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Journal Article
Published: 01 August 1982
Bulletin of the Seismological Society of America (1982) 72 (4): 1069–1083.
...R. D. List abstract A method of obtaining the displacement field of the Haskell model of an earthquake source, based on the well-known equivalence of seismic dislocations and body force, is described. It is shown that the solution of Madariaga (1978) can be generalized and that the two methods...
Journal Article
Published: 01 August 1978
Bulletin of the Seismological Society of America (1978) 68 (4): 869–887.
...Raúl Madariaga abstract We study the near-field generated by Haskell's rectangular fault model used extensively to interpret seismic data. By means of the Cagniard-de Hoop method we have been able to find an exact solution for the near-field particle velocities in the case of a step-function source...
Journal Article
Published: 01 August 1974
Bulletin of the Seismological Society of America (1974) 64 (4): 1275–1293.
... by Haskell (1967) and one by Mueller and Murphy (1971a), are compared with each other and they agree well for frequencies around 1 Hz and for yields in the range 3 to 300 kt. The Haskell model for tuff is modified to be more compatible with the models for salt, granite and alluvium. The Haskell model...
Journal Article
Published: 01 June 1996
Bulletin of the Seismological Society of America (1996) 86 (3): 750–760.
... for an elastic layer having velocities and density varying linearly with depth were computed by integrating numerically the governing differential systems and compared with results based on the Haskell model of splitting the linear layer in homogeneous sublayers. Even an adaptive process with a variable step...
Journal Article
Published: 05 January 2016
Bulletin of the Seismological Society of America (2016) 106 (1): 93–103.
... models, that is, the classical Haskell’s model ( HM ) and the modified HM with radial rupture propagation ( HM‐RRP ). The DSM accounts for directivity effects in the fault‐parallel direction, as well as fault‐normal ground motions, and overcomes the unrealistic uniform slip and stress singularities...
FIGURES | View All (7)
Journal Article
Published: 08 January 2019
Bulletin of the Seismological Society of America (2019) 109 (1): 358–371.
...) to forward‐model the rupture directions of the target events assuming the 1D Haskell model. The typical notion is that rupture tends to propagate away from the injection site where fluid pressure is the highest. Our analysis of four target earthquakes indicates various rupture styles with respect...
FIGURES | View All (10)
Journal Article
Published: 01 February 1964
Bulletin of the Seismological Society of America (1964) 54 (1): 141–149.
... be satisfactorily explained by a half-space model, because calculations based on such a model require a larger value of the P -wave velocity for the shorter period waves. However, calculations based upon Haskell's model of a crustal layer over a half-space give a satisfactory fit to the observed data. 15 7...
Image
Overview of the directivity evaluation process (event 29). (a) After the station corner frequencies are converted to source rupture durations (circles), a best‐fit Haskell model is determined. The horizontal line shows the true source duration. (b) Similar plot as (a), but now in terms of corner frequency. The horizontal line shows the rupture corner frequency, with the uncertainty indicated by the width of a lighter shaded line behind. (c) Bootstrap analysis, with plus or minus standard deviation shown as two vertical, solid lines. (d) A polar plot of the station corner frequencies (circles), model (dashed line), and model rupture azimuth (solid line). The color version of this figure is available only in the electronic edition.
Published: 20 August 2019
Figure 4. Overview of the directivity evaluation process (event 29). (a) After the station corner frequencies are converted to source rupture durations (circles), a best‐fit Haskell model is determined. The horizontal line shows the true source duration. (b) Similar plot as (a), but now in terms
Image
The spatial pattern of the seismic-wave spectral amplitude at 5 sec period calculated for a far-field Haskell model of the unilateral rupture (Aki and Richards, 1980). Shading shows relative amplitude variations, with lighter shading indicating larger amplitudes. The fault locations and rupture directions are indicated by the horizontal lines and arrows, respectively. As the rupture length (listed under each fault) grows (a-c) the focusing of radiated seismic waves becomes more pronounced in the direction of rupture propagation (becomes “directive”). Our hypothesis is illustrated by the stars, which denote epicenters of aftershocks triggered by the directive rupture on the larger fault. As the focusing becomes stronger, if aftershocks are dynamically triggered they should be relatively more abundant in the direction of focusing. Panel (d) shows that a bilateral rupture may be considered as the superposition of two unilateral ruptures and will be directive toward the end of the longer fault segment as long as half or more of the moment is released along that segment. The dynamically triggered seismicity will be asymmetric with a greater rate increase in the directive direction.
Published: 01 February 2003
Figure 1. The spatial pattern of the seismic-wave spectral amplitude at 5 sec period calculated for a far-field Haskell model of the unilateral rupture ( Aki and Richards, 1980 ). Shading shows relative amplitude variations, with lighter shading indicating larger amplitudes. The fault locations
Image
(a) Fault‐parallel section across the computational domain, with rupture patch location denoted by a solid rectangle for the Haskell’s model with radial rupture propagation (HM‐RRP) and the distributed slip model (DSM) and a dotted rectangle for the HM, which is offset in the x direction to match the epicenter location of the other models. Velocity and density profiles of the computational domain are plotted on the left: VP and VS are P‐ and S‐wave velocity in kilometers per second, ρ is density in grams per cubic centimeters. The shaded bar plotted on the right corresponds to the slip distribution of the rupture models below. (b) Point‐source model (PSM): location of the nucleation point (denoted by a star) relative to the rupture patch. (c) HM, unilateral rupture initiating at the left edge of the rupture patch, denoted by the thick, dashed line. Uniform color represents uniform slip Davg of 0.97 m. Rupture time isochrones (in seconds) are plotted in white. (d) HM‐RRP: radial rupture initiating at the nucleation point, same location as (b). Uniform shaded fill represents uniform slip Davg of 0.97 m. Rupture time isochrones (in seconds) are plotted in white. (e) DSM: radial rupture initiating at the nucleation point, same location as (b). The shaded gradient represents nonuniform slip according to the shaded bar in (a); white lines mark rupture time isochrones in seconds.The color version of this figure is available only in the electronic edition.
Published: 05 January 2016
Figure 1. (a) Fault‐parallel section across the computational domain, with rupture patch location denoted by a solid rectangle for the Haskell’s model with radial rupture propagation ( HM‐RRP ) and the distributed slip model ( DSM ) and a dotted rectangle for the HM , which is offset in the x
Journal Article
Published: 01 June 1984
Bulletin of the Seismological Society of America (1984) 74 (3): 843–862.
... and compared with the predictions of the Haskell, Mueller-Murphy, and finite difference numerical models. Several recent studies of high-frequency, near-field signals and teleseismic short-period P waves for LONGSHOT, MILROW, and CANNIKIN constrain the source functions at periods of 0.5 to 2.0 sec. Teleseismic...
Image
Computational time versus number of layers in models for Love waves. Circles represent computational time taken by the fast-generalized RT method, crosses by the Thomson–Haskell method, and triangles by the modified Thomson–Haskell method. Obviously, the modified Thomson–Haskell method is the most efficient.
Published: 01 October 2010
Figure 2. Computational time versus number of layers in models for Love waves. Circles represent computational time taken by the fast-generalized RT method, crosses by the Thomson–Haskell method, and triangles by the modified Thomson–Haskell method. Obviously, the modified Thomson–Haskell
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Computational time versus number of layers in models for Rayleigh waves. Circles represent computational time taken by the fast-generalized RT method, crosses by the Thomson–Haskell method, and triangles by the modified Thomson–Haskell method. Similar to the Love-wave case, the modified Thomson–Haskell method is the most efficient.
Published: 01 October 2010
Figure 3. Computational time versus number of layers in models for Rayleigh waves. Circles represent computational time taken by the fast-generalized RT method, crosses by the Thomson–Haskell method, and triangles by the modified Thomson–Haskell method. Similar to the Love-wave case, the modified
Journal Article
Published: 01 April 1984
Bulletin of the Seismological Society of America (1984) 74 (2): 395–415.
... polarity. These models are shown to simulate well the principal features of common circular and Haskell type of models, including the corner frequency shift of P waves with respect to S waves, and the relation between rupture velocity and maximum seismic efficiency. Spectral bandwidths...
Journal Article
Published: 01 October 1976
Bulletin of the Seismological Society of America (1976) 66 (5): 1501–1523.
... in a Haskell type fault model to derive scaling laws relating seismic moment to M S (20-sec surface-wave magnitude), M S to S and m b (1-sec body-wave magnitude) to M S . Observed data agree well with the predicted scaling relation. The “source spectrum” depends on both azimuth and apparent velocity...
Journal Article
Published: 01 August 2006
Bulletin of the Seismological Society of America (2006) 96 (4A): 1241–1256.
... to a unilateral rupture Haskell fault model, and the synthetic seismograms of different models calculated by the higher-degree moment tensors are compared with the theoretical solutions for a propagating source. Our results show that, the representation of higher- degree moment tensors up to degree 2 can describe...
FIGURES | View All (14)
Journal Article
Published: 01 October 2010
Bulletin of the Seismological Society of America (2010) 100 (5A): 2310–2316.
...Figure 2. Computational time versus number of layers in models for Love waves. Circles represent computational time taken by the fast-generalized RT method, crosses by the Thomson–Haskell method, and triangles by the modified Thomson–Haskell method. Obviously, the modified Thomson–Haskell...
FIGURES | View All (6)
Image
Flowchart showing how the teleseismic seismograms for the four models are made. For the three dynamic models, we start with frictional constitutive laws used in the 3D dynamic rupture simulations: (1) zero sliding friction, (2) constant sliding friction, and (3) slip- and rate-weakening friction. The 3D dynamic rupture simulations produce slip histories. The resultant slip histories are kinematic descriptions of slip on the fault during rupture. Yet at the same time, they account for dynamic effects by expressing reslipping episodes or other modifications to their shape. In addition to the three slip histories that are a result of our dynamic rupture simulations we also produce analytically a traditional Haskell-like slip history. The Haskell-like slip history is designed to have parameters similar to the slip- and rate-weakening friction model, but without reslipping. Hence, the traditional kinematic Haskell-like model slip history should be completely transparent to reflected seismic energy. Then we take all four kinematic slip histories and use them as input for teleseismic calculations to produce our resultant displacement seismograms as seen in the Results section.
Published: 01 June 2005
to the three slip histories that are a result of our dynamic rupture simulations we also produce analytically a traditional Haskell-like slip history. The Haskell-like slip history is designed to have parameters similar to the slip- and rate-weakening friction model, but without reslipping. Hence
Image
Synthetic model: (a) model parameters; (b) theoretical modal curves (Haskell and Thomson).
Published: 22 December 2011
Figure 5. Synthetic model: (a) model parameters; (b) theoretical modal curves (Haskell and Thomson).
Journal Article
Published: 01 October 1970
Bulletin of the Seismological Society of America (1970) 60 (5): 1491–1520.
...-of-precision con- trol feature and is about 38 per cent faster than the reducedmatrix extension; in fact, it is about 12 per cent faster than the fastest of the Thomson-Haskell versions. Explicit forms of the new representation are given for the layered-half-space analogs of continental and oceanic models...