Bruce S. Gibson

Modeling and processing of scattered waves in seismic reflection surveys

Various wave-scattering mechanisms are known to degrade reflection signals by producing noise in seismic reflection data. Synthetic 2-D acoustic-wave finite-difference data sets illustrate the effects of two such mechanisms. Twenty-five shot gathers were generated for each of two models and the data were processed as standard CMP surveys. In one model, an irregular low-velocity surface layer produced multiply scattered surface waves that appear as linear noise trains in common-shot gathers and stacked sections. The scattering of upcoming reflections at the lower interface of the layer also produced a significant amount of noise. When predictive deconvolution was applied before stack to reduce reverberations, the spectral character of the scattered surface waves seriously inhibited the action of that process.In the second model, a zone of smooth, random velocity variation was imposed between two reflectors deeper in the model. The heterogeneous zone (+ or -5 percent rms velocity variation) substantially degraded the signal reflected from below it; events produced by body-wave scattering are characterized by higher phase velocities than those seen in the first model. Conventional CMP stacking produced discontinuous subhorizontal events from the disturbed zone. The limited bandwidth of the propagating signal and spatial filtering attributable to CMP stacking cause these events to bear no simple relation to the velocity anomalies of the model, even after migration.

Wide‐angle seismic reflections from two‐dimensional random target zones

We have analyzed the shot gather seismic response of a buried zone of isotropic random velocity fluctuations. Scattering analysis predicts that events at offsets greater than the depth of the target zone will appear more continuous and coherent than events at zero and small offsets due to an effective dip filter inherent to the source-target-receiver geometry. The scattering theory is confirmed with finite difference synthetic seismograms calculated for an idealized crustal model. The closely spaced synthetic seismograms show bright events having the appearance of refraction arrivals which suggest a horizontally layered structure in the target zone. These effects appear to be independent of the magnitude of the velocity fluctuations, provided that the magnitude of the fluctuations is small (σ< 3.0% of the mean velocity). We have made a second finite difference calculation of a crustal scale model to reinterpret previously published wide-angle data from the Black Forest, Germany [Sandmeier and Wenzel, 1986]. The response of the lower crust seen in the conventionally recorded field data can be explained by a lower crustal model of isotropic, small-amplitude, random velocity fluctuations. We present this in contrast to a laterally homogeneous model of a finely layered lower crust of alternating high and low velocities proposed by Sandmeier and Wenzel [1986]. The synthetic studies and the scattering analysis demonstrate that the geometry of the wide-angle experiment produces signals which appear to be from layered target zones, even where no layering exists. They also underscore the importance of conducting seismic surveys which make use of closely spaced receivers and which integrate vertical incidence and wide-angle recording.

Apparent layering in common-midpoint stacked images of two-dimensionally heterogeneous targets

Model studies with finite‐difference synthetic data demonstrate a fundamental spatial bias in the appearance of common‐midpoint (CMP) stacked images. The CMP stack of data recorded over a target having 2-D random variations in velocity shows numerous short reflection segments; similar reflection patterns in field data are often interpreted in terms of 1-D fine‐scale layering. The stacked image appears layered because of enhanced lateral continuity attributable to the well‐known dip filter of the stacking process. The stack filter can be characterized using the formulation of Bolondi et al. (1982). Lateral correlation in the target and its seismic image is quantified with a measure based on the spectral coefficient of coherence. Broadband primary reflectivity (defined as the vertical‐incidence, primaries‐only reflection coefficients of the 2-D target) is often taken as an ideal seismic image. The primary reflectivity section of a 2-D random target, however, shows greater apparent lateral correlation than i...

Nonlinear least-squares inversion of traveltime data for a linear velocity-depth relationship

Nonlinear least‐squares inversion of traveltime data is applied to the problem of determining thicknesses, velocities, and velocity gradients in laterally homogeneous, horizontally layered structures. The parametric forms of the traveltime equations are used for the calculations. Results of inversions on randomly inaccurate synthetic data show that the method will not determine the gradient consistently when using reflection traveltimes. Good results are obtained, however, when using traveltimes of energy refracted in a layer by the velocity gradient. Thicknesses and average velocity in the case of reflections, or velocity at the top of the layer in the case of refractions, are also determined. Partial derivatives determined during the course of the least‐squares inversion can be used to place limits on errors in the determined parameters.

Predictive deconvolution and the zero-phase source

Predictive deconvolution is commonly applied to seismic data generated with a Vibroseisr® source. Unfortunately, when this process invokes a minimum‐phase assumption, the phase of the resulting trace will not be correct. Nonetheless, spiking deconvolution is an attractive process because it restores attenuated higher frequencies, thus increasing resolution. For detailed stratigraphic analyses, however, it is desirable that the phase of the data be treated properly as well. The most common solution is to apply a phase‐shifting filter that corrects for errors attributable to a zero‐phase source. The phase correction is given by the minimum‐phase spectrum of the correlated Vibroseis wavelet. Because no minimum‐phase spectrum truly exists for this bandlimited wavelet, white noise is added to its amplitude spectrum in order to design the phase‐correction filter. Different levels of white noise, however, produce markedly different results when field data sections are filtered. A simple argument suggests that th...

Comparison of amplitude decay rates in reflection, refraction, and local earthquake records

Three types of seismic data recorded near Coalinga, California were analyzed to study the behavior of scattered waves: 1) aftershocks of the May 2, 1983 earthquake, recorded on verticalcomponent seismometers deployed by the USGS; 2) regional refraction profiles using large explosive sources recorded on essentially the same arrays above; 3) three common-midpoint (CMP) reflection surveys recorded with vibrator sources over the same area. Records from each data set were bandpassed filtered into 5 Hz wide passbands (over the range of 1–25 Hz), corrected for geometric spreading, and fit with an exponential model of amplitude decay. Decay rates were expressed in terms of inverse codaQ (Qc−1).Qc−1 values for earthquake and refraction data are generally comparable and show a slight decrease with increasing frequency. Decay rates for different source types recorded on proximate receivers show similar results, with one notable exception. One set of aftershocks shows an increase ofQc−1 with frequency.Where the amplitude decay rates of surface and buried sources are similar, the coda decay results are consistent with other studies suggesting the importance of upper crustal scattering in the formation of coda. Differences in the variation ofQc−1 with frequency can be correlated with differences in geologic structure near the source region, as revealed by CMP-stacked reflection data. A more detailed assessment of effects such as the depth dependence of scattered contributions to the coda and the role of intrinsic attenuation requires precise control of source-receiver field geometry and the study of synthetic seismic data calculated for velocity models developed from CMP reflection data.

Reply by the authors to W. Harry Mayne

We agree that in some circumstances nonlinear sweeps can improve the signal‐to‐noise bandwidth of our processed data; a paper by Anstey (1980) gives an excellent review of what these improvements might cost. While the use of nonlinear sweeps has been advocated to combat earth attenuation, it is useful to keep in mind the limitations of its role in the battle. We can command the use of nonlinear sweeps in those situations where the source amplitude spectrum required to compensate for earth attenuation has a slope that is modest enough to be practically attainable in the field. Usually, however, that source function can be tailored to flatten spectral amplitude for only a restricted target zone. Great care is thus required in selecting the nonlinear sweep; the geophysicist must know the target zone well and must be careful not to sacrifice data quality in other time windows.