S U M M A R YA tomographic inversion method is presented for the determination of 3-D velocity and interface structure from a wide range of body-wave seismic traveltime data types. It is applicable to refraction, wide-angle reflection, normal-incidence and multichannel seismic data, and is best suited to a combination of these that provides good independent constraints on seismic velocities and interface depths. The inversion process seeks a layer-interface minimum-structure model that is able to explain the given data satisfactorily by inverting to minimize data misfit and model roughness norms simultaneously. This regularized inversion, and the use of smooth functions to describe velocities and depths, allows the highly non-linear tomographic problem to be approximated as a series of linear steps. The inversion process begins by optimizing the fit to the data of a highly-smoothed initial model. In each subsequent step, structure is allowed to develop in the model with successively greater detail evolving until a satisfactory fit to the data is obtained. Parameter uncertainties for the final model are then estimated using an a posteriori covariance matrix analysis. Smooth layer-interface models are parametrized using regular grids of velocity and depth nodes from which spline-interpolated interface surfaces and velocity fields are defined. Forward modelling is achieved using ray perturbation theory and a two-point ray tracing method that is optimized for a large number of closely-spaced shot or receiver points. The method may be used to generate 1-and 2-D models (from, for example vertical seismic profile data or 2-D surveys) in which the 3-D geometry of a survey is correctly accounted for. The ability of the method to resolve typical target structures is tested in a synthetic salt dome inversion. From a set of noisy traveltime data, the model converges quickly to a well-resolved final model from different starting models. The application of this method to real data is demonstrated with a combined 3-D inversion of refraction and reflection data which provide P-wave velocity constraints on the methane hydrate stability zone in the Cascadia Margin offshore Vancouver Island.

No abstract

We present a new method for correcting the amplitudes of arrivals in an acoustic finite-difference simulation for elastic effects. In this method, we selectively compute an estimate of the error incurred when the acoustic wave equation is used to approximate the behavior of the elastic wave equation. This error estimate is used to generate an effective source field in a second acoustic simulation. The result of this second simulation is then applied as a correction to the original acoustic simulation. The overall cost is approximately twice that of an acoustic simulation but substantially less than the cost of an elastic simulation. Because both simulations are acoustic, no S-waves are generated, so dispersed converted waves are avoided. We tested the characteristics of the method on a simple synthetic model designed to simulate propagation through a strong acoustic impedance contrast representative of sedimentary geology. It corrected amplitudes to high accuracy for reflected arrivals over a wide range of incidence angles. We also evaluated results from simulations on more complex models that demonstrated that the method was applicable in realistic sedimentary models containing a wide range of seismic contrasts. However, its accuracy was reduced for wide-angle reflections from very high impedance contrasts such as a shallow top-salt interface. We examined the influence of modeling at coarse grid resolutions, in which converted S-waves in the equivalent elastic simulation are dispersed. These results provide some validation for the accuracy of the method when applied using finite-difference grids designed for acoustic modeling. The method appears to offer a cost-effective means of modeling elastic amplitudes for P-wave arrivals in a useful range of velocity models. It has several potential applications in imaging and inversion.

Finite-difference simulations are an important tool for studying elastic and acoustic wave propagation, but remain computationally challenging for elastic waves in three dimensions. Computations for acoustic waves are significantly simpler as they require less memory and operations per grid cell, and more significantly can be performed with coarser grids, both in space and time. In this paper, we present a procedure for correcting acoustic simulations for some of the effects of elasticity, at a cost considerably less than full elastic simulations. Two models are considered: the full elastic model and an equivalent acoustic model with the same P velocity and density. In this paper, although the basic theory is presented for anisotropic elasticity, the specific examples are for an isotropic model. The simulations are performed using the finite-difference method, but the basic method could be applied to other numerical techniques. A simulation in the acoustic model is performed and treated as an approximate solution of the wave propagation in the elastic model. As the acoustic solution is known, the error to the elastic wave equations can be calculated. If extra sources equal to this error were introduced into the elastic model, then the acoustic solution would be an exact solution of the elastic wave equations. Instead, the negative of these sources is introduced into a second acoustic simulation that is used to correct the first acoustic simulation. The corrected acoustic simulation contains some of the effects of elasticity without the full cost of an elastic simulation. It does not contain any shear waves, but amplitudes of reflected P waves are approximately corrected. We expect the corrected acoustic solution to be useful in regions of space and time around a P-wave source, but to deteriorate in some regions, for example, wider angles, and later in time, or after propagation through many interfaces. In this paper, we outline the theory of the correction method, and present results for simulations in a 2-D model with a plane interface. Reflections from a plane interface are simple enough that an analytic analysis is possible, and for plane waves, we give the correction to the acoustic reflection and transmission coefficients. Finally, finite-difference calculations for plane waves are used to confirm the analytic results. Results for wave propagation in more complicated, realistic models will be presented elsewhere.

A seismic study in the Cascadia Margin in June 1993 focused upon the bottom simulating reflector (BSR) around Hole 889B of the Ocean Drilling Program. Extensive wide-angle and normal-incidence data were collected during two deployments of five ocean bottom hydrophones (OBHs). We have applied a new two-dimensional travel-time inversion method to data from one line within the survey. Data from four OBHs and normal-incidence arrivals are inverted simultaneously, and a distribution of P-wave velocities above the BSR is obtained. These velocities are found to be slightly higher than those given by vertical seismic profile (VSP) and sonic log data from Hole 889B, with velocities of 1.83–1.95 km s −1 occurring immediately above the BSR. Estimates of hydrate concentration derived using two different methods range from 2 to 24% of the pore space. The velocity model provides some support for the existence of a correlation between BSR strength and hydrate concentration above the BSR in this region.