Density contrasts in the lower mantle, recently imaged using seismic tomography, drive convective flow which results in kilometers of dynamically maintained topography at the core-mantle boundary and at the Earth's surface. The total gravity field due to interior density contrasts and boundary topography predicts the largest wavelength components, of the geoid remarkably well.Neglecting dynamic surface deformation leads to geoid anomalies of opposite sign than are observed.

Synthetic seismograms produced by the finite difference method are used to study the scattering of elastic and acoustic waves in two-dimensional media with random spatial variations in seismic velocity. The results of this study provide important insights about the propagation of short-period (< 1 s) seismic waves in the earth's crust and place significant constraints on the fluctuation spectrum of crustal heterogeneity on length scales from tens of kilometers to tens of meters. The synthetic seismograms are analyzed to determine the variation in travel times and waveforms across arrays of receivers. The apparent attenuation caused by scattering and the time decay and amplitude of the seismic coda are also quantified with the numerical simulations. Random media with Gaussian and exponential correlation functions are considered, as well as a self-similar medium with equal variations in seismic velocity over a broad range of length scales. These media differ in the spectral falloff of their velocity fluctuations at wavelengths smaller than 2rr times the correlation distance a. The synthetic seismograms demonstrate that a random medium with self-similar velocity fluctuations at length scales less than about 50 km (a > 10 km) can explain both travel time anomalies reported for teleseismic arrivals across large-scale seismic arrays (e.g., LASA and NORSAR) and the presence of seismic coda at frequencies of 30 Hz and greater commonly observed in microearthquake waveforms. Media with Gaussian and exponential correlation functions in velocity do not account for both sets of observations for reasonable standard deviations in velocity (< 10%). The scattering attenuation (Q-•) observed in the simulations for Gaussian media is peaked at ka between 1 and 2, where k is the seismic wave number. The observed attenuation in exponential media increases with frequency for ka < 1 and remains about constant for 1 < ka < 5.6. At high frequencies (ka > 5), the self-similar medium is characterized by a scattering Q that is constant with frequency, whereas theory predicts that the apparent Q in an exponential medium is proportional to frequency. These alternative models of crustal heterogeneity can thus be tested by improved measurements of the frequency dependence of crustal Q at frequencies greater than about 1 Hz, assuming that scattering is responsible for most of the attenuation at these frequencies. Measurements of the time decay of the synthetic coda waves clearly show that the single scattering model of coda decay is not appropriate in the presence of moderate amounts of scattering attenuation (scattering Q < 200). In these cases, Q values derived from the coda decay rate using the single scattering theory do not correspond to the transmission Q of the medium. The cross correlation of synthetic waveforms observed for an array of receivers along the free surface is observed to be dependent on the correlation distance of the medium. The self-similar random medium proposed here for the crust produces waveform variations at high freq...

The standard boundary conditions used at the sides of a seismic section in wave-equation migration generate artificial reflections. These reflections from the edges of the computational grid appear as artifacts in the final section. Padding the section with zero traces on either side adds to the cost of migration and simply delays the ine\ itable reflections.We develop stable absorbing boundary conditions that annihilate almost all of the artificial reflections. This is demonstrated analytically and with synthetic examples. The absorbing boundary conditions presented can be used with any of the different types of finite-difference wave-equation migration, at essentially no extra cost.

Based on analysis of data from a trans‐Mexico temporary broadband seismic network centered on Mexico City, we report that the subducting Cocos Plate beneath central Mexico is horizontal, and tectonically underplates the base of the crust for a distance of 250 km from the trench. It is decoupled from the crust by a very thin low viscosity zone. The plate plunges into the mantle near Mexico City but is truncated at a depth of 500 km, probably due to an E‐W propagating tear in the Cocos slab. Unlike the shallow slab subduction in Peru and Chile, there is active volcanism along the Trans Mexican Volcanic Belt (TMVB) that lies much further inland than regions to either side where subduction dip is not horizontal. Geodynamical modeling indicates that a thin weak layer such as imaged by the seismic experiment can explain the flat subduction geometry.

Oceanic microseisms are small oscillations of the ground, in the frequency range of 0.05-0.3 Hz, associated with the occurrence of energetic ocean waves of half the corresponding frequency. In 1950, Longuet-Higgins suggested in a landmark theoretical paper that (i) microseisms originate from surface pressure oscillations caused by the interaction between oppositely travelling components with the same frequency in the ocean wave spectrum, (ii) these pressure oscillations generate seismic Stoneley waves on the ocean bottom, and (iii) when the ocean depth is comparable with the acoustic wavelength in water, compressibility must be considered. The efficiency of microseism generation thus depends on both the wave frequency and the depth of water. While the theory provided an estimate of the magnitude of the corresponding microseisms in a compressible ocean, its predictions of microseism amplitude heretofore have never been tested quantitatively. In this paper, we show a strong agreement between observed microseism and calculated amplitudes obtained by applying Longuet-Higgins' theory to hindcast ocean wave spectra from the North Atlantic Ocean. The calculated vertical displacements are compared with seismic data collected at stations in North America, Greenland, Iceland and Europe. This modelling identifies a particularly energetic source area stretching from the Labrador Sea to south of Iceland, where wind patterns are especially conducive to generating oppositely travelling waves of same period, and the ocean depth is favourable for efficient microseism generation through the 'organ pipe' resonance of the compression waves, as predicted by the theory. This correspondence between observations and the model predictions demonstrates that deep ocean nonlinear wave -wave interactions are sufficiently energetic to account for much of the observed seismic amplitudes in North America, Greenland and Iceland.