Consistency of stress state,locations and source mechanisms of events induced by hydraulic fracturing: downhole monitoring

We present results of processed microseismic events induced by hydraulic fracturing and detected using dual downhole monitoring arrays. The results provide valuable insight into hydraulic fracturing. For our study, we detected and located microseismic events and determined their magnitudes, source mechanisms and inverted stress field orientation. Event locations formed a distinct linear trend above the stimulated intervals. Source mechanisms were only computed for high‐quality events detected on a sufficient number of receivers. All the detected source mechanisms were dip‐slip mechanisms with steep and nearly horizontal nodal planes. The source mechanisms represented shear events and the non‐double‐couple components were very small. Such small, non‐double‐couple components are consistent with a noise level in the data and velocity model uncertainties. Strikes of inverted mechanisms corresponding to the nearly vertical fault plane are (within the error of measurements) identical with the strike of the location trend. Ambient principal stress directions were inverted from the source mechanisms. The least principal stress, σ₃, was determined perpendicular to the strike of the trend of the locations, indicating that the hydraulic fracture propagated in the direction of maximum horizontal stress. Our analysis indicated that the source mechanisms observed using downhole instruments are consistent with the source mechanisms observed in microseismic monitoring arrays in other locations. Furthermore, the orientation of the inverted principal components of the ambient stress field is in agreement with the orientation of the known regional stress, implying that microseismic events induced by hydraulic fracturing are controlled by the regional stress field.     

Determining the focal mechanisms and depths of relatively small earthquakes using a few stations by full‐waveform modelling

Determining the focal mechanism of earthquakes helps us to better define faults and understand the stress regime. This technique can be helpful in the oil and gas industry where it can be applied to microseismic events. The objective of this paper is to find double couple focal mechanisms, excluding scalar seismic moments, and the depths of small earthquakes using data from relatively few local stations. This objective is met by generating three‐component synthetic seismograms to match the observed normalized velocity seismograms. We first calculate Green's functions given an initial estimate of the earthquake's hypocentre, the locations of the seismic recording stations and a 1D velocity model of the region for a series of depths. Then, we calculate the moment tensor for different combinations of strikes, dips and rakes for each depth. These moment tensors are combined with the Green's functions and then convolved with a source time function to produce synthetic seismograms. We use a grid search to find the synthetic seismogram with the largest objective function that best fits all three components of the observed velocity seismogram. These parameters define the focal mechanism solution of an earthquake. We tested the method using three earthquakes in Southern California with moment magnitudes of 5.0, 5.1 and 4.4 using the frequency range 0.1–2.0 Hz. The source mechanisms of the events were determined independently using data from a multitude of stations. Our results obtained, from as few as three stations, generally match those obtained by the Southern California Earthquake Data Center. The main advantage of this method is that we use relatively high‐frequency full‐waveforms, including those from short‐period instruments, which makes it possible to find the focal mechanism and depth of earthquakes using as few as three stations when the velocity structure is known.     

Cross double‐difference inversion for simultaneous velocity model update and microseismic event location

Microseismic monitoring is an approach for mapping hydraulic fracturing. Detecting the accurate locations of microseismic events relies on an accurate velocity model. The one‐dimensional layered velocity model is generally obtained by model calibration from inverting perforation data. However, perforation shots may only illuminate the layers between the perforation shots and the recording receivers with limited raypath coverage in a downhole monitoring problem. Some of the microseismic events may occur outside of the depth range of these layers. To derive an accurate velocity model covering all of the microseismic events and locating events at the same time, we apply the cross double‐difference method for the simultaneous inversion of a velocity model and event locations using both perforation shots and microseismic data. The cross double‐difference method could provide accurate locations in both the relative and absolute sense, utilizing cross traveltime differences between P and S phases over different events. At the downhole monitoring scale, the number of cross traveltime differences is sufficiently large to constrain events locations and velocity model as well. In this study, we assume that the layer thickness is known, and velocities of P‐ and S‐wave are inverted. Different simultaneous inversion methods based on the Geiger's, double‐difference, and cross double‐difference algorithms have been compared with the same input data. Synthetic and field data experiments suggest that combining both perforation shots and microseismic data for the simultaneous cross double‐difference inversion of the velocity model and event locations is available for overcoming the trade‐offs in solutions and producing reliable results.     

Back‐projection stacking of P‐ and S‐waves to determine location and focal mechanism of microseismic events recorded by a surface array

We present an automatic method of processing microseismic data acquired at the surface by a star‐like array. The back‐projection approach allows successive determination of the hypocenter position of each event and of its focal mechanisms. One‐component vertical geophone groups and three‐component accelerometers are employed to monitor both P‐ and S‐waves. Hypocenter coordinates are determined in a grid by back‐projection stacking of the short‐time‐average‐to‐long‐time‐average ratio of absolute amplitudes at vertical components and polarization norm derived from horizontal components of the P‐ and S‐waves, respectively. To make the location process more efficient, calculation is started with a coarse grid and zoomed to the optimum hypocenter using an oct‐tree algorithm. The focal mechanism is then determined by stacking the vertical component seismograms corrected for the theoretical P‐wave polarity of the focal mechanism. The mechanism is resolved in the coordinate space of strike, dip, and rake angles. The method is tested on 34 selected events of a dataset of hydraulic fracture monitoring of a shale gas play in North America. It was found that, by including S‐waves, the vertical accuracy of locations improved by a factor of two and is equal to approximately the horizontal location error. A twofold enhancement of horizontal location accuracy is achieved if a denser array of geophone groups is used instead of the sparse array of three‐component seismometers. The determined focal mechanisms are similar to those obtained by other methods applied to the same dataset.     

Comparison of migration‐based location and detection methods for microseismic events

Microseismic monitoring in the oil and gas industry commonly uses migration‐based methods to locate very weak microseismic events. The objective of this study is to compare the most popular migration‐based methods on a synthetic dataset that simulates a strike‐slip source mechanism event with a low signal‐to‐noise ratio recorded by surface receivers (vertical components). The results show the significance of accounting for the known source mechanism in the event detection and location procedures. For detection and location without such a correction, the ability to detect weak events is reduced. We show both numerically and theoretically that neglecting the source mechanism by using only absolute values of the amplitudes reduces noise suppression during stacking and, consequently, limits the possibility to retrieve weak microseismic events. On the other hand, even a simple correction to the data polarization used with otherwise ineffective methods can significantly improve detections and locations. A simple stacking of the data with a polarization correction provided clear event detection and location, but even better results were obtained for those data combined with methods that are based on semblance and cross‐correlation.     

Non-double-couple mechanism of moderate earthquakes near Zakynthos, Greece, April 2006; explanation in terms of complexity

Deviation of earthquakes from the double‐couple mechanism is an important, but delicate tool to study their source processes. For assessing the double‐couple percentage, the paper suggests to complement the standard least‐square moment‐tensor retrieval with a hierarchic spatio‐temporal grid search, progressively closer to the true source position and time. It enables identification of the double‐couple percentage convergence, while its limit is the resulting double‐couple percentage value, or range. The so‐called double‐couple percentage (DC%) versus correlation plots are introduced and difficulties of the double‐couple percentage assessment are discussed. It is proved that even close to the true source position, where the strike‐dip‐rake angles are already stable (within a few degrees), the double‐couple percentage may still vary by dozens of per cent. Moreover, even at the optimum spatial position, the double‐couple percentage estimate is extremely sensitive (0 to 100%) to small variations of the subevent origin time. This behaviour is explained in terms of the source complexity, implying a time‐dependent moment tensor. Therefore, the double‐couple percentage of complex events depends on the studied frequency band and, in general, also on the station azimuth. This explains broad variations of the double‐couple percentage reports among seismic agencies. Three earthquakes of mutually close epicentres were investigated (Zakynthos, Western Greece, April 2006, magnitudes ～5.5) and a strong non‐double‐couple component of one of them was identified (double‐couple percentage of about 20%). Two equivalent models of this earthquake were found: a single‐event non‐ double‐couple model, and a double‐event model consisting of two double‐couple sources with highly different mechanisms.     

Full‐waveform based microseismic event detection and signal enhancement: An application of the subspace approach

Microseismic monitoring has proven invaluable for optimizing hydraulic fracturing stimulations and monitoring reservoir changes. The signal to noise ratio of the recorded microseismic data varies enormously from one dataset to another, and it can often be very low, especially for surface monitoring scenarios. Moreover, the data are often contaminated by correlated noises such as borehole waves in the downhole monitoring case. These issues pose a significant challenge for microseismic event detection. In addition, for downhole monitoring, the location of microseismic events relies on the accurate polarization analysis of the often weak P‐wave to determine the event azimuth. Therefore, enhancing the microseismic signal, especially the low signal to noise ratio P‐wave data, has become an important task. In this study, a statistical approach based on the binary hypothesis test is developed to detect the weak events embedded in high noise. The method constructs a vector space, known as the signal subspace, from previously detected events to represent similar, yet significantly variable microseismic signals from specific source regions. Empirical procedures are presented for building the signal subspace from clusters of events. The distribution of the detection statistics is analysed to determine the parameters of the subspace detector including the signal subspace dimension and detection threshold. The effect of correlated noise is corrected in the statistical analysis. The subspace design and detection approach is illustrated on a dual‐array hydrofracture monitoring dataset. The comparison between the subspace approach, array correlation method, and array short‐time average/long‐time average detector is performed on the data from the far monitoring well. It is shown that, at the same expected false alarm rate, the subspace detector gives fewer false alarms than the array short‐time average/long‐time average detector and more event detections than the array correlation detector. The additionally detected events from the subspace detector are further validated using the data from the nearby monitoring well. The comparison demonstrates the potential benefit of using the subspace approach to improve the microseismic viewing distance. Following event detection, a novel method based on subspace projection is proposed to enhance weak microseismic signals. Examples on field data are presented, indicating the effectiveness of this subspace‐projection‐based signal enhancement procedure.     

An automated cross‐correlation based event detection technique and its application to a surface passive data set

In studies on heavy oil, shale reservoirs, tight gas and enhanced geothermal systems, the use of surface passive seismic data to monitor induced microseismicity due to the fluid flow in the subsurface is becoming more common. However, in most studies passive seismic records contain days and months of data and manually analysing the data can be expensive and inaccurate. Moreover, in the presence of noise, detecting the arrival of weak microseismic events becomes challenging. Hence, the use of an automated, accurate and computationally fast technique for event detection in passive seismic data is essential. The conventional automatic event identification algorithm computes a running‐window energy ratio of the short‐term average to the long‐term average of the passive seismic data for each trace. We show that for the common case of a low signal‐to‐noise ratio in surface passive records, the conventional method is not sufficiently effective at event identification. Here, we extend the conventional algorithm by introducing a technique that is based on the cross‐correlation of the energy ratios computed by the conventional method. With our technique we can measure the similarities amongst the computed energy ratios at different traces. Our approach is successful at improving the detectability of events with a low signal‐to‐noise ratio that are not detectable with the conventional algorithm. Also, our algorithm has the advantage to identify if an event is common to all stations (a regional event) or to a limited number of stations (a local event). We provide examples of applying our technique to synthetic data and a field surface passive data set recorded at a geothermal site.     

基于“剪切+张裂”一般位错模型频率域求解微震震源机制

研究微地震的震源机制,获得压裂区域的破裂方向、尺度和应力状态等信息,在非常规油气开采过程中具有重要意义.对于微震,通常采用剪切位错或者矩张量模型对震源进行描述.本文从其实际发震机制出发,使用了"剪切+张裂"的一般位错点源模型,并基于此模型发展了一种利用全波形信息,通过波形振幅谱相关和初至约束,在频率域求解微震震源机制的方法.该方法适用于地面和井中观测,能够在得到常规震源参数（断层走向、倾角和滑动角）的同时给出裂缝断层剪切和张裂错动的距离信息,更直观体现破裂程度.理论数值测试证明方法有效、可行,在未滤波的情况下,实际数据的波形拟和结果仍较为一致,同时还发现错动距离与应力降等常规破裂参数并不严格相关,说明剪切、张裂错距可作为独立的新参数来定量评估水压致裂效果,指导工程开发进行.     

A review of the microseismic focal mechanism research

Reservoir reconstructions implemented in unconventional oil and gas exploration usually adopt hydraulic fracturing techniques to inject high-pressure fluid into the reservoir and change its pore-fracture connection structure to enhance production. Hydraulic fracturing changes the reservoir stress and causes the rocks to crack, thus generating microseismic events.One important component of microseismic research is the source mechanism inversion. Through the research on the microseismic focal mechanism, information on the source mechanisms and in-situ stress status variations can be quantitatively revealed to effectively optimize the reservoir reconstruction design for increasing production. This paper reviews the recent progress in hydraulic fracturing induced microseismic focal mechanism research. We summarize their main principles and provide a detailed introduction of the research advances in source modeling, microseismic data synthesis, and focal mechanism inversion. We also discuss the challenges and limitations in the current microseismic focal mechanism research and propose prospects for future research ideas and directions.     

Detection of multiple fracture sets using observations of shear‐wave splitting in microseismic data

The hydrocarbon industry is moving increasingly towards tight sandstone and shale gas resources – reservoirs that require fractures to be produced economically. Therefore, techniques that can identify sets of aligned fractures are becoming more important. Fracture identification is also important in the areas of coal bed methane production, carbon capture and storage (CCS), geothermal energy, nuclear waste storage and mining. In all these settings, stress and pore pressure changes induced by engineering activity can generate or reactivate faults and fractures. P‐ and S‐waves are emitted by such microseismic events, which can be recorded on downhole geophones. The presence of aligned fracture sets generates seismic anisotropy, which can be identified by measuring the splitting of the S‐waves emitted by microseismic events. The raypaths of the S‐waves will have an arbitrary orientation, controlled by the event and geophone locations, meaning that the anisotropy system may only be partly illuminated by the available arrivals. Therefore to reliably interpret such splitting measurements it is necessary to construct models that compare splitting observations with modelled values, allowing the best fitting rock physics parameters to be determined. Commonly, splitting measurements are inverted for one fracture set and rock fabrics with a vertical axis of symmetry. In this paper we address the challenge of identifying multiple aligned fracture sets using splitting measured on microseismic events. We analyse data from the Weyburn CCS‐EOR reservoir, which is known to have multiple fracture sets, and from a hydraulic fracture stimulation, where it is believed that only one set is present. We make splitting measurements on microseismic data recorded on downhole geophone arrays. Our inversion technique successfully discriminates between the single and multiple fracture cases and in all cases accurately identifies the strikes of fracture sets previously imaged using independent methods (borehole image logs, core samples, microseismic event locations). We also generate a synthetic example to highlight the pitfalls that can be encountered if it is assumed that only one fracture set is present when splitting data are interpreted, when in fact more than one fracture set is contributing to the anisotropy.     

Convolutional neural networks for automated microseismic detection in downhole distributed acoustic sensing data and comparison to a surface geophone array

Distributed acoustic sensing is a growing technology that enables affordable downhole recording of strain wavefields from microseismic events with spatial sampling down to ∼1 m. Exploiting this high spatial information density motivates different detection approaches than typically used for downhole geophones. A new machine learning method using convolutional neural networks is described that operates on the full strain wavefield. The method is tested using data recorded in a horizontal observation well during hydraulic fracturing in the Eagle Ford Shale, Texas, and the results are compared to a surface geophone array that simultaneously recorded microseismic activity. The neural network was trained using synthetic microseismic events injected into real ambient noise, and it was applied to detect events in the remaining data. There were 535 detections found and no false positives. In general, the signal-to-noise ratio of events recorded by distributed acoustic sensing was lower than the surface array and 368 of 933 surface array events were found. Despite this, 167 new events were found in distributed acoustic sensing data that had no detected counterpart in the surface array. These differences can be attributed to the different detection threshold that depends on both magnitude and distance to the optical fibre. As distributed acoustic sensing data quality continues to improve, neural networks offer many advantages for automated, real-time microseismic event detection, including low computational cost, minimal data pre-processing, low false trigger rates and continuous performance improvement as more training data are acquired.     

Imaging pre‐existing natural fractures using microseismic data

In hydraulic fracturing treatments, locating not only hydraulic fractures but also any pre‐existing natural fractures and faults in a subsurface reservoir is very important. Hydraulic fractures can be tracked by locating microseismic events, but to identify the locations of natural fractures, an additional technique is required. In this paper, we present a method to image pre‐existing fractures and faults near a borehole with virtual reverse vertical seismic profiling data or virtual single‐well profiling data (limited to seismic reflection data) created from microseismic monitoring using seismic interferometry. The virtual source data contain reflections from natural fractures and faults, and these features can be imaged by applying migration to the virtual source data. However, the imaging zone of fractures in the proposed method is strongly dependent on the geographic extent of the microseismic events and the location and direction of the fracture. To verify our method, we produced virtual reverse vertical seismic profiling and single‐well profiling data from synthetic microseismic data and compared them with data from real sources in the same relative position as the virtual sources. The results show that the reflection travel times from the fractures in the virtual source data agree well with travel times in the real‐source data. By applying pre‐stack depth migration to the virtual source data, images of the natural fractures were obtained with accurate locations. However, the migrated section of the single‐well profiling data with both real and virtual sources contained spurious fracture images on the opposite side of the borehole. In the case of virtual single‐well profiling data, we could produce correct migration images of fractures by adopting directional redatuming for which the occurrence region of microseismic events is divided into several subdivisions, and fractures located only on the opposite side of the borehole are imaged for each subdivision.     

基于密集台阵研究2019辽宁抚顺M2.4矿震震源参数

分析矿震破裂机制及微震的时空分布能够为矿区灾害评估提供更多的有效信息.本研究基于密集台阵观测对2019 年11 月12 日辽宁抚顺2.4 级矿震开展震源参数研究,震源机制解显示地震破裂包含明显的非双力偶分量,表现为体积压缩的塌陷机制,且震源深度较浅,最佳拟合矩心深度为0.6 km.同时,对 11 月3 日—25 日记录...     

One‐ and two‐dimensional modelling of overland flow in semiarid shrubland,Jornada basin,New Mexico

Two distributed parameter models, a one‐dimensional (1D) model and a two‐dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event‐based and represent each watershed by an array of 1‐m² cells, in which the cell size is approximately equal to the average area of the shrubs. Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite‐difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second‐order predictor–corrector finite‐difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions. The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large‐scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration. Copyright © 2006 John Wiley & Sons, Ltd.     

基于波形相似特征的微地震事件初至拾取及全局校正

微地震事件初至拾取是井下微地震监测数据处理的关键步骤之一.初至误差的存在会使微地震震源定位结果产生较大偏差,进而影响后续的压裂裂缝解释.通常初至拾取过程对所有的微地震事件选择相同的特征函数并采用一致的拾取参数进行统一处理,然而当事件的能量、震源机制、传播路径以及背景噪声等存在明显差异时,所得初至拾取结果差别显著.为了提高微地震事件初至拾取标准一致性,本文提出基于波形相似特征的初至拾取及全局校正方法.该方法首先利用互相关函数对每个事件内的各道记录进行时差校正,得到初始初至信息并形成叠加道,再对所有事件的叠加道进行全局互相关得到事件间初至相对校正量,最终初至结果可以通过各个事件的初始初至信息与其相对校正量相加得到.方法将所有微地震事件初至结果作为一个整体处理,从而能够克服常规方法初至拾取标准一致性差的缺陷.实际资料处理结果表明,相比于常规方法,该方法可以有效提高事件初至拾取和定位结果的一致性.     

Earthquake soil‐structure interaction of nuclear power plants,differences in response to 3‐D, 3 × 1‐D,and 1‐D excitations

In soil‐structure interaction modeling of systems subjected to earthquake motions, it is classically assumed that the incoming wave field, produced by an earthquake, is unidimensional and vertically propagating. This work explores the validity of this assumption by performing earthquake soil‐structure interaction modeling, including explicit modeling of sources, seismic wave propagation, site, and structure. The domain reduction method is used to couple seismic (near‐field) simulations with local soil‐structure interaction response. The response of a generic nuclear power plant model computed using full earthquake soil‐structure interaction simulations is compared with the current state‐of‐the‐art method of deconvolving in depth the (simulated) free‐field motions, recorded at the site of interest, and assuming that the earthquake wave field is spatially unidimensional. Results show that the 1‐D wave‐field assumption does not hold in general. It is shown that the way in which full 3‐D analysis results differ from those which assume a 1‐D wave field is dependent on fault‐to‐site geometry and motion frequency content. It is argued that this is especially important for certain classes of soil‐structure systems of which nuclear power plants subjected to near‐field earthquakes are an example.     

Determination of Stress State from Focal Mechanisms of Microseismic Events Induced During Hydraulic Injection at the Hijiori Hot Dry Rock Site

—?The stress state at the Hijiori hot dry rock site was estimated based on the inversion from focal mechanisms of microseismic events induced during hydraulic injection experiments. The best fit stress model obtained by inverting 58 focal mechanisms of seismic events simultaneously indicates that the maximum principal stress σ₁ is vertical, while the minimum principal stress σ₃ is horizontal and trends north-south. The average misfit between the stress model and all the data is 6.8°. The inversion results show that the average misfit is small enough to satisfy the assumption of homogeneity in the focal mechanism data and that the 95% confidence regions of σ₁ and σ₃ are well constrained, i.e., they do not overlap, suggesting that the inversion results are acceptable. The stress estimates obtained by the focal mechanism inversion essentially agree with other stress estimates previously obtained. It is therefore concluded that the focal mechanism inversion method provides a useful tool for estimating the stress state. The hypocentral distributions of microseismic events associated with the hydraulic fracturing experiments are distributed around the plane that spreads to almost east–west from the injection wells and declines to the north at a high angle. The vertical orientation and east–west strike of the seismic events are essentially coplanar with the caldera ring-fault structure in the southern portion of the Hijiori Caldera. This indicates that tensile fractures of intact rock were not being created, but pre-existing fractures were being re-opened and developed in the direction of the maximum horizontal principal stress, although microseismic events were caused by shear failures.     

陕西地区小微震震源机制研究

小微震事件的震源机制是区域应力场及诸多地球动力学研究的基础资料。陕西地区为多个地震带的交汇区,近些年积累了丰富的小微震波形资料。运用新近发展的适用于求解小微震震源机制的广义极性振幅技术(GPAT),结合陕西2015地壳速度模型,求解陕西测震台网2011年4月至2015年12月间记录的121次ML1.5~3.5事件的震源机制。反演结果表明:(1)以上事件的震源机制大部分为走滑及正断类型,其比例占64.5%;逆断型机制占22.3%。(2)反演震源机制得到的震源深度与定位深度具有良好的一致性;矩震级与近震震级间存在差别,且这种差别随事件的变小而增大。(3)对比渭河断陷带相关研究成果,验证了该区域震源机制以正断型为主,具有拉张应力状态。     

Stability of source mechanisms inverted from P‐wave amplitude microseismic monitoring data acquired at the surface

We study the stability of source mechanisms inverted from data acquired at surface and near‐surface monitoring arrays. The study is focused on P‐wave data acquired on vertical components, as this is the most common type of acquisition. We apply ray modelling on three models: a fully homogeneous isotropic model, a laterally homogeneous isotropic model and a laterally homogeneous anisotropic model to simulate three commonly used models in inversion. We use geometries of real arrays, one consisting in surface receivers and one consisting in ‘buried’ geophones at the near‐surface. Stability was tested for two of the frequently observed source mechanisms: strike‐slip and dip‐slip and was evaluated by comparing the parameters of correct and inverted mechanisms. We assume these double‐couple source mechanisms and use quantitatively the inversion allowing non‐double‐couple components to measure stability of the inversion. To test the robustness we inverted synthetic amplitudes computed for a laterally homogeneous isotropic model and contaminated with noise using a fully homogeneous model in the inversion. Analogously amplitudes computed in a laterally homogeneous anisotropic model were inverted in all three models. We show that a star‐like surface acquisition array provides very stable inversion up to a very high level of noise in data. Furthermore, we reveal that strike‐slip inversion is more stable than dip‐slip inversion for the receiver geometries considered here. We show that noise and an incorrect velocity model may result in narrow bands of source mechanisms in Hudson's plots.