A probability model for regional focal mechanism solutions

1980 ◽  
Vol 70 (1) ◽  
pp. 149-170
Author(s):  
D. R. Brillinger ◽  
A. Udias ◽  
B. A. Bolt
Keyword(s):  
Principal Stress ◽  
Probability Model ◽  
P Wave ◽  
Probability Models ◽  
Fault Plane Solutions ◽  
Focal Mechanism Solutions ◽  
Regional Basis ◽  
Local Tectonics ◽  
Solution Estimates

abstract The increase in the number of determinations of fault-plane solutions and their use for inferences on regional and local tectonics and stress fields makes it advisable to treat them in a standard way in groups on a regional basis. Probability models for joint group estimation of the shear dislocations, involving data from I earthquakes and J observations of the same region, are presented. The general model gives the probability πij of reading a compression (Yij = 1) for the P wave from event i at station j as Prob { Y i j = 1 } = γ i + ( 1 − 2 γ i ) Φ ( ρ i A i j ) where γ and ρ are precision parameters and Φ is the normal cumulative. This probability depends on Aij (θ), the theoretical amplitudes from a particular orientation of the greatest and least axes of principal stress for the regional solution. Estimates of the principal stress axes T and P and their variances are computed by constructing a loss function based on the likelihood. The algorithm allows for the estimation of a mean regional solution and one for each event. A treatment of measures of fit and the winnowing of clusters of solutions is given. The resulting program has been applied to the determination of the regional solution and exceptional mechanisms for the main shock and 25 aftershocks of the great 1964 Alaskan earthquake and 19 small earthquakes in Bear Valley, California.

scholarly journals Microearthquake Source Locations and Mechanisms: Ice Stream B, West Antarctica (Abstract)

1988 ◽  
Vol 11 ◽  
pp. 199-199
Author(s):  
S. Anandakrishnan ◽  
D. D. Blankenship ◽  
C. R. Bentley
Keyword(s):  
Depth Profile ◽  
Fault Plane ◽  
P Wave ◽  
West Antarctica ◽  
Precise Location ◽  
Fault Plane Solutions ◽  
Ice Flow ◽  
Ice Stream ◽  
Ice Stream B

An array of nine seismographic stations, each sensitive to all three components of motion, was deployed on Ice Stream B, West Antarctica, during the austral summer of 1985–86. The network was sensitive to high-frequency (=400 Hz) seismic activity within a 350 km2 area of the ice stream, and the deployment geometry allows the precise determination of depths for events beneath the 10 km2 array. Microearthquakes from both beneath and beside the ice stream were detected and recorded (Blankenship and others 1987). Inversion of P-wave and S-wave travel times and radiation patterns allows the determination of locations and fault-plane solutions for many of these events.We find that bottom events involve low-angle thrusting, in the down-stream direction, of ice or till; displacement is ∼½ cm per event over a (15 m)2 area. Such faulting is rare and releases an insignificant part of the total energy dissipated by ice flow. However, this is a possible mechanism for plucking of the ice-stream bed.Fault-plane solutions for most major surface events are consistent with the opening of tensional fractures oriented transverse to ice flow. Precise location of these events shows that they correspond to open crevasses, mapped by Vornberger and Whillans (1986), that are oriented transverse to ice flow.In addition, shear-wave splitting observed on some of the microearthquakes shows that the c-axes in the ice stream are slightly, but not strongly, anisotropic. Precise location of the sources requires the use of a detailed velocity-depth profile in the firn, which was obtained by seismic short-refraction studies (Anandakrishnan and others 1988, this volume). A density-depth profile calculated from these velocities agrees well with direct density measurements on a single core nearby (Alley and Bentley 1988, this volume).

scholarly journals Microearthquake Source Locations and Mechanisms: Ice Stream B, West Antarctica (Abstract)

1988 ◽  
Vol 11 ◽  
pp. 199
Author(s):  
S. Anandakrishnan ◽  
D. D. Blankenship ◽  
C. R. Bentley
Keyword(s):  
Depth Profile ◽  
Fault Plane ◽  
P Wave ◽  
West Antarctica ◽  
Precise Location ◽  
Fault Plane Solutions ◽  
Ice Flow ◽  
Ice Stream ◽  
Ice Stream B

An array of nine seismographic stations, each sensitive to all three components of motion, was deployed on Ice Stream B, West Antarctica, during the austral summer of 1985–86. The network was sensitive to high-frequency (=400 Hz) seismic activity within a 350 km2 area of the ice stream, and the deployment geometry allows the precise determination of depths for events beneath the 10 km2 array. Microearthquakes from both beneath and beside the ice stream were detected and recorded (Blankenship and others 1987). Inversion of P-wave and S-wave travel times and radiation patterns allows the determination of locations and fault-plane solutions for many of these events. We find that bottom events involve low-angle thrusting, in the down-stream direction, of ice or till; displacement is ∼½ cm per event over a (15 m)2 area. Such faulting is rare and releases an insignificant part of the total energy dissipated by ice flow. However, this is a possible mechanism for plucking of the ice-stream bed. Fault-plane solutions for most major surface events are consistent with the opening of tensional fractures oriented transverse to ice flow. Precise location of these events shows that they correspond to open crevasses, mapped by Vornberger and Whillans (1986), that are oriented transverse to ice flow. In addition, shear-wave splitting observed on some of the microearthquakes shows that the c-axes in the ice stream are slightly, but not strongly, anisotropic. Precise location of the sources requires the use of a detailed velocity-depth profile in the firn, which was obtained by seismic short-refraction studies (Anandakrishnan and others 1988, this volume). A density-depth profile calculated from these velocities agrees well with direct density measurements on a single core nearby (Alley and Bentley 1988, this volume).

scholarly journals Focal mechanisms and the stress field in the aftershock area of the 2018 Hokkaido Eastern Iburi earthquake (MJMA = 6.7)

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Yuki Susukida ◽  
◽  
Kei Katsumata ◽  
Masayoshi Ichiyanagi ◽  
Mako Ohzono ◽  
...  
Keyword(s):  
Stress Field ◽  
Principal Stress ◽  
Focal Mechanism ◽  
P Wave ◽  
Japan Meteorological Agency ◽  
Inversion Method ◽  
Reverse Fault ◽  
Focal Mechanism Solutions ◽  
Fault Type ◽  
Aftershock Area

AbstractThe tectonic stress field was investigated in and around the aftershock area of the Hokkaido Eastern Iburi earthquake (MJMA = 6.7) occurred on 6 September 2018. We deployed 26 temporary seismic stations in the aftershock area for approximately 2 months and located 1785 aftershocks precisely. Among these aftershocks, 894 focal mechanism solutions were determined using the first-motion polarity of P wave from the temporary observation and the permanent seismic networks of Hokkaido University, Japan Meteorological Agency (JMA), and High Sensitivity Seismograph Network Japan (Hi-net). We found that (1) the reverse faulting and the strike-slip faulting are dominant in the aftershock area, (2) the average trend of P- and T-axes is 78° ± 33° and 352° ± 51°, respectively, and (3) the average plunge of P- and T-axes is 25° ± 16° and 44° ± 20°, respectively: the P-axis is close to be horizontal and the T-axis is more vertical than the average of the P-axes. We applied a stress inversion method to the focal mechanism solutions to estimate a stress field in the aftershock area. As a result, we found that the reverse fault type stress field is dominant in the aftershock area. An axis of the maximum principal stress (σ1) has the trend of 72° ± 7° and the dipping eastward of 19° ± 4° and an axis of the intermediate principal stress (σ2) has the trend of 131° ± 73° and the dipping southward of 10° ± 9°, indicating that both of σ1- and σ2-axes are close to be horizontal. An axis of the minimum principal stress (σ3) has the dipping westward of 67° ± 6° that is close to be vertical. The results strongly suggest that the reverse-fault-type stress field is predominant as an average over the aftershock area which is in the western boundary of the Hidaka Collision Zone. The average of the stress ratio R = (σ1 − σ2)/(σ1 − σ3) is 0.61 ± 0.13 in the whole aftershock area. Although not statistically significant, we suggest that R decreases systematically as the depth is getting deep, which is modeled by a quadratic polynomial of depth.

scholarly journals DETERMINATION OF FAULT PLANE SOLUTIONS USING WAVEFORM AMPLITUDES AND RADIATION PATTERN

2004 ◽  
Vol 36 (3) ◽  
pp. 1529
Author(s):  
D. A. Vamvakaris ◽  
C. B. Papazachos ◽  
E. E. Karagianni ◽  
E. M. Scordilis ◽  
P. M. Chatzidimitriou
Keyword(s):  
Radiation Pattern ◽  
Multiple Solutions ◽  
Fault Plane ◽  
Synthetic Data ◽  
P Wave ◽  
Original Version ◽  
Fault Plane Solutions ◽  
S Waves ◽  
Short Period

In the present work a modified version of the program FPFIT (Reasenberg and Oppenheimer, 1985) is developed, in order to improve the calculation of the fault plane solutions. The method is applied on selected earthquakes from short period waveform data in the Mygdonia basin (N. Greece) as recorded by the permanent network of the Seismological Station of Aristotle University of Thessaloniki during the period 1989-1999. The proposed modification of the FPFIT program was developed in order to minimize the derivation of multiple solutions, as well as the uncertainties in the location of Ρ and Τ axis of the determined fault plane solutions. Compared to the original version of FPFIT the modified approach takes also into account the radiation pattern of SV and SH waves. For each earthquake horizontal and vertical components of each station were used and the first arrivals of Ρ and S waves were picked. Using the maximum peak-to-peak amplitude of Ρ and S waves the ratio Pmax/(S/\/2max+SE2max)1/2 was estimated, where S/Vmax and SEmax are the maximum amplitudes of the two horizontal components (N-S, E-W) for the S waves and Pmax is the maximum amplitude of the vertical one for the P- waves. This ratio for the observed data, as well as the corresponding ratio Prad/iS/Aad+SlAad)1'2 of the synthetic data was used as a weight for the determination of the observed and theoretical P-wave polarities, respectively. The method was tested using synthetic data. A significant improvement of the results was found, compared to the original version of FPFIT. In particular, an improved approximation of the input focal mechanism is found, without multiple solutions and the best-estimated Ρ and Τ axes exhibit much smaller uncertainties. The addition of noise in the synthetic data didn't significantly change the results concerning the fault plane solutions. Finally, we have applied the modified program on a real data set of earthquakes that occurred in the Mygdonia basin.

scholarly journals Focal Mechanisms and the Stress Field in the Aftershock Area of the 2018 Hokkaido Eastern Iburi Earthquake (MJMA = 6.7)

2020 ◽  
Author(s):  
Yuki Susukida ◽  
Kei Katsumata ◽  
Masayoshi Ichiyanagi ◽  
Mako Ohzono ◽  
Hiroshi Aoyama ◽  
...  
Keyword(s):  
Stress Field ◽  
Principal Stress ◽  
Focal Mechanism ◽  
P Wave ◽  
Japan Meteorological Agency ◽  
Inversion Method ◽  
Reverse Fault ◽  
Focal Mechanism Solutions ◽  
Fault Type ◽  
Aftershock Area

Abstract The tectonic stress field was investigated in and around the aftershock area of the Hokkaido Eastern Iburi earthquake (MJMA = 6.7) occurred on 6 September 2018. We deployed 26 temporary seismic stations in the aftershock area for approximately 2 months and located 1785 aftershocks precisely. Among these aftershocks 818 focal mechanism solutions were determined using the first motion polarity of P wave from the temporary observation and the permanent seismic networks of Hokkaido University, Japan Meteorological Agency (JMA), and High Sensitivity Seismograph Network Japan (Hi-net). We found that (1) the reverse faulting and the strike-slip faulting are dominant in the aftershock area, (2) the average azimuths of P- and T-axes are N78° ± 33°E and N3° ± 52°W, respectively, and (3) the average dips of P- and T-axes are 25° ± 16° and 46° ± 20°, respectively: the P-axis is close to be horizontal and the T-axis is close to be vertical. We applied a stress inversion method to the focal mechanism solutions to estimate a stress field in the aftershock area. As a result, we found that the reverse fault type stress field is dominant in the aftershock area. An axis of the maximum principal stress (σ1) has the azimuth of N73° ± 8°E and the dipping eastward of 17° ± 6° and an axis of the medium principal stress (σ2) has the azimuth of N126° ± 91°E and the dipping southward of 16° ± 13°, indicating that both of σ1- and σ2-axes are close to be horizontal. An axis of the minimum principal stress (σ3) has the dipping westward of 64° ± 9° that is close to be vertical. The results strongly suggest that the reverse-fault-type stress field is predominant as an average over the aftershock area which is in the western boundary of the Hidaka Collision Zone. Although the average of the stress ratio is R = 0.6 ± 0.2 in the whole aftershock area, R decreases systematically as the depth is getting deep, which is modeled by a quadratic polynomial of depth.

The S wave project for focal mechanism studies earthquakes of 1962

1964 ◽  
Vol 54 (6B) ◽  
pp. 2199-2208 ◽  
Author(s):  
William Stauder ◽  
G. A. Bollinger
Keyword(s):  
Focal Mechanism ◽  
P Wave ◽  
S Wave ◽  
Polarization Data ◽  
Saint Louis ◽  
Saint Louis University ◽  
S Waves ◽  
Focal Mechanism Solutions ◽  
First Motion

Abstract The Department of Geophysics of Saint Louis University has instituted a routine program for the determination of the focal mechanism of the larger earthquakes of each year using methods developed for the use of S waves in focal mechanism studies. Suites of records from selected stations are assembled from the WWSS microfilm file for each earthquake of interest. A combination of P-wave first motion and S-wave polarization data is then used to determine graphically the mechanism of the earthquakes. Thirty-six earthquakes of 1962 were selected for study. The focal mechanism solutions are presented for twenty-three of these shocks. There is evidence of patterns characteristic of the focal mechanism of earthquakes occurring in Kamchatka, the Aleutian Islands and South America. A complete presentation of all the data and of all the solutions is available in a more lengthy report.

scholarly journals Calculation of Misjudgment Probability for Product Inspection Based on Measurement Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xiao-huai Chen ◽  
Yin-bao Cheng ◽  
Han-bin Wang ◽  
Hong-li Li ◽  
Zhen-ying Cheng ◽  
...  
Keyword(s):  
Measurement Uncertainty ◽  
Conditional Probability ◽  
Probability Model ◽  
Probability Models ◽  
Estimation Formula ◽  
Sampling Inspection ◽  
Measurement Results ◽  
Absolute Probability ◽  
Selection Of

It is important to research into the misjudgment probability of product inspection based on measurement uncertainty, which is of great significance to improve the reliability of inspection results. This paper mainly focused on total inspection and sampling inspection methods and regarded the misjudgment probability as the index to provide quantitative misjudgment risk results for both producer and consumer sides. Through the absolute probability and the conditional probability model, the estimation formula of the total inspection misjudgment rate is deduced, respectively, and the calculation methods of qualification determination and misjudgment rate of the full inspection results are studied. According to the total inspection misjudgment rate, the methods of misjudgment rate of sampling inspection and qualification determination of measurement results are researched. The misjudgment rate of measurement results is calculated based on the exhaustive method and the Monte-Carlo simulation. The estimation results show that the misjudgment probabilities calculated by absolute probability models can be used as the basis for the selection of the measurement plan for product inspection. The misjudgment probability calculated by conditional probability models is more directly to reflect the risks for both producer and consumer sides, and it prompts inspectors to make decisions more carefully.

Aftershocks of the February 21, 1973 Point Mugu, California earthquake

1976 ◽  
Vol 66 (6) ◽  
pp. 1931-1952
Author(s):  
Donald J. Stierman ◽  
William L. Ellsworth
Keyword(s):  
Fault Zone ◽  
Main Shock ◽  
Fault Plane ◽  
Body Wave ◽  
P Wave ◽  
Fault System ◽  
Wave Radiation ◽  
Fault Plane Solutions ◽  
Complex Deformation ◽  
Transverse Ranges

abstract The ML 6.0 Point Mugu, California earthquake of February 21, 1973 and its aftershocks occurred within the complex fault system that bounds the southern front of the Transverse Ranges province of southern California. P-wave fault plane solutions for 51 events include reverse, strike slip and normal faulting mechanisms, indicating complex deformation within the 10-km broad fault zone. Hypocenters of 141 aftershocks fail to delineate any single fault plane clearly associated with the main shock rupture. Most aftershocks cluster in a region 5 km in diameter centered 5 km from the main shock hypocenter and well beyond the extent of fault rupture estimated from analysis of body-wave radiation. Strain release within the imbricate fault zone was controlled by slip on preexisting planes of weakness under the influence of a NE-SW compressive stress.

P-wave backazimuth anomalies observed by a small-aperture seismic array at Pinyon Flat, southern California: Implications for structure and source location

1996 ◽  
Vol 86 (2) ◽  
pp. 470-476 ◽  
Author(s):  
Cheng-Horng Lin ◽  
S. W. Roecker
Keyword(s):  
Southern California ◽  
Seismic Array ◽  
P Wave ◽  
Small Aperture ◽  
Data Set ◽  
Single Interface ◽  
Seismic Networks ◽  
Dense Seismic Array ◽  
Beamforming Technique

Abstract Seismograms of earthquakes and explosions recorded at local, regional, and teleseismic distances by a small-aperture, dense seismic array located on Pinyon Flat, in southern California, reveal large (±15°) backazimuth anomalies. We investigate the causes and implications of these anomalies by first comparing the effectiveness of estimating backazimuth with an array using three different techniques: the broadband frequency-wavenumber (BBFK) technique, the polarization technique, and the beamforming technique. While each technique provided nearly the same direction as a most likely estimate, the beamforming estimate was associated with the smallest uncertainties. Backazimuth anomalies were then calculated for the entire data set by comparing the results from beamforming with backazimuths derived from earthquake locations reported by the Anza and Caltech seismic networks and the Preliminary Determination of Epicenters (PDE) Bulletin. These backazimuth anomalies have a simple sinelike dependence on azimuth, with the largest anomalies observed from the southeast and northwest directions. Such a trend may be explained as the effect of one or more interfaces dipping to the northeast beneath the array. A best-fit model of a single interface has a dip and strike of 20° and 315°, respectively, and a velocity contrast of 0.82 km/sec. Application of corrections computed from this simple model to ray directions significantly improves locations at all distances and directions, suggesting that this is an upper crustal feature. We confirm that knowledge of local structure can be very important for earthquake location by an array but also show that corrections computed from simple models may not only be adequate but superior to those determined by raytracing through smoothed laterally varying models.

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