GEOPHYSICAL RESEARCH LEITERS, VOL. 18, NO. 8, PAGES 1385-1388, AUGUST 1991 THE DETERMINATION OF SOURCE PARAMETERS FOR SMALL EARTHQUAKES FROM A SINGLE, VERY BROADBAND SEISMIC STATION Guangwei Fan and Terry Wallace Department of Geosciences, University of Arizona Abstract. The installation of very broadband seismic stations makes it possible to recover the source parameters of small earthquakes (2.5 < ML < 5.0) which occurat local and regional distances. If the grosscrustal structure along the travel path is known, it is possible to use the P, SV and SH displacement waveforms from a single station to determine the seismic momenttensor. Althoughthe detailsof the crustal structure strongly affect the body waveforms at regional distances, the signature of theseismic source orientation on the waveform is robust at frequencies less than 1-3 Hz. We explore the trade-offs betweencrustal model, hypocentral depth and filtering for a linear moment tensor inversion procedure. The procedure is tested on two smallearthquakes which occurred in the Rio Grande Rift and were recorded at the IRIS/USGS station ANMO. The agreement between the single station moment tensor inversion fault planeparameters and those determined from local first motions is excellent. Introduction Determination of the source parameters of shallow, moderate sized earthquakes (ML < 5.5) is an important seismological problem for several reasons. Earthquakes of thistypehavewidespread geographic occurrence, andin some cases, theseearthquakes provide the only clue to the active tectonics of a region. A considerable amount of effort has been expended to determine the source parameters of thissize earthquake, although such determinationsare beset with difficulties. Most of these events are too small to be well recorded teleseismically, soregional waveforms mustbe used to determine the source parameters. Wallace andHelmberger (1982) and Patton (1988) have developed inversion procedures for regionalbodyand surface waves respectively. These methodologies allow theroutine determination of source parameters for events as smallasML = 5 when recorded by 3 or more stations. The installation of high quality, very broadband seismic stations suggests that these methods may lower the magnitude threshold to less than4.5. Unfortunately, as the magnitude of events is reduced the number of recording stationsis correspondingly reduced. Several authors have suggested that fairly completesource information can be extractedfrom a single seismicstation given certain conditions. Langston(1982) usedP and SH waveforms to discriminate between fault types. Ekstrom et al. (1986) applied the centroid moment tensor (CMT) method to retrieve focal mechanisms of large events, and Jimenez et al. (1989) developed a technique utilizingthe regional distance surfacewaves. In this paper we presenta simple linear moment tensor inversionprocedure to retrieve the seismic source parameters at a single station which is situated at local to regional distances fromanepicenter. At this distance range the structure of the crust hasa strong effecton thebodywaves and therefore there is a trade-offs between modeling assumptions andsource parameters. Fortunately, the effect of the source orientation on the waveforms is fairly decoupled from the effects of the structural details, and essential information, such asthetype of faulting, can beretrieved with Copyright 1991 by the American Geophysical Union. Paper number 91GL01804 0094-8534 / 91 / 91GL-01804 $3. O0 very simple assumptions about thecrustal model. The inversion procedure is tested on two small earthquakes which were recorded on an IRIS/USGS GSN station located 65 km from theepicenter. The events werealso well recorded on a local short-period network,which provides a basis for comparison of the fault plane parameters. The ability to recover accurate source parameters from a single station will be proven useful on at least two counts:(1) it will lower the magnitude threshold for whichaccurate source parameters can be determined from sparse broadbandnetworks, and (2) it will greatly improve the information that can be recovered from portable instrumentation, suchas a PASSCAL field recorder(with broadband sensors) which might be usedfor monitoring aftershocks or low levelseismicity. The Inversion Procedure Linear moment tensor inversion techniques using body wave synthetic seismograms have been developed by numerous investigators (StumpandJohnson, 1977; Langston, 1981; Wallaceand Helmberger, 1982). Here we minimize the difference between observed and predicted ground displacements in threecomponents. Observed seismograms are windowed from theonset of P (or S) to arrivals of multiply reflectedS (or surface wave). The synthetics are calculated using the generalized ray theory. Following Langston (1981) the displacement from a purely deviatoricpoint source in a layered stack canbe represented as d(t,r,z) = s(t) * • Hdi(t,r,z) A'i ( 1 ) i=l where d=w, q or v is the vertical, radial or tangential displacement respectively,s(t) is the normalizedfar-field source time function and (*) represents convolution. The Hdi represent the Green'sfunctions for the three fundamental faults: verticalstrike-slip, verticaldip-slipand450 dip-slip. The coefficients of the horizontal radiation pattern, A i can be written as A'I = 0.5(Myy -Mxx) cos(2•) - Mxy sin(2•) A'2 = Myz cos(•) - Myz sin(•) A'3 = 0.5(Mxx -Myy) A'4 = 0.5(Mxx-Myy) sin(2•) - Mxy cos(2•) A'5 = Myz cos(•) - Mxz sin(•) where ß is the azimuth between the source and receiver measured in a clockwise manner. Most smallevents have simple time functions, whichcan be treated as "known" in equation (1). The otherterms in (1) can be rearrangedso that the moment tensor elements are factored; we can rewrite thedisplacements in terms of a linear combination of the moment tensor elements: dw = 0.5{ Gw3- GwlCOS(2•)} Mxx + 0.5{Gw3 + Gwl cos(2•)}Myy- Gwl sin(2•)Mxy + Gw2 cos(•)Mxz + Gw2 sin(•)Myz dq = 0.5{ Gq3 - GqlCOS(2•) } Mxx + 0.5{Gq3 + Gql cos(2•)}Myy- Gqlsin(2•)Mxy + Gq2 cos(•)Mxz + Gq2 sin(•)Myz (2) dv = 0.5Gvl sin(2•)Mxx - 0.5Gvlsin(2•)Myy - Gvlcos(2•)Mxy - Gv2 sin(•)Mxz + Gv2 cos(•)Myz 1385