Surface Wave Radiation Pattern Research Articles

Improving relative earthquake locations using surface-wave source corrections

SUMMARYWe develop a procedure to improve estimates of relative earthquake locations using Rayleigh and Love wave arrivals for multiple earthquakes recorded at common stations. We fit predicted differential traveltimes to those measured using a cross-correlation technique, and correct the phases of the cross-correlation functions for phase delays that result from the surface-wave radiation patterns. We develop an empirical measure of uncertainty that provides realistic estimates of the errors in the earthquake locations. We investigate the effectiveness of the relocation procedure by first applying it to two suites of synthetic earthquakes. We then relocate real earthquakes in three separate regions: two ridge-transform systems and one subduction zone. We demonstrate that the inclusion of source corrections in the relocation procedure results in improved location estimates compared to relocations without source corrections. The source correction also allows for automated application of the relocation procedure, even in regions with a wide range of earthquake focal mechanisms.

Ground effects for VHF/HF antennas on helicopter airframes

In this paper, the finite element method (FEM) is used to predict the space and surface wave radiation patterns of VHF/HF antennas mounted on a helicopter in the presence of a lossy ground. The equivalent sources of the radiation system are obtained by solving an FEM problem in conjunction with an absorbing boundary condition (ABC) or an impedance boundary condition (IBC). From the equivalent sources, the total radiated field is calculated using the equivalence principle and superposition; the original problem is converted into a set of properly combined Hertzian dipoles referred to as the Sommerfeld problem. Instead of evaluating the Sommerfeld integral rigorously, Norton's approximation is used to improve the overall computational efficiency. The validation of this method is accomplished in two steps: first, the FEM is compared with the finite-difference time-domain method (FDTD) in the absence of a lossy ground; second, the Hertzian dipole problem is solved in the presence of a lossy ground and the results are compared with analytic solutions. Finally, this technique is extended to analyze an antenna on a helicopter above a lossy ground.

High-frequency reciprocity based circuit model for the incidence of electromagnetic waves on general circuits in layered media

Traditionally a circuit on a high-speed multichip module (MM) or a microwave monolithic integrated circuit (MMIC) is represented in an equivalent circuit by S-parameters for the different components, such as filters or bends, and by transmission lines for the interconnections between the components. Nowadays the S-parameters of the components are easily determined by a numerical electromagnetic analysis. Different components close to each other will interact, often this interaction is unwanted. In the present contribution we develop a circuit model for these interactions without having to perform a global electromagnetic analysis of the interacting components. These interactions are then represented by discrete and distributed sources in the equivalent circuit. Our technique is based on reciprocity and is focused on the surface wave interaction which is often the most important one. Each component is characterized by a surface wave radiation pattern.

Reflection and transmission of surface waves in laterally varying media

SUMMARY The T-matrix description of surface wave scattering is viewed in a reflection/transmission context reminiscent of problems involving elastic wave propagation in stratified media. This approach exploits the orthogonality properties of the surface wave basis functions and permits a description of surface wave propagation in environments exhibiting a degree of quasi-concentric multilayering about a vertical axis. In the first case we consider a multilayered environment where the individual layers are laterally homogeneous and where the layer boundaries need not be circularly cylindrical. The reflection/transmission treatment incorporates all higher order scattering processes and may be used to examine both scattering from multilayered obstacles and the outward evolution of a wavefield from a source acting along the vertical coordinate axis. We then examine the form taken by the reflection/transmission matrices where arbitrary lateral variations in material properties are confined to a broad cylindrical band surrounding the vertical axis. The total response is assembled by considering the band as a succession of infinitesimally thin, heterogeneous shells in welded contact. This treatment relies on the use of invariant embedding techniques and the expansion of the Green's function for a stratified medium in terms of surface wave basis functions. It is demonstrated that the theory is the 3-D extension of coupled mode techniques used to model surface wave propagation in strictly 2-D waveguides. The theory is applied to investigate the effect of near-source, continuously varying heterogeneity on surface wave radiation patterns in the far-field. The general character of the transmitted wavefield agrees with that expected from arguments based on geometrical optics. Despite the suggestive behaviour of the surface wave basis functions in the near-field, wavetype coupling by continuously varying heterogeneity is not especially efficient in this regime. This implies that large transverse components of displacement frequently observed on regional seismograms from explosive sources are the result of other mechanisms, for example abrupt changes in structure or anisotropy.

Determinations of focal depths of earthquakes associated with the bending of oceanic plates at trenches

The earthquakes examined in this paper are all within the oceanic lithosphere and are associated with the bending of plates before subduction. Accurate determinations of the depth of these earthquakes are needed to study the stress pattern within a bending plate. Routinely-determined depths of shallow sub-oceanic earthquakes published in bulletins are unreliable. The depths can be accurately determined to within a few kilometers if the original seismograms from these events are studied. In some cases, the reflected phases pP and pwP can be clearly identified. There exists the possibility that the wave reflected at the water-air interface, pwP, may be misidentified as pP, leading to erroneous estimates of depth. Additional methods of analysis, such as surface wave radiation patterns or the apparent frequency-dependence of reflection at the crust-water interface, can remove this possible source of confusion. One of the most powerful techniques for depth analysis is the modelling of long-period waveforms. The pattern of stresses within the bending oceanic lithosphere revealed by the depths and focal mechanisms of these intraplate earthquakes is one of horizontal, deviatoric tension down to a depth of about 25 km, with horizontal compression at greater depths.

The source mechanism of the August 7, 1966 El Golfo earthquake

abstract The El Golfo earthquake of August 7, 1966 (mb = 6.3, MS = 6.3) occurred near the mouth of the Colorado River at the northern end of the Gulf of California. Synthetic seismograms for this event were computed for both the body waves and the surface waves to determine the source parameters of the earthquake. The body-wave model indicated the source was a right lateral, strike-slip source with a depth of 10 km and a far-field time function 4 sec in duration. The body-wave moment was computed to be 5.0 × 1025 dyne-cm. The surface-wave radiation pattern was found to be consistent with that of the body waves with a surface-wave moment of 6.5 × 1025 dyne-cm. The agreement of the two different moments indicates that the earthquake had a simple source about 4 sec long. A comparison of this earthquake source with the Borrego Mountain and Truckee events demonstrates that all three of these earthquakes behaved as high stress-drop events. El Golfo was shown to be different from the low stress-drop, plate-boundary events which were located on the Gibbs fracture zone in 1967 and 1974.

Surface-wave constraints on the August 1, 1975, Oroville earthquake

abstractObservations of Love and Rayleigh waves on WWSSN and Canadian Network seismograms have been used to place constraints upon the source parameters of the August 1, 1975, Oroville earthquake. The 20-sec surface-wave magnitude is 5.6. The surface-wave radiation pattern is consistent with the fault geometry determined by the body-wave study of Langston and Butler (1976). The seismic moment of this event was determined to be 1.9 × 1025 dyne-cm by both time-domain and long-period (T ≥ 50 sec) spectral amplitude determinations. This moment value is significantly greater than that determined by short-period studies. This difference, together with the low seismic efficiency of this earthquake, indicates that the character of the source is intrinsically different at long periods from those aspects which dominate the shorter-period spectrum.

Sonobuoy and teleseismic study of Gulf of California transform fault earthquake sequences

abstract Sonobuoys have been used in the study of two Gulf of California transform fault aftershock sequences. Uncertainties in epicentral locations are no larger than navigational uncertainties. The first local study of an oceanic transform fault aftershock sequence followed a M S = 5.5 event on March 25, 1973. The sonobuoy data suggest that the main event did not lie along the main transform fault scarp. Surface-wave radiation patterns and a P -wave fault-plane solution give a strike of 327, about 20 different from local bathymetric trends. Subsidiary faulting near a locked transform fault, perhaps a result of local tectonic complication, is a possible explanation for this difference. The second study followed a M S = 6.3 event on May 31, 1974. Sonobuoy data limit the aftershock zone to be about 25 km long, trending approximately parallel to local bathymetric features. All earthquakes located with sonobuoys were shallow. Arrival times limit the depths to be less than 7 km, and when good depth control is present, depths were 3 to 5 km. The calculated stress drop for the March 25, 1973 event is 8 to 30 bars. The historic seismic slip rate along Gulf of California transform faults has been estimated from the published seismicity to be 6.1 to 3.7 cm/yr, assuming fault thicknesses of 3 to 5 km, respectively, in good agreement with estimates of Pacific-American relative plate motion from geologic and geodetic methods. One 240-km section of transform fault appears to have been locked since about 1955, accumulating strain for a large earthquake. The good agreement between the calculated slip rate and the geologic and geodetic estimates supports the sonobuoy-based observation that the earthquake generating zone is very thin, perhaps only 3 to 5 km thick.

Surface-wave radiation pattern and source parameters of Koyna earthquake of December 10, 1967

abstract The fundamental-mode Rayleigh waves for the Koyna earthquake of December 10, 1967 recorded on long-period vertical component seismograms of 30 WWSSN stations have been Fourier analyzed. The radiation patterns have been plotted at six wave periods. Comparison of these data with the theoretical radiation patterns computed for various fault parameters favored the strike of the fault in N10°E direction, dip 78°W, slip 175°, and the depth of focus to be 10 km. Strike-slip faulting on a near-vertical fault plane has been inferred. The S -wave polarization angles, which have been obtained for 13 stations, also favor the above solution. Surface-wave magnitude has been determined to be 6.3 and the fault surface area to be 252 km 2 . Using the Rayleigh-wave spectral amplitude for 50-sec period, the seismic moment, M o , is determined to be 0.82 × 10 26 dyne-cm. The values of average dislocation, seismic energy, apparent stress, and apparent strain are calculated to be 108 cm, 2.25 × 10 21 ergs, 15.4 bars and 5.3 × 10 −5 , respectively. For a rupture velocity of 1.5 km/sec, the values of fault length and stress drop are found to be about 23 km and 19.8 bars, and for a rupture velocity of 3.0 km/sec these values are about 40 km and 6.2 bars, respectively.

Ray Description for Point Source Excited Surface Waves in Stratified Anisotropic Media

A ray‐optical description for the surface wave contribution to the far fields radiated by an electromagnetic point source in the presence of a planar interface between two lossless, homogeneous, anisotropic media is formulated. The surface wave rays are viewed as extending radially along the interface from the normal projection of the source onto the interface. Locally, the ray fields are those of the modal surface waves carrying energy in the ray direction. The effect of anisotropy on the surface wave radiation pattern is also considered.

Surface wave radiation pattern and source mechanism of the September 1, 1962, Iran earthquake

Surface waves recorded at stations surrounding the Iran earthquake of September 1, 1962, were Fourier-analyzed; the amplitudes have been corrected for instrumental response, geometric spreading, and absorption and are presented as a function of azimuth and frequency. The patterns thus derived are compared with theoretical radiation patterns for different source types, orientation of motion vectors, and other parameters. It is found that the source of the Iran earthquake can be represented as a double couple equivalent to a sinistral reverse shear fault with strike N 80°W, dip 78° to the southwest, slip angle 63° and a depth of 11 km. This solution agrees well with the conclusion obtained from a first motion study. It is remarkable that solutions obtained over such a wide frequency range conform to each other.

Surface wave radiation patterns for underground nuclear explosions and small-magnitude earthquakes

The surface wave radiation patterns (amplitude and initial phase) were determined for several of the larger underground nuclear explosions in Nevada. Initial phases of surface waves from explosions and earthquakes were obtained by performing a Fourier analysis of the record and equalizing the phase to the source, using long-period records from the temporary long-range seismic measurement stations installed by the Geotechnical Corporation. Rayleigh waves from explosions in tuff and alluvium appear to have nearly the same initial phase at all azimuths, indicating an explosive force acting as a step function in time as the probable approximate source mechanism. However, the presence of Love waves, along with some asymmetry in Rayleigh wave amplitudes, indicates that some asymmetrical forces are also acting at the origin. The collapses following these explosions generate Rayleigh waves with polarities apparently reversed from those of the explosions. The collapses generate much weaker Love waves relative to Rayleigh waves than the explosions, and therefore the Love waves must be generated at or very near the source. The one explosion in granite (Hardhat) gave a surface wave radiation pattern with double-couple symmetry in both phase and amplitude, a symmetry very different from that found for the explosions in tuff and alluvium. Such a radiation pattern cannot be explained by a simple, symmetric explosive force. Several explanations of this double-couple symmetry are considered, including the possibilities that the surface waves were generated by cracking or forced motion along pre-existing cracks, tectonic strain release resulting from cavity formation, or, more probably, triggering of tectonic motion. The latter hypothesis would explain the radiation pattern, and it is supported by the occurrence of an aftershock sequence, outside the cavity zone, similar to that common for earthquakes. Analysis of surface waves from earthquakes indicates that, in many cases, the earthquake sources are more complicated than the explosion sources. The information about source mechanisms obtained in this study is of fundamental importance to the problem of the identification of explosions and earthquakes.