Source analysis using regional empirical Green's functions: The 2008 Wells, Nevada, earthquake



[1] We invert three-component, regional broadband waveforms recorded for the 21 February 2008 Wells, Nevada, earthquake using a finite-fault methodology that prescribes subfault responses using eight MW∼4 aftershocks as empirical Green's functions (EGFs) distributed within a 20-km by 21.6-km fault area. The inversion identifies a seismic moment of 6.2 x 1024 dyne-cm (5.8 MW) with slip concentrated in a compact 6.5-km by 4-km region updip from the hypocenter. The peak slip within this localized area is 88 cm and the stress drop is 72 bars, which is higher than expected for Basin and Range normal faults in the western United States. The EGF approach yields excellent fits to the complex regional waveforms, accounting for strong variations in wave propagation and site effects. This suggests that the procedure is useful for studying moderate-size earthquakes with limited teleseismic or strong-motion data and for examining uncertainties in slip models obtained using theoretical Green's functions.

1. Introduction

[2] The M∼6 normal-faulting earthquake of 21 February 2008 northeast of Wells, Nevada, was recorded by several permanent broadband stations of the Advanced National Seismic System (ANSS) and by numerous portable broadband stations of the Earthscope Transportable Array (USArray), a regionally dense network (∼70-km spacing) of 400 seismic stations placed at temporary sites and progressively moved from west to east across the conterminous United States. After 2 years of continuous recording, stations on the western edge of the array are dismantled and re-installed east of the network, resulting in a comprehensive seismic coverage designed to explore the structure and evolution of the North American continent [Levander et al., 1999].

[3] In February 2008, USArray stations extended east across Nevada into western Utah and widely recorded the Wells earthquake. The USArray stations also recorded many of the aftershocks, offering an unprecedented opportunity for a detailed analysis of the earthquake source using empirical Green's functions based on the observed aftershock recordings. In this study, we examine the rupture characteristics of the Wells earthquake using a finite-fault inversion technique that uses the observed regional aftershock records to quantify the seismic response of point sources near the earthquake source region. We invert the three-component velocity waveforms recorded at unclipped stations located within 300 km of the mainshock epicenter. These regional waveforms are relatively complicated due to propagation effects that vary with azimuth across the geologically complex Basin and Range province (Figure 1). This variability in waveform complexity can be clearly seen in the observed vertical records shown in Figure 1. For example, stations M14, L11 and O13 are located at a similar distance, but at different azimuths, from the source and exhibit simple, pulse-like waveforms. However, stations M10 and N10, which are located at a similar distance, show complicated high-frequency waveforms. The primary purpose of using aftershock records to identify the seismic responses of point sources along the fault is thus to account for these complicated propagation effects.

Figure 1.

Broadband stations that recorded the 2008 Wells, Nevada, earthquake within 300 km of the epicenter (star). Stations are USArray sites except ELK and BMN, which are ANSS sites. Vertical, broadband velocity waveforms are shown in order of increasing distance from top to bottom and left to right. Numbers to the right indicate the peak amplitude of each record (in 106 digital counts). The geologic base map shows the complexity of the various regional travel paths with colors given as follows: light gray, Quaternary sediments; yellow, Tertiary continental deposits; orange, Tertiary volcanic rocks; green, Mesozoic volcanic and intrusive rocks; and blue, Paleozoic volcanic and intrusive rocks.

2. Inversion Procedure

[4] The waveform inversion method is based on the finite-fault analysis of Hartzell and Heaton [1983], where a fault plane with prescribed dimensions is used to recover the distribution of coseismic slip. In the Hartzell and Heaton [1983] formulation, the fault plane is subdivided into a given number of subfaults with point sources distributed uniformly along their length and width. Rupture is assumed to propagate radially from the hypocenter along the fault at a given speed, and synthetic records are calculated for each subfault and recording site based on the point-source responses (Green's functions) calculated for an assumed crustal structure. The Green's functions are delayed by times corresponding to the designated rupture velocity and then summed to simulate a smooth rupture across the subfault. The subfault synthetics for all stations are then used to fill an m-by-n matrix A where m is the total number of record data points and n is the total number of subfaults. The earthquake data records are similarly concatenated to produce an m-length vector b that together with the A matrix define an overdetermined system of linear equations of the form Ax = b, where x is the solution vector containing the dislocation weights required of each subfault to reproduce the observations. The linear system is solved using a Householder reduction method [Lawson and Hanson, 1974] that invokes a positivity constraint to prevent the mapping of negative slip on the fault. Also, spatial smoothing and moment-minimization constraints are added to recover the simplest possible solution.

[5] Green's functions calculated for an assumed crustal structure, however, are generally imprecise due to the difficulty in defining accurate velocity models. Thus, point-source responses can be more realistically approximated using actual observed waveforms that correspond to seismic energy propagating across the source-to-station travel path, as is the case for aftershock recordings [Hartzell, 1978]. This empirical Green's function (EGF) approach uses the observed records of aftershocks occurring in the earthquake source region to identify responses for point sources distributed across each subfault. The method assumes that the source mechanisms of the aftershocks are the same as the section of the mainshock rupture where they are used, which is required to prevent distortions due to differences in the seismic-wave radiation pattern.

[6] We apply the EGF procedure previously used by Hartzell [1989] to model the near-source strong motions recorded for the 1986 ML 5.9 North Palm Springs, California earthquake. In that study, Hartzell [1989] used numerous ML ∼ 3.0 aftershocks located along the length and width of the fault to account for differences in response due to depth variations updip and downdip along the fault and to minimize errors due to departures of individual aftershock mechanisms from the mainshock fault geometry. The use of many aftershocks, however, may not be necessary to define appropriate Green's functions in EGF finite-fault studies. Fukuyama [1991], for example, used one to two aftershocks to derive coseismic slip models for three M 6.7–7.7 earthquakes in Japan. Mori and Hartzell [1990], Dreger [1994], and Dreger et al. [1995] used a single-aftershock deconvolution approach to recover source-time functions and infer the distribution of slip on a finite fault for several M 4.6–6.7 earthquakes in California and Oregon. Also, in a study of the 1999 MW 7.6 Chi-Chi, Taiwan earthquake, Xu et al. [2002] used two aftershocks to retrieve far-field (epicentral distances between 7.5° and 166°) P and S source-time functions and to derive a spatio-temporal image of the mainshock slip consistent with results previously obtained by other investigators from the analysis of strong-motion, teleseismic, and/or Global Positioning System (GPS) data. More recently, Mendoza and Hartzell [2008] used regional Pnl records from a single aftershock of the 2004 MW 6.0 Parkfield, California earthquake, to retrieve a source model similar to those obtained by other investigators using different data types.

3. EGF Finite-Fault Analysis

[7] We use a total of eight aftershocks large enough to be well recorded at most of the stations that recorded the Wells earthquake. Magnitudes for these aftershocks vary between 3.8 and 4.6 MW (Table 1). Epicentral locations for the aftershocks and mainshock are shown in Figure 2 together with the surface projection of the fault plane used to model the coseismic slip. We use the SE-dipping nodal plane (N36°E strike, 44° dip) from the Global CMT Project ( to represent the fault. This fault orientation is consistent with the distribution of aftershocks relocated by K. Smith ( The fault dimensions are set at 20 km along strike and 21.6 km downdip, and the fault is subdivided into 100 2-km by 2.2-km subfaults with point sources distributed every 0.1 km. The fault covers depths between 1 and 16 km, and the hypocenter is placed near the center of the fault at a source depth of 7.2 km, which is within the location error of the consensus depth of 7 km reported for the mainshock. Rupture is assumed to propagate radially from the hypocenter along the fault at a constant speed of 2.8 km/sec, a typical value for earthquakes of this size [e.g., Somerville et al., 1999]. For each regional station, the response of each point source is selected from the suite of eight aftershock recordings based on the location of the nearest aftershock along the fault, scaled from its original seismic moment to a common value of 1 × 1020 dyne-cm. This scaling is necessary to prescribe a uniform slip for each subfault across the fault [Hartzell, 1978, 1989].

Figure 2.

Geographic map showing the epicenter of the 2008 Wells earthquake (star) and the eight aftershocks (solid circles) used in this study. Aftershocks are labeled according to the listing given in Table 1. The rectangle shows the surface projection of the fault plane used to model the mainshock rupture.

Table 1. Source Parameters of the 2008 Wells Earthquake and the Eight Aftershocks Used As Empirical Green's Functionsa
EventDateOTLat-LonDepth (km)MWStrike (deg)Dip (deg)Rake (deg)
  • a

    MS is the mainshock. Hypocenters are from the University of Nevada Reno Seismological Laboratory. Magnitudes and focal mechanisms are from the Saint Louis University Earthquake Center.

MS2 211416 02.741.16 −114.887.95.92540−90
12 211620 02.241.20 −114.865.33.935448−129
22 212357 51.041.15 −114.9310.64.61968−118
32 220150 05.241.14 −114.928.53.9545−126
42 222327 45.341.10 −114.9215.64.33850−94
52 270759 38.241.18 −114.838.84.135980175
62 281510 37.741.16 −114.935.34.02261−118
74 011316 17.241.23 −114.8411.04.18550−15
84 222040 09.341.22 −114.817.63.84530−55

[8] The orientation of the fault is used primarily to select the appropriate aftershock record for each point source, since the focal mechanism of the mainshock is specified from the aftershock fault geometry. Source mechanisms obtained by the Saint Louis University Earthquake Center ( for the eight aftershocks from inversion of the regional broadband waveforms generally show normal faulting similar to that of the mainshock except for aftershocks 5 and 7, which show a significant strike-slip component (see Table 1). These aftershock mechanisms may reflect a true spatial variation in faulting geometry across the fault or may correspond to secondary post-seismic deformation away from the main fault plane. Since we do not know which of these is more likely, we maintain our approach of using as many aftershocks as possible to allow a more complete representation of particular points across the fault. The results presented later for the Wells earthquake indicate that this is a reasonable approach. Also, we prefer this approach because it allows a more timely analysis of the mainshock source before specific information on the aftershock fault geometries is available. Nonetheless, we perform an additional EGF inversion of the Wells data set without the strike-slip events to examine the effects on the inferred source model.

[9] A record length of 80 sec is used in the inversion, with mainshock records at each station aligned with the waveforms constructed for the subfault containing the earthquake hypocenter. This 80-sec record length includes the entire body- and surface-wave energy recorded at the majority of the sites within the 300-km distance range. Since the mainshock and aftershocks are recorded by the same stations, there is no need to remove the instrument effects, although we bandpass-filter both data sets between 0.02 and 0.5 Hz to coincide with the principal band of seismic energy recorded at the regional distances. Note also that in this EGF parameterization, there is no prior specification of the fault dislocation time, and the inversion assumes a rise time that corresponds to the source duration of the aftershocks used to construct the subfault waveforms. These durations include finiteness effects but are relatively small compared to the short-period limit (2 sec) of the filtered records. Therefore, the subfault waveforms appear as step-function responses within the bandwidth used in the inversion.

4. Results and Discussion

[10] The results of the EGF inversion show coseismic slip concentrated in a single relatively compact region extending primarily updip from the hypocenter and covering an approximately 6.5-km by 4-km area (Figure 3). This source model was derived using all eight aftershocks from Table 1. When we exclude the two strike-slip events (aftershocks 5 and 7), we obtain a result almost identical to that shown in Figure 3, indicating that the exclusive use of events with mechanisms similar to that of the mainshock is not required to effectively image the Wells earthquake rupture. The total moment of the inferred slip model is 6.2 × 1024 dyne-cm (equivalent to magnitude MW 5.8) for a shear rigidity of 3.23 × 1011 dyne/cm2. Two-thirds of the moment lies within the principal region of coseismic slip. The slip reaches a maximum of 88 cm near the hypocenter, and the rupture duration is about 2 seconds. The rupture zone falls in an area of limited aftershock activity along or near the mainshock fault. When projected onto the fault, the aftershocks relocated by K. Smith (personal communication, 2008) plot primarily outside or near the edges of the principal slip region (see Figure 3). This observation is similar to those presented in other mainshock-aftershock comparisons and may indicate a relatively complete release of accumulated stress resulting in stress concentrations at the edges of the rupture region [e.g., Mendoza and Hartzell, 1988a; Hartzell et al., 1991].

Figure 3.

Coseismic slip inferred for the Wells earthquake using the three-component regional USArray and ANSS waveforms. The fault is subdivided into 100 2-km by 2.2-km subfaults. The star shows the mainshock hypocenter, and contours indicate the rupture time in seconds corresponding to a fixed rupture velocity of 2.8 km/sec. Triangles are relocated aftershock hypocenters provided by K. Smith (personal communication, 2008) projected perpendicularly onto the earthquake fault.

[11] We estimate the static stress drop Δσ within the localized hypocentral rupture area of the 2008 Wells earthquake using the Brune [1970] relation

equation image

where Mo is the seismic moment within a circular rupture of radius r. The seismic moment within the 6.5-km by 4-km rupture area is 3.9 × 1024 dyne-cm and the equivalent radius is 2.9 km, yielding an estimated stress drop of 72 bars. Stress drops for normal-faulting earthquakes in the western United States are generally smaller than this value. For example, the 1983 MW ∼7 Borah Peak, Idaho earthquake has an estimated stress drop of about 25 bars [Boatwright and Choy, 1986; Mendoza and Hartzell, 1988b], although local stress drops estimated for the regions of maximum slip are closer to 45–50 bars. Nonetheless, our stress-drop estimate for the 2008 Wells earthquake is higher than expected, suggesting that Basin and Range normal faults are capable of producing higher stress-drop seismic events.

[12] Waveforms predicted by the inferred slip model fit the observed complex regional records remarkably well (Figure 4), including those recorded at similar distances but at different azimuths from the source, properly accounting for the different travel paths to the regional recording sites. The highly accurate prediction of the complex regional broadband waveforms recorded at the USArray sites indicates that the EGF methodology provides a superior alternative to the use of theoretical Green's functions that are based on regional 1D crustal models that may not accurately identify the complicated propagation effects along the seismic-wave travel paths. The use of incorrect Green's functions in finite-fault inversion studies generally result in indeterminable errors that map directly onto the source. The EGF approach generally serves to minimize these errors, although there are clearly several factors that affect the ability of an aftershock record to accurately identify the path effects, including differences in location between the aftershock hypocenter and the point source along the fault, uncertainties in the aftershock locations themselves, and differences in mechanism between the aftershock and the mainshock. Other factors that can affect the accuracy of the inversion process are errors in the aftershock seismic moments and departures from the assumed rupture velocity. A complete evaluation of the effect of these uncertainties is difficult but may be accomplished by conducting systematic sensitivity tests [e.g., Dreger, 1994].

Figure 4.

Fits between observed (solid) and predicted (dotted) vertical and horizontal (north–south and east–west) velocity records corresponding to the source model inferred for the 2008 Wells earthquake. Numbers below each record pair indicate the ratio of predicted-to-observed amplitudes. Records are shown in order of increasing epicentral distance from the earthquake and incorporate a bandpass filter with corners at 0.02 and 0.5 Hz.

[13] Although the widespread recording of both mainshock and aftershocks by dense regional networks is not common, the worldwide increase in permanent seismic-station deployment suggests that the routine use of an EGF approach in regional finite-fault source studies may ultimately provide a more accurate estimate of the coseismic rupture properties of seismic events. The methodology could thus be useful for ascertaining the degree of uncertainty inherent in finite-fault studies that rely strictly on numerically-calculated theoretical Green's functions. The approach may also be useful for studies of moderate-sized earthquakes with limited teleseismic data or that occur in areas with little or no strong motion records.


[14] Travel support was provided by UNAM (DGAPA Proj. IN-101708) and the U.S. Geological Survey. M. Meremonte provided technical assistance, and K. Smith gave us with his relocated hypocenters. Seismic waveform data were obtained from the IRIS Data Management Center ( This manuscript was improved by comments from J. Dewey, M. Petersen, and two anonymous reviewers.