Fault plane solutions using relative amplitudes of P and surface reflections: further studies

Summary. The method of computing fault plane solutions for small shallow earthquakes using relative amplitudes of P and pP , as described in an earlier paper, is extended to include sP. It is shown theoretically that even a single relative amplitude observation can impose a severe constraint on the orientation of an assumed double couple source, and earthquakes studied in the earlier paper are reprocessed with the inclusion of sP information. The method is also extended to deep earthquakes using long period seismograms, and to undersea earthquakes by allowing for the effect of a sea layer on the surface-reflected phases. Also described are options to search only a restricted range of source orientations, and to identify those orientations which are incompatible with one or more relative amplitudes. These options are applied to several earthquakes, to demonstrate the scope of the relative amplitude method. Results are illustrated using the seismic modelling method of Hudson (1969a, b) and Douglas, Hudson & Blamey (1972).     

A fault plane solution using theoretical P seismograms

We use the method of Hudson and Douglas, Hudson & Blarney to compute seismograms which simulate the codas of 10 short period P -wave seismograms from a shallow earthquake. The polarities and relative amplitudes of P and pP measured from seven of the observed seismograms are used to compute a fault plane solution with confidence limits, assuming that the source radiates as a double couple. This solution is in approximate agreement with that given for the same earthquake by Sykes & Sbar, who used only the onset polarities of short-period P waves. The small difference between the two solutions can be explained by interference between the true first motion of P and microseismic noise at two stations.
The results show that, for some shallow earthquakes, the relative amplitude method has the following advantages over the first motions method. First, a P/pP amplitude ratio (with appropriate confidence limits) can always be measured, even in seismograms which are so noisy that the first motion of P is uncertain. Second, the fault plane solutions obtained from relative amplitudes have known confidence limits. Finally, by using more information from each seismogram, the relative amplitude method requires considerably fewer seismograms than the first motions method.     

Magnitude and Q determinations in southern Africa using Lg wave amplitudes

b
The amplitude of vertical, short period (1 s) Lg -waves from 575 shallow earthquakes recorded within the distance range 0|Mo-30|Mo by the Rhodesian seismograph network during the period 1968–77 are analysed to separate the effects of earthquake size, epicentral distance and station structure.
When corrected for geometrical spreading and Airy phase dispersion the decay of amplitude with distance yields an estimate of anelastic attenuation of 0.160 deg^-1 which gives an average value of Q (the specific quality factor) of 603 |Mp 50 for propagation paths that lie along and across the East African Rift System. Inversion of the amplitude—distance curve gives the calibration or distance normalizing function. Thereby the amplitude of Lg can be used to provide an estimate of the size of small, local earthquakes in terms of the teleseismic body wave magnitude m_b (after Henderson). The station effects of the six seismograph stations making up the network all lie within |Mp0.1 magnitude units. Since three of the stations lie on the Rhodesian craton while the remaining three lie on Precambrian mobile belts adjacent to the craton, the Precambrian basement geology does not significantly affect the amplitude of Lg     

Tectonics of the Marmara Sea region of Turkey: new evidence from microearthquake fault plane solutions

Summary. Composite and single-event fault plane solutions for microearthquakes in the Izmit Bay area of the Marmara Sea indicate right-lateral strike-slip motion and tension on this extension of the North Anatolian Fault. This interpretation is consistent with teleseismically determined fault-plane solutions obtained for large earthquakes on the Marmara Sea seismic lineation. Consideration of the microplate geometry of north-western Turkey, inferred from seismicity as well as earthquake mechanisms, suggests that the region comprises two seismotectonic units with differing styles of deformation. The (Anatolid) structures of south- and central-western Anatolia are undergoing major extension, whereas the (Pontid) structures of the Marmara Sea region are being sheared, resulting in a mixed regime of both strike-slip and extensional faulting.     

Sensitivities of seismic traveltimes and amplitudes in reflection tomography

Seismic traveltimes and amplitudes in reflection-seismic data show different dependences on the geometry of reflection interfaces, and on the variation of interval velocities. These dependences are revealed by eigenanalysis of the Hessian matrix, defined in terms of the Fréchet matrix and its adjoint associated with different norms chosen in the model space. The eigenvectors and eigenvalues of the Hessian clearly show that for reflection tomographic inversion, traveltime and amplitude data contain complementary information. Both for reflector-geometry and for interval-velocity variations, the traveltimes are sensitive to the model components with small wavenumbers, whereas the amplitudes are more sensitive to the components with high wavenumbers. The model resolution matrices, after the rejection of eigenvectors corresponding to small eigenvalues, give us some insight into how the addition of amplitude information could potentially contribute to the recovery of physical parameters.
In order to cooperatively invert seismic traveltimes and amplitudes simultaneously, we propose an empirical definition of the data covariance matrix which balances the relative sensitivities of different types of data. We investigate the cooperative use of both data types for, separately, interface-geometry and 2-D interval-velocity variations. In both cases we find that cooperative inversions can provide better solutions than those using traveltimes alone. The potential benefit of including amplitude-data constraints in seismic-reflection traveltime tomography is therefore that it may be possible to resolve the known ambiguity between the reflector-depth uncertainty and the interval-velocity uncertainty better.     

Synchronising geometric representations for map mashups using relative positioning and Linked Data

Map mashups, as a common way of presenting geospatial information on the Web, are generally created by spatially overlaying thematic information on top of various base maps. This simple overlay approach often raises geometric deficiencies due to geometric uncertainties in the data. This issue is particularly apparent in a multi-scale context because the thematic data seldom have synchronised level of detail with the base map. In this study, we propose, develop, implement and evaluate a relative positioning approach based on shared geometries and relative coordinates to synchronise geometric representations for map mashups through several scales. To realise the relative positioning between datasets, we adopt a Linked Data–based technical framework in which the data are organised according to ontologies that are designed based on the GeoSPARQL vocabulary. A prototype system is developed to demonstrate the feasibility and usability of the relative positioning approach. The results show that the approach synchronises and integrates the geometries of thematic data and the base map effectively, and the thematic data are automatically tailored for multi-scale visualisation. The proposed framework can be used as a new way of modelling geospatial data on the Web, with merits in terms of both data visualisation and querying.