Anton M. Dainty

Seismic codas on the earth and the moon - A comparison

The phenomenon of the seismic coda, which is composed of seismic energy delayed by scattering, is seen on both the Earth and the Moon. On the Moon the scattered coda is very large relative to body wave arrivals with a delay of the time of maximum energy, whereas on Earth scattered codas are relatively small and show no delay of the energy maximum. In both cases the form of the coda is controlled by three distance scales, the mean free path L, which is the average distance seismic energy travels before it is scattered, the attenuation distance x∗, which is the average distance seismic energy travels before it is attenuated, and the source-receiver distance R. Two coda models are discussed based on these parameters; a strong scattering (diffusion) model, and a weak scattering (single scattering) model. A discussion of the diffusion scattering model indicates that if x∗/L ⪢ 1, diffusion scattering is an appropriate model, but if x∗/L ⩽ 1, single scattering is the appropriate model, within the appropriate range of R. A survey of the literature indicates that for the frequency range 0.5–10 Hz, diffusion scattering is important in lunar codas, but for the frequency range 1–25 Hz single scattering is important in terrestrial codas. Another important effect of attenuation is the elimination of scattering paths much longer than x∗. On the Moon, this means that seismic energy in the coda can only propagate directly in the near-surface strong scattering zone between surface sources and the seismometer for source-seismometer separations of the order of (x∗L)12; otherwise, scattering is limited to regions near the source and the receiver. On Earth, this effect probably prevents multiple scattering.

Seismic scattering and shallow structure of the moon in oceanus procellarum

Long, reverberating trains of seismic waves produced by impacts and moonquakes may be interpreted in terms of scattering in a surface layer overlying a non-scattering elastic medium. Model seismic experiments are used to qualitatively demonstrate the correctness of the interpretation. Three types of seismograms are found, near impact, far impact and moonquake. Only near impact and moonquake seismograms contain independent information. Details are given in the paper of the modelling of the scattering processes by the theory of diffusion.Interpretation of moonquake and artificial impact seismograms in two frequency bands from the Apollo 12 site indicates that the scattering layer is 25 km thick, with a Q of 5000. The mean distance between scatterers is approximately 5 km at 25 km depth and approximately 2 km at 14 km depth; the density of scatterers appears to be high near the surface, decreasing with depth. This may indicate that the scatterers are associated with cratering, or are cracks that anneal with depth. Most of the scattered energy is in the form of scattered surface waves.

A Model for Attenuation and Scattering in the Earth’s Crust

The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda wavesRg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1–10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constantQ), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedoB0=0.8–0.9 and a scattering extinction length of 17–32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. TheRg results indicate thatQ increases with depth in the upper kilometer or two of the crust, at least in New England. CodaQ appears to be equivalent to intrinsic (anelastic)Q and indicates that thisQ increases with frequency asQ=Qofn, wheren is in the range of 0.2–0.9. The intrinsic attenuation in the crust can be explained by a high constantQ (500≤Qo≤2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence (Q≃Qof0.5) similar to those determined from the analysis of coda waves of regional seismograms.Q is low near the surface and high in the body of the crust.

Lunar crust - Structure and composition.

Lunar seismic data from artificial impacts recorded at three Apollo seismometers are interpreted to determine the structure of the moons interior to a depth of about 100 kilomneters. In the Fra Mauro region of Oceanus Procellarum, the moon has a layered crust 65 kilometers thick. The seismic velocities in the upper 25 kilometers are consistent with those in lunar basalts. Between 25 and 65 kilometers, the nearly constant velocity (6.8 kilometers per second) corresponds to velocities in gabbroic and anorthositic rocks. The apparent velocity is high (about 9 kilometers per second) in the lunar mantle immediately below the crust.

Velocity structure and properties of the lunar crust.

Lunar seismic data from three Apollo seismometers are interpreted to determine the structure of the Moons interior to a depth of about 100 km. The travel times and amplitudes ofP arrivals from Saturn IV B and LM impacts are interpreted in terms of a compressional velocity profile. The most outstanding feature of the model is that, in the Fra Mauro region of Oceanus Procellarum, the Moon has a 65 km thick layered crust. Other features of the model are: (i) rapid increase of velocity near the surface due to pressure effects on dry rocks, (ii) a discontinuity at a depth of about 25 km, (iii) near constant velocity (6.8 km/s) between 25 and 65 km deep, (iv) a major discontinuity at 65 km marking the base of the lunar crust, and (v) very high velocity (about 9 km/s) in the lunar mantle below the crust. Velocities in the upper layer of the crust match those of lunar basalts while those in the lower layer fall in the range of terrestrial gabbroic and anorthositic rocks.

Studies of coda using array and three-component processing

The application of standard array processing techniques to the study of coda presents difficulties due to the design criteria of these techniques. Typically the techniques are designed to analyze isolated, short arrivals with definite phase velocity and azimuth and have been useful in the frequency range around 1 Hz. Coda is long in time and may contain waves of different types, phase velocities and azimuths. Nonetheless, it has proved possible to use or adapt array methods to answer two questions: what types of waves are present in coda and where are they scattered? Most work has been carried out on teleseismicP coda; work on local coda has lagged due to lack of suitable data and the difficulties of dealing with high frequencies. The time domain methods of beamforming and Vespagram analysis have shown that there is coherent energy with a high phase velocity comparable toP orPP in teleseismicP coda. These methods can detect this “coherent” coda because it has a fairly definite phase velocity and the same, or close to, azimuth as firstP orPP. This component must consist ofP waves and is either scattered near the source, or reflected in the mantle path as apdpP or precursorPP reflection. The Fourier transform method of the frequency-wavenumber spectrum has been adapted by integrating around circles of constant phase velocity (constant total wavenumber) to produce the wavenumber spectrum, which shows power as a function of wavenumber, or phase velocity. For teleseismicP coda, wavenumber spectra demonstrate that there is a “diffuse” coda of shear,Lg or surface waves scattered from teleseismicP near the receiver. Wavenumber spectra also suggest that the coherent coda is produced by near-source scattering in the crust, not mantle reflection, since it is absent or weak for deep-focus events. Crustal earthquakes have a very strong coherent component of teleseismic coda, suggesting scattering from shear to teleseismicP near the source. Three-component analysis of single-station data has shown the presence of off-azimuth arrivals and may lead to the identification of waves scattered from a single scatterer.

Coherency of ground motion at regional distances and scattering

Abstract In the absence of local scattering the ground motion due to major phases at an array should be perfectly coherent between different seismometers. We have studied the coherency of ground motion for the regional phase Lg as a function of frequency and spatial separation for the NORESS, ARCESS and FINESA arrays. The events examined are quarry blasts at a distance of 200–400 km from the array, and coherency was estimated for 10–25 s windows containing Lg. In the 1–10 Hz range coherency decreases with increasing spatial separation. The decrease is faster for higher frequencies, but if the separation is scaled to the wavelength then the decay curves are similar and indicate that coherency decreases to

Spatial variation of ground motion due to lateral heterogeneity

Abstract To examine the effect of propagation on coherency of ground motion, a study of data from seismic arrays on hard rock has been carried out. In addition coherency results using finite difference seismograms for a layer over a half-space with heterogeneities are presented. The hard rock sites are three arrays in Fennoscandia; maximum array spacings are 1500–3000 m. The data analysed are S-waves from quarry blasts at ranges of 240–350 km. Analyses at 2, 4 and 6 Hz show high coherency as a function of separation compared to sites with alluvium or soil layers. Tentatively, we conclude that the decay of coherency with separation at each site follows a single relation for all frequencies if the separation is scaled by the wavelength. The two-dimensional finite difference results indicate that even with no heterogeneities the mixing of reflected P and S phases in a surface layer can substantially reduce the coherency for the vertical component if the source is below the layer. For the horizontal (radial) component, the effect of velocity heterogeneity is to reduce the coherency while layering and irregular layer interfaces have less effect, at least for sources below the layer.

Lunar velocity structure and compositional and thermal inferences

Seismic data from the Apollo Passive Seismic Network stations are analyzed to determine the velocity structure and to infer the composition and physical properties of the lunar interior. Data from artificial impacts (S-IVB booster and LM ascent stage) cover a distance range of 70–1100 km. Travel times and amplitudes, as well as theoretical seismograms, are used to derive a velocity model for the outer 150 km of the Moon. TheP wave velocity model confirms our earlier report of a lunar crust in the eastern part of Oceanus Procellarum.The crust is about 60 km thick and may consist of two layers in the mare regions. Possible values for theP-wave velocity in the uppermost mantle are between 7.7 km s−1 and 9.0 km s−1. The 9 km s−1 velocity cannot extend below a depth of about 100 km and must decrease below this depth. The elastic properties of the deep interior as inferred from the seismograms of natural events (meteoroid impacts and moonquakes) occurring at great distance indicate that there is an increase in attenuation and a possible decrease of velocity at depths below about 1000 km. This verifies the high temperatures calculated for the deep lunar interior by thermal history models.

Application of 3-D crustal and upper mantle velocity model of North America for location of regional Seismic events

Abstract — Seismic event locations based on regional 1-D velocity-depth sections can have bias errors caused by travel-time variations within different tectonic provinces and due to ray-paths crossing boundaries between tectonic provinces with different crustal and upper mantle velocity structures. Seismic event locations based on 3-D velocity models have the potential to overcome these limitations. This paper summarizes preliminary results for calibration of IMS for North America using 3-D velocity model. A 3-D modeling software was used to compute Source-Station Specific Corrections (SSSCs(3-D)) for Pn travel times utilizing 3-D crustal and upper mantle velocity model for the region. This research was performed within the framework of the United States/Russian Federation Joint Program of Seismic Calibration of the International Monitoring System (IMS) in Northern Eurasia and North America.¶An initial 3-D velocity model for North America was derived by combining and interpolating 1-D velocity-depth sections for different tectonic units. In areas where no information on 1-D velocity-depth sections was available, tectonic regionalization was used to extrapolate or interpolate. A Moho depth map was integrated. This approach combines the information obtained from refraction profiles with information derived from local and regional network data. The initial 3-D velocity model was tested against maps of Pn travel-time residuals for eight calibration explosions; corrections to the 3-D model were made to fit the observed residuals. Our goal was to find a 3-D crustal and upper mantle velocity model capable predicting Pn travel times with an accuracy of 1.0–1.5 seconds (r.m.s.).¶The 3-D velocity model for North America that gave the best fit to the observed travel times, was used to produce maps of SSSCs(3-D) for seismic stations. The computed SSSCs(3-D) vary approximately from +5 seconds to −5 seconds for the western USA and the Pre-Cambrian platform, respectively. These SSSCs(3-D) along with estimated modeling and measurement errors were used to relocate, using regional data, an independent set of large chemical explosions (with known locations and origin times) detonated within various tectonic provinces of North America. Utilization of the 3-D velocity model through application of the computed SSSCs(3-D) resulted in a substantial improvement in seismic event location accuracy and in a significant decrease of error ellipse area for all events analyzed in comparison both with locations based on the IASPEI91 travel times and locations based on 1-D regional velocity models.