Seismic interpretation of structures usually involves identifying and mapping marker reflections in the time domain; however, forward modeling has shown that it can be difficult to map the complex reflection images arising from geologic structures. Inverse modeling by ray techniques offers the potential of computing a structure in the depth domain where it is comparatively easy to evaluate a structural target. An interactive algorithm is presented which has its basis in the eikonal equation and results in a practical procedure to compute models with complex geometries and inhomogeneous layers. Input consists of interpreted reflection times from a CDP‐stacked section and spatial velocity functions determined externally to the algorithm. Output is a two‐dimensional (2-D) model having curvilinear reflectors that can terminate within the model, at faults, and at unconformities. Benefits of structural inverse modeling are realized in the rapid construction of models that have velocity fields defined in the depth domain, explicitly accounting for ray curvature and ray kinking. To illustrate the inverse technique, examples of a complex synthetic thrust fault model and a field‐recorded growth fault model are included. The capability to inverse model steeply dipping structures is of particular interest because it completes a full modeling cycle of (1) theoretical prediction that steep‐dip reflections should be observable, (2) processing of field‐recorded CDP trace data to produce interpretable steep‐dip reflections, and finally (3) computation of steep‐dip reflector positions in the depth domain. An interesting benefit is the application of this algorithm to computing image rays on complex structures and the subsequent implications about time migration of CDP‐stacked sections.

Traveltimes from an offset vertical seismic profile (VSP) are used to estimate subsurface two‐dimensional dip by applying an iterative least‐squares inverse method. Tests on synthetic data demonstrate that inversion techniques are capable of estimating dips in the vicinity of a wellbore by using the traveltimes of the direct arrivals and the primary reflections. The inversion method involves a “layer stripping” approach in which the dips of the shallow layers are estimated before proceeding to estimate deeper dips. Examples demonstrate that the primary reflections become essential whenever the ratio of source offset to layer depth becomes small. Traveltime inversion also requires careful estimation of layer velocities and proper statics corrections. Aside from these difficulties and the ubiquitous nonuniqueness problem, the VSP traveltime inversion was able to produce a valid earth model for tests on a real data case.

Synthetic seismic sections computed during forward modeling differ depending upon the type of media used to define the model. Four media types considered here are acoustic, elastic, elliptically anisotropic, and vertically inhomogeneous; significant differences are found among the seismic sections for these cases. Automatic ray generation, using kinematic and dynamic analog groups, permits retention and explicit identification of all significant arrivals, including primaries, multiples, converted waves, etc., for three‐dimensional, horizontally layered structures. Comparisons between arrivals common to the various models are shown by synthetic trace sections, amplitude‐distance plots, and velocity spectra. Results show significant energy in converted waves in the elastic models and marked differences between amplitude‐distance curves for elastic and acoustic cases. Anisotropic media produce noticeable differences in both amplitude‐ and time‐distance curves as a function of the degree of anisotropy. Modeling with vertically inhomogeneous media is practical and appealing because of how velocity and density functions are defined. Interestingly, a diving wave of high amplitude shown in our seismograms closely resembles the strong first arrival often present on field‐recorded seismograms.

Synthetic seismograms can be very useful in aiding understanding of wave propagation through models of real media, verification of geologic models derived from interpretation of field seismic data, and understanding the nature and complexity of wave phenomena. If meaningful results are to be obtained from synthetic seismograms, the method of their computation must, in general, include three-dimensional geometrical spreading of wavefronts associated with highly concentrated (i.e., point) sources. The method should also adequately represent the seismic response of solid-layered media by including enough primaries, multiples, and converted phases to accurately approximate the total wavefield. In addition to these features, it is also very helpful, although not always essential, if the method of seismogram computation provides for explicit identification of wave type and ray path for each arrival. Various seismograms, computed via asymptotic ray theory and an automatic ray generation scheme, are presented for a highly simplified North Sea velocity structure. This is done to illustrate the importance of the above features and to demonstrate the inadequacy of the plane-wave synthesis method of seismogram computation for point sources and the limitations of acoustic models of solid-layered media.

Recent laboratory and field studies indicate that the P-wave velocity in Athabasca tar sands decreases when temperature increases during steam injection. In this paper we derive time variant velocity models from seismic traveltime inversions of both reflection and borehole data. Prior to steam injection, three‐dimensional (3-D) reflector velocity‐depth models are established using image‐ray conversions of traveltimes to depth. The changes in velocity due to steam injection are modeled by inverting traveltime data from seismic monitor surveys after steam injection and comparing these results to velocities computed prior to steam injection. Velocity models are essentially determined by traveltimes from the 3-D seismic reflection survey. The surface‐to‐wellbore data traveltimes show the expected delay caused by steam injection but do not significantly alter the velocity model produced by reflection traveltimes. For seismic monitor surveys, low‐velocity zones show a very good correlation with zones of temperature increase at injector well positions. The results indicate that velocity models obtained from seismic traveltimes may prove useful in detecting steam fronts in tar sands.