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Abstract--We present finite difference forward models of elastic wave propagation through laterally heterogeneous upper oceanic crust. The finite difference formulation is a 2-D solution to the elastic wave equation for heterogeneous media and implicitly calculates P and SV propagation, compressional to shear conversion, interference effects and interface phenomena. Random velocity perturbations with Gaussian and self-similar autocorrelation functions and different correlation lengths (a) are presented which show different characteristics of secondary scattering. Heterogeneities scatter primary energy into secondary body waves and secondary Stoneley waves along the water-solid interface. The presence of a water-solid interface in the model allows for the existence of secondary Stoneley waves which account for much of the seafloor 'noise' seen in the synthetic seismograms for the laterally heterogeneous models.'Random' incoherent secondary scattering generally increases as ka (wavenumber, k, and correlation length, a) approaches one. Deterministic secondary scattering from larger heterogeneities is the dominant effect in the models as ka increases above one. Secondary scattering also shows up as incoherence in the primary traces of the seisograms when compared to the laterally homogeneous case. Cross-correlation analysis of the initial P-diving wave arrival shows that, in general, the correlation between traces decreases as ka approaches one. Also, because many different wave types exist for these marine models, the correlation between traces is range dependent, even for the laterally homogeneous case.

We use a full-waveform acousto-elastic finite difference technique to investigate seismic propagation across the East Pacific Rise at 9ø30'N for a two-dimensional velocity model based on that proposed by Vera and others (1990). The primary feature of the model is an upper crustal low-velocity region, corresponding to the axial magma charnber, which includes a small magma body located 1.6 km beneath the seafloor at the rise axis. The high velocity gradients in this region result in a complex pattern of propagation which includes considerable scattering of energy above and below the magma chamber. A qualitative comparison of finite difference seismograms with data collected by receivers located 9 km and 20 km off axis during a tomography experiment at 9ø30'N shows generally good agreement. For paths that cross the rise axis, the first arrival in the finite difference solutions diffracts above the magma chamber. This phase has a very low amplitude and at larger offsets falls below the ambient noise levels observed during the tomography experiment. In such cases, the first arrival with significant energy is a diffraction from below the magma chamber. A high-amplitude Mohoturning (PrnP) phase which results from the large velocity change across the Moho beneath the rise axis is apparent in both the finite difference solutions and the observations. Ray-theoretical calculations of the paths of the diffracted arrivals are very unstable, and for the diffractions above the magma chamber no solution can be found with a single-precision algorithm. Synthetic delay-time inversions using an approximate ray-tracing algorithm demonstrate the importance of ensuring that picked arrival times are assigned to paths that pass to the correct side of the magma body. Synthetic inversions of spectral estimates of t* show that Q-1 models are compromised not only if the ray paths are inco•ect but also if t* estimates include significant contributions from more than one phase. Deterministic scattering from the magma chamber may contribute noticeably to spectral estimates of t*, but the results of the finite difference experiments imply that high levels of attenuation observed for phases passing below the magma chamber are predominantly the result of intrinsic attenuation. ], it is necessary to ensure that arrival time picks are assigned to the correct phase.The spectral method of attenuation tomography involves inversions of estimates of apparent attenuation derived from the power spectra of waveforms to yield models of the reciprocal of the quality factor Q. Since the technique requires knowledge of the velocity structure and ray paths, errors in the assumed velocity model will propagate into the attenuation model. Additional errors will result if attenuation estimates are obtained for a time window that includes more than one phase or if estimates are assigned to the incorrect phase. Q-1 models obtained by the spectral technique will inevitably include contributions from effects other than intrinsic attenuation such as scattering [e.g., Cor...

Tools for analyzing aquifer test data at the pumping or injection well are limited for aquifer conditions that are not axially symmetric about the pumping well. Accurate simulations of head change at a pumping well can be generated with MODFLOW using a discretization scheme that (1) captures steep gradients adjacent to the cell(s) containing the pumping or injection well and (2) approximates radial flow despite rectangular prism well cell(s). This scheme is based on a very small incremental cell width adjacent to the pumping or injection well cell, and then a logarithmic increase in cell width outward with the expansion factor, α, in the range of 1.2 to 1.5. The validity of this scheme has been demonstrated by comparing model results with analytical solutions and RADMOD (axisymmetric adaptation of MODFLOW) for three radially symmetric confined aquifer scenarios, and with the analytical solution for a nonaxisymmetric confined aquifer scenario. Utility of this scheme is demonstrated with simulation of time-drawdown behavior at the Goddard2 pumping well in Boise, Idaho where four observation wells did not respond during a pumping test and where 28.8 m of drawdown occurred in the pumping well during the first 2 min of the test. The hydrogeologic setting for the test is interpreted to be a partially penetrating well pumping from a sand-stringer aquifer that receives leakage from surrounding finer grained sediments, and includes a fault (no-flow boundary) truncating the aquifer