Abstract.New regional seismological data acquired in Colombia during 1993 to 1996 and tectonic field data from the Eastern Cordillera (

Summary A simple and unified approach is presented to solve both the elasto‐dynamic and elasto‐static problems of point sources in a multi‐layered half‐space by using the Thompson‐Haskell propagator matrix technique. It is shown that the apparent incompatibility between the two is associated with the degeneracy of the dynamic problem when ω= 0 and both can be handled uniformly using the Jordan canonical forms of matrices. We re‐derive the propagator matrices for both the dynamic and static cases. We then show that the dynamic propagator matrix and the solution converge to their static counterparts as ω→ 0. Satisfactory static deformation can be obtained numerically using the dynamic solution at near‐zero frequency.

Source parameter scaling for major and great thrust‐faulting events on circum‐Pacific megathrusts is examined using uniformly processed finite‐fault inversions and radiated energy estimates for 114 Mw ≥ 7.0 earthquakes. To address the limited resolution of source spatial extent and rupture expansion velocity (Vr) from teleseismic observations, the events are subdivided into either group 1 (18 events) having independent constraints on Vr from prior studies or group 2 (96 events) lacking independent Vr constraints. For group 2, finite‐fault inversions with Vr = 2.0, 2.5, and 3.0 km/s are performed. The product Vr3ΔσE, with stress drop ΔσE calculated for the slip distribution in the inverted finite‐fault models, is very stable for each event across the suite of models considered. It has little trend with Mw, although there is a baseline shift to low values for large tsunami earthquakes. Source centroid time (Tc) and duration (Td), measured from the finite‐fault moment rate functions vary systematically with the cube root of seismic moment (M0), independent of assumed Vr. There is no strong dependence on magnitude or Vr for moment‐scaled radiated energy (ER/M0) or apparent stress (σa). ΔσE averages ~4 MPa, with direct trade‐off between Vr and estimated stress drop but little dependence on Mw. Similar behavior is found for radiation efficiency (ηR). We use Vr3ΔσE and Tc/M01/3 to explore variation of stress drop, Vr and radiation efficiency, along with finite‐source geometrical factors. Radiation efficiency tends to decrease with average slip for these very large events, and fracture energy increases steadily with slip.

Summary This note is devoted to the confrontation of intuitive ideas in the field of inverse problems, especially in tomographic seismological studies, with the results of a more rigorous approach. With the help of a simple example, we show that tests commonly used to illustrate the quality of inversion results can be misleading. Based on a classical mathematical analysis, we explain the origin of the problems that we have seen. Our main conclusion is that, in circumstances not so unrealistic, and in contradiction to a generally idea, small‐size structures like in the ‘checker‐board test’ can be well retrieved while larger structures are poorly retrieved.

SUMMARY W phase is a long period phase arriving before S wave. It can be interpreted as superposition of the fundamental, first, second and third overtones of spheroidal modes or Rayleigh waves and has a group velocity from 4.5 to 9 km s−1 over a period range of 100–1000 s. The amplitude of long period waves better represents the tsunami potential of an earthquake. Because of the fast group velocity of W phase, most of W phase energy is contained within a short time window after the arrival of the P wave. At a distance of 50°, W phase energy is contained within 23 min after the origin time which is the distinct advantage of using W phase for rapid tsunami warning purposes. We use a time domain deconvolution method to extract W phases from the broad‐band records of global seismic networks. The bandwidth of W phase is approximately from 0.001 to 0.01 Hz, and we bandpass filter the data from 0.001 to 0.005 Hz in most cases. Having extracted W phase from the vertical component records, we perform a linear inversion using a point source to determine Mw and the source mechanism for several large earthquakes including the 2004 Sumatra–Andaman earthquake, the 2005 Nias earthquake, the 2006 Kuril Is. earthquake and the 2007 Sumatra earthquake. W phase inversion yields reliable solutions and holds promise of the use of W phase for rapid assessment of tsunami potential.

Supplemental Information on Rupture Analyses P and SH Wave Finite Fault InversionThe body wave inversions yield predominantly bilateral slip, although there may be a slight asymmetry in the slip distribution with greater extent toward the northwest. The P-and SH-waveform matches for our preferred finite source model are shown in Fig. S3. The slip model accounts for about 78% of the weighted signal power in the 120-s-long interval used in the inversion, with the source time function representing slip during the first 60 s of rupture. The seismic moment was estimated as 2.5 x 10 21 Nm (M w 8.2), but experience indicates that this may be less reliable than a determination made at longer periods and we adopt a final moment of 1.8 x 10 21 Nm (M w 8.1) based on composite source modeling of 714-1000 s period Rayleigh waves. There are clearly some P wave motions about 100 s after the first arrival in the waveforms of stations in Asia (TATO, ENH, BJT) that are not matched by the source model.Using very long fault models extending toward the northwest allows the normal fault model to match this late energy, but as discussed below, the late signal appears to originate from a secondary event with different fault mechanism. The depth extent of rupture is not well resolved, but we find that localized regions of significant slip are present in all models extending to depths of 30-36 km (>24 km below the 6 km thick ocean layer). The likelihood that rupture during the mainshock extended this deep is strongly supported by the depth of the largest aftershock in the trench-slope region with a location and mechanism consistent with being on the mainshock rupture surface. This is the event of October 19, 2009 (22:49:37 UTC, 15.3°S, 172.2°W, M w 5.9). The W-phase and GCMT solutions (Fig. 1) for this event have compatible normal fault geometries, with the W-phase centroid depth being 32.5 km. We inverted 40 azimuthally welldistributed teleseismic P waves for a finite source model for this event, assuming a hypocentral depth of 30 km. The resulting slip model and examples of fits to the data are shown in Fig. S4.The rupture centroid is confirmed to be about 32 km deep.The rupture velocity of predominantly bilateral ruptures is usually not well resolved by teleseismic body wave data because their high apparent velocities provide limited resolution.Essentially, the slip distribution scales spatially directly with the assumed rupture velocity.However, surface waves have lower apparent velocities and are thus more sensitive to directivity effects. We compared observed and predicted of short-arc Rayleigh wave (R1) source time functions (discussed below) for many body wave models to bound the rupture velocity and spatial extent of the slip model. We compared predicted R1 STFs for the model in Fig. S2 with azimuthally binned and stacked STF observations, finding little evidence for azimuthal variation of STF duration, consistent with a largely bilateral rupture. Preferred rupture velocities based on fitting the STF characteristics are less tha...

We investigate the partitioning of energy released during an earthquake to radiated, fracture and thermal energies in an attempt to link various observational results obtained in different disciplines. The fracture energy, E G , used in seismology is different from that commonly used in mechanics where it is the energy used to produce new crack surface. In the seismological language it includes the energies used for off-fault cracking, and various thermal processes. The seismic moment, M o ' the radiated energy, E R , and rupture speed, V R , are key macroscopic parameters. The static stress drop can be a complex function of space, but if an average can be defined as f11, it is also a useful source parameter. From the combination of M o ' E R , and, f11 we can estimate the radiation efficiencY11R' or EG which can also be estimated independently from V R . 11R provides a link to the results of dynamic modeling of earthquakes which determines the displacement and stress on the fault plane. Theoretical and laboratory results can also be compared with earthquake data through 11K Also, the fracture energy estimated from the measurement of the volume and grain size of gouge of an exhumed fault can be linked to seismic data through 11K In these comparisons, the thermal energy is not included, and it must be estimated independently from estimates of sliding friction during faulting. One of the most challenging issues in this practice is how to average the presumably highly variable slip, stress and frictional parameters to seismologically determinable parameters.

SUMMARY Rapid characterization of the earthquake source and of its effects is a growing field of interest. Until recently, it still took several hours to determine the first‐order attributes of a great earthquake (e.g. Mw≥ 7.5), even in a well‐instrumented region. The main limiting factors were data saturation, the interference of different phases and the time duration and spatial extent of the source rupture. To accelerate centroid moment tensor (CMT) determinations, we have developed a source inversion algorithm based on modelling of the W phase, a very long period phase (100–1000 s) arriving at the same time as the P wave. The purpose of this work is to finely tune and validate the algorithm for large‐to‐moderate‐sized earthquakes using three components of W phase ground motion at teleseismic distances. To that end, the point source parameters of all Mw≥ 6.5 earthquakes that occurred between 1990 and 2010 (815 events) are determined using Federation of Digital Seismograph Networks, Global Seismographic Network broad‐band stations and STS1 global virtual networks of the Incorporated Research Institutions for Seismology Data Management Center. For each event, a preliminary magnitude obtained from W phase amplitudes is used to estimate the initial moment rate function half duration and to define the corner frequencies of the passband filter that will be applied to the waveforms. Starting from these initial parameters, the seismic moment tensor is calculated using a preliminary location as a first approximation of the centroid. A full CMT inversion is then conducted for centroid timing and location determination. Comparisons with Harvard and Global CMT solutions highlight the robustness of W phase CMT solutions at teleseismic distances. The differences in Mw rarely exceed 0.2 and the source mechanisms are very similar to one another. Difficulties arise when a target earthquake is shortly (e.g. within 10 hr) preceded by another large earthquake, which disturbs the waveforms of the target event. To deal with such difficult situations, we remove the perturbation caused by earlier disturbing events by subtracting the corresponding synthetics from the data. The CMT parameters for the disturbed event can then be retrieved using the residual seismograms. We also explore the feasibility of obtaining source parameters of smaller earthquakes in the range 6.0 ≤Mw < 6.5. Results suggest that the W phase inversion can be implemented reliably for the majority of earthquakes of Mw= 6 or larger.