Green's Function-based Matched Filter Method For Small Earthquake Detection And Location

Detection and location of earthquakes is an important field of seismology.Small earthquakes are difficult to detect and locate due to their weak energy and high-frequency signals.The big and small earthquakes are relative concepts,and there is no clear distinction.Small earthquakes usually refer to earthquakes whose magnitude is so small that they cannot be detected by identifying the phases under the existing technology and observation system.Matched filter or say template matching can effectively suppress noise by virtue of crosscorrelation and superposition of cross-correlation waveforms,which is a series of effective and mature methods for detecting and locating small earthquakes.The summary and further development of such methods can strengthen the detection and location of small earthquakes,contribute to the related research on seismic activity,and ultimately promote the understanding of natural seismic phenomena and the dynamic processes of the solid Earth.According to whether the template waveforms are observed waveforms of natural earthquakes or theoretical waveforms synthesized based on the wave equation,the matched filter methods are classified as real and theoretical waveforms.The thesis introduces the classic matched filter method and Match and Locate method of the predecessors,then introduces a theoretical waveform matched filter method jointly developed by the author and the instructor,called Green's function-based matched filter,referred to as GFMF.The thesis uses numerical experiments to analyze and discuss the relevant factors that affect the detection and positioning of the matched filter method.After that,two applied studies are shown,which cover the fields of natural seismology and exploration seismology respectively.The first study is to apply the matched filter method of theoretical waveforms to a natural earthquake sequence and compare it with the matched filter method of real waveforms.The second study is to apply the theoretical waveform matched filter method to hydraulic fracturing microseismic and compare it with the seismic detection method based on machine learning.The following is a brief introduction to the above content.This thesis first reviews the representative studies of the real waveform matched filter methods: the classic matched filter and the M&L method(Match and Locate).This thesis firstly derives the principle of the classic matched filter mathematically and then focuses on the mathematical theory of threshold which is multiples of the median absolute deviation.All matched filter methods need to assume only one earthquake can occur within a certain fixed time window.This thesis points out that the duration of this fixed time window is as important as the threshold in matched filter methods,which should be taken seriously.This paper proposes that a fixed time window with a reasonable length can be obtained according to the possible size of the time in the area.This thesis summarizes the development of the M&L relative to the classic matched filter method and states its technical process.This thesis proposes Green's function-based matched filter(GFMF).This method divides the study area into three-dimensional spatial grids.The virtual earthquakes on each spatial grid are with multiple focal mechanism solutions including all possible double-couple sources discretely.The GFMF method is described as based on Green's functions because it does not directly use the theoretical waveforms synthesized by the computer but uses the theoretical Green's functions to do a sliding cross-correlation with the continuous observed waveforms.This technique is borrowed from the cut-and-paste method(CAP),which can reduce the number of cross-correlations and save time without changing the calculation results.The GFMF package has been open sourced to promote related research.A series of numerical experiments of matched filter methods are carried out in this thesis.To carry out related analysis,I define the threshold range that can avoid missed detection and false detection at the same time as the double-avoiding range and define the ratio of the difference between the upper and lower limits of the double-avoiding range to the absolute deviation of the median as a robustness value.If the robustness value is a positive number,there is a threshold that can avoid both missed detections and false detections.If the robustness value is a negative number,it is impossible to have a threshold that can avoid both missed detections and false detections.The robustness value can be used to judge the influence of any factor and any technique on the matched filter methods.In the numerical experiments where the target and the template events have different source-time functions ranging from 0 to 0.4 seconds,and the minimum and the median number of robustness values obtained is 18.2 and 35.5.This shows that the difference of source-time functions between the target and template evens has negligible influence on the matched filter methods.In numerical experiments where the target and template events have different focal mechanisms,the minimum and median number of robustness values is-3.4 and 31.8.This indicates that the difference of focal mechanisms between target and template events may have non-negligible impact on the matched filter methods.In the numerical experiment where the target template events have different source locations,the great-circle distances between them range from 0° to 0.5°.The proportions of the three focal depths of the target events with negative robustness values are 78.56%,73.6% and74.72%.This shows that even if there is no noise at all,the matched filter is difficult to correctly detect the distant earthquake when the cross-correlation waveform is superimposed.Numerical experiments on seismic stations show that among various station factors,the only signal-tonoise ratio of seismic stations will change the mean cross-correlation coefficient;the signal-tonoise ratio and the number of seismic stations together determine the median absolute deviation of the amplitudes of the mean cross-correlation waveforms.Increasing the number of stations can reduce the median absolute deviation but cannot increase the mean cross-correlation coefficient of the detections.This thesis applies the GFMF method and M&L to detect and locate a natural earthquake sequence in California,United States.GFMF and M&L detect 3,273 and 3,213 seismic events,respectively,and the detection rates for a total of 1,056 cataloged events from the Southern California Seismic Data Center(SCEDC)are 97.1% and 96.4%,respectively.This shows that both methods can accurately and effectively detect small earthquakes.By comparing with the SCEDC earthquake catalog,the GFMF method can accurately reflect the temporal and spatial distribution characteristics of the earthquake sequence by the grid search of the seismic source location,indicating that the virtual earthquakes can be used as template events to detect and locate small earthquakes.Further tests have shown that if the grid search is not performed on the focal mechanisms,the number of detections obtained will be reduced by more than 70%.The median number of positioning accuracies of M&L and GFMF is 0.734 and 0.733,respectively(if the positioning accuracy is 1,the best possible result of the grid search is reached,and 0 means the worst one).The median and average of the positioning accuracy of Match and Locate are 0.734 and 0.753,respectively,while the median and average of the GFMF method are 0.733 and 0.698,respectively.M&L's positioning accuracy is more concentrated than that of GFMF.M&L's positioning is more accurate and more stable than the GFMF method.Because the filtering frequency band of 1-9 Hz is relatively high,the one-dimensional velocity model is not good enough to simulate the Earth's medium,which makes the positioning of the GFMF method not good as M&L and the focal mechanism results are unreliable.If lowfrequency filtering can be applied,the GFMF method can obtain the right focal parameters(including focal mechanisms)of all earthquakes with a magnitude greater than 3 in the region.If only the template earthquakes that occurred before the end of the earthquake sequence are used,the number of M&L detections will drop to 2,422,and the detection rate to the SCEDC earthquake catalog will drop to 91.2%.The great-circle distance of related template earthquakes is no more than 2.5 km,which shows that short-distance template earthquakes cannot be replaced by each other in M&L.However,the GFMF method does not require real earthquakes as template events,and there is no problem of lack of template earthquakes.This thesis uses the GFMF method to detect and locate the microseisms induced by a hydraulic fracturing activity in well Wei-H3-1 in Weiyuan County,China.At the same time,EQTransformer,a kind of machine learning method,is also used to detect the same microseismic sequence and pick phases for them.According to the results from the GFMF method,the water injection operation effectively induced micro-seismic events.At the beginning of the water injection operation,the local rock at the perforation was subjected to extreme hydraulic pressure,which caused an extremely unbalanced stress distribution in the nearby medium,which induced many micro-earthquakes.With the continuation of water injection and the flow of fracturing fluid,the stress gradually restored balance,and the number of earthquakes per unit time began to gradually decrease.When the water injection is over,the external force suddenly disappears,the stress state of the medium undergoes a sudden change again,and the number of micro-seismic events increases again.The micro-seismic events induced by this water injection operation were mainly distributed near the perforations where the water injection operation was carried out.The three-dimensional spatial distribution of micro-seismic events presents a domelike characteristic.The top of the dome has the most earthquakes,followed by the northeastsouthwest and south by southeast-north by northwest lines.The reason for these characteristics may be the existence of local fracturing fluid in the subsurface medium that facilitates the diffusion of fracturing fluid.These areas are more likely to have micro-earthquakes.Among them,the micro-seismic development in the north by northwest direction is obviously farther than the other three directions.The possible reason is that there is a channel for fracturing fluid diffusion in this direction,which may be a fracture or a fault.The number of micro-seismic events obtained by the EQTransformer is 158,far less than the GFMF method(857 under the condition of 12 times MAD threshold).The time-evolution of earthquakes obtained by the EQTransformer over time does not reflect the relationship between micro-seismic activity and water injection operations.Because the number of earthquake events obtained by the machine learning method is very small,it has no reference value.Because the machine learning method does not provide any source parameter information including the time of occurrence and the location of the source,it is impossible to analyze the spatial distribution characteristics of microseisms.No matter how to modify the seismic source correlation parameters,the number of earthquake events obtained at the time based on the machine learning method and the fundamentals of changes over time will not change.The inspection found that there are also errors in the calibration of the machine learning method.Compared with the machine learning method,the matched filter method has four advantages: The first advantage is that the matched filter method(GFMF)can provide a preliminary positioning position,while the machine learning method does not provide location information at all.The second advantage is that the operation of summarizing cross-correlation waveforms in the matched filter method can suppress noise,which is more conducive to detecting weak seismic signals,which is not available in machine learning methods.The third advantage is that each result given by the matched filter method is based on data from multiple stations,while each result of the machine learning method uses data from a single station.The matched filter method can better prevent false detections.The fourth advantage is that the matched filter method statistically estimates false detections,but the machine learning method cannot.At the end of the thesis,I summarize the above-mentioned research work and give feasible suggestions for future studies.