival

Abstract We have developed a model for the time delay of pulse arrival between stations on the Moon and Earth. Comparison of the lunar and terrestrial time scales is proposed to be carried out by comparing the arrival time moments of giant pulses from pulsars. A method for such a comparison has been developed based on the cross-correlation analysis of the received pulses. Using the example of giant pulses from the pulsar PSR 0531+21, we showed that the error of comparing scales in the case of a high signal-to-noise ratio reaches a sub-discrete level and, thus, is determined by the reception band of the recording equipment.

Using the value of the crosscorrelation coefficient to locate microseismic events

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. MA47-MA52 ◽  
Author(s):  
J. Kummerow
Keyword(s):  
Oil Recovery ◽  
Arrival Time ◽  
A Priori ◽  
Empirical Relation ◽  
Microseismic Monitoring ◽  
Seismic Events ◽  
Small Magnitude ◽  
Near Surface ◽  
Arrival Times ◽  
Receiver Array

A procedure to locate seismic events uses the value of the crosscorrelation coefficient between waveforms of different events. First, an empirical relation between spatial event separation and maximum crosscorrelation coefficient is established for a subset of a priori located reference events. Then this relation is used to determine the hypocenters of an increasing number of events by a grid-search strategy. Measured arrival-time differences between S- and P-waves also constrain the location. Although the reference events are located by a standard method using the arrival-time measurements at three or more receivers, the correlation-based location requires only one receiver. The method has been applied to microseismic data recorded at a single borehole sensor during the 2004/05 injection experiment at the Continental Deep Drilling Site (KTB) in Germany. With the approach, significantly more weak seismic events were located, compared to the number of events recorded by a near-surface receiver array and by inversion of arrival times. The proposed location method is particularly well suited to locate small-magnitude earthquakes within dense event clouds when too few arrival-time observations for part of the events are available and standard location methods fail. These conditions are frequently met in the case of microseismic monitoring of geothermal or enhanced oil recovery experiments.

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