Seismic migration and inversion describe a class of closely related processes sharing common objectives and underlying physical principles. These processes range in complexity from the simple NMO‐stack to the complex, iterative, multidimensional, prestack, nonlinear inversion used in the elastic seismic case. By making use of amplitudes versus offset, it is, in principle, possible to determine the three elastic parameters from compressional data. NMO‐stack can be modified to solve for these parameters, as can prestack migration. Linearized, wave‐equation inversion does not inordinately increase the complexity of data processing. The principal part of a migration‐inversion algorithm is the migration. Practical difficulties are considerable, including both correctable and intrinsic limitations in data quality, limitations in current algorithms (which we hope are correctable), and correctable (or perhaps intrinsic) limitations in computer power.

Migration and inversion of seismic data

Common midpoint data are now being collected with ever increasing source-receiver offsets. For wide aperture seismic data classical methods of interpretation fail, since velocity analyses and signal-to-noise enhancement methods based on hyperbolic traveltime curves are no longer appropriate. Therefore, the goals of increased velocity resolution and signal enhancement, which motivate the increase in offset, are not achieved. Approximate methods, involving higher order traveltime curves or extrapolations, have been developed for velocity analysis but these are ineffective in the presence of refracted arrivals, and lack a physical basis. These problems can be minimized by transforming the observational data to the domain of intercept or vertical delay time τ and horizontal ray parameter p . In this domain headwave refractions are collapsed into points and both near vertical and wide angle reflections can be analyzed simultaneously to derive velocity-depth information, even in the presence of velocity gradients or low velocity zones.

Velocity analysis for wide aperture seismic data

The determination of the gross velocity distribution in the ground from CDP reflection data depends primarily on the determination of the velocity producing maximum coherency in the stacked data. This stacking velocity is a mathematical quantity which has no physical significance. The interval and average velocities describe meaningful physical parameters and are related to the maximum coherency stacking velocity through the r.m.s. velocity. The relationship between these velocities is illustrated. The limitations to the horizontal resolution of the velocity tool are discussed.

Velocity Determination from Seismic Reflection Data

The results of 84 deep seismic sounding recordings scattered over an area of 250,000 km 2 (average spacing, 25 km) with each recording yielding up to 3 depth points for each interface mapped, are compiled on maps giving crustal thickness and depth to the transition between an upper and a lower crustal layer. Ranges are from a few kilometers up to about 700 km. A velocity model is derived as follows: upper crustal layer, α = 6.05 km/sec, β, = 3.46 km/sec; lower crustal layer, α = 6.85 km/sec, β, = 4.00 km/sec (with the strong possibility that these values are averages, with a small vertical velocity gradient in the lower layer); uppermost part of upper mantle, α = 7.92 km/sec, β, = 4.60 km/sec. A sub-Mohorovicic event, showing triplication, is found. It may represent a boundary in a layered medium, or a second-order discontinuity in a medium with a vertical gradient. If it is the former, a velocity transition to a velocity in the range 8.3 to 8.4 km/sec is indicated at an average depth of 50 km. Lateral velocity variation was found to be small. A method of calculating velocities from wide-angle reflections for a 3-layer medium overlying a uniform half-space is given. The derived deep crustal structure yields important geological information, showing downward extension of geological features visible at the surface. These include the boundary between the Churchill and Superior geological provinces of the Canadian shield, and a trough-like thickening of the upper crustal layer (accompanied by a thinning of the total crustal section) which has been traced 350 km from the English River area of Ontario, across the south basin of Lake Winnipeg, Manitoba. It lies beneath a geological unit known as the English River gneissic belt. In addition, faulted boundaries of crustal blocks are shown in the deep seismic structure. The derived seismic structure shows correlation with regional gravity and magnetic data.

Deep seismic crustal studies in Manitoba

SUMMARY

As part of an intensive study of a small area of oceanic lithosphere, the British Institutions Reflection Profiling Syndicate (BIRPS) acquired closely spaced deepseismic-reflection profiles over the Early Cretaceous crust of the Cape Verde abyssal plain off West Africa. The survey consisted of profiles spaced at 4 km arranged into strike lines parallel to the old sea-floor spreading axis (‘isochron’ profiles) and orthogonal dip lines oriented in the original direction of spreading (‘flow’ profiles). A large-capacity, well-tuned airgun source and very quiet shooting conditions ensured a high signal-to-noise ratio for deep reflection. Devising a strategy for mitigating contamination from ‘wrap-around’ multiples arriving from previous shots enabled us to use the minimum possible shot-point interval (50 m) allowed for collecting long (18 s) records. Data processing was oriented towards a medium with low root-mean-square velocity, steeply dipping structure, and pervasive low apparent velocity noise from diffraction at the top of the igneous crust. The contrast between the isochron and flow profiles is striking. Isochron profiles are typically highly reflective throughout the igneous crust, consisting of bright, bidirectionally dipping reflection sets that extend in places from the top of the igneous basement down to the interpreted Moho reflection. These reflections do not offset intracrustal or top-basement structure and thus are not interpreted as faults: an igneous intrusive origin seems more likely. Flow profiles are more sparsely reflective but show individual steeply dipping reflections best developed in the upper igneous crust, continuing down in places to the Moho. Dipping reflections on the flow profiles are interpreted as major normal faults since they are clearly associated with offsets of the top of the basement as well as truncation of horizontal reflections within the igneous crust. The dominant dip of these reflections is to the west towards the spreading ridge axis. Reflections from the vicinity of the Moho, while well developed in some places, are not particularly prominent across the survey area. Moho reflections appear to show a different structural relation to crustal features on the isochron and flow profiles: on isochron profiles, dipping reflections occasionally flatten out into, and may merge with, the Moho reflection; on flow profiles, as dipping crustal reflections approach the Moho reflection, they are usually abruptly cut off by it without extending deeper. This survey shows how oceanic crustal structure can vary rapidly over relatively small areas, provides convincing evidence that a structurally complex fabric dominates oceanic igneous crust, and gives a conclusive observation of faults that penetrate the entire oceanic crust.

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Complex structure along a Mesozoic sea‐floor spreading ridge: BIRPS deep seismic reflection, Cape Verde abyssal plain

Normal moveout may be used to distinguish primary from multiple reflections when the average velocity changes with depth. Approximate values of normal moveout may be found using an average velocity formula, but such values are always too large. The error appears to be controlled by the ratio of the standard deviation of the velocities within the section to the average velocity. Ray tracing provides normal moveout values which agree much better with observations. As a consequence of large dip, the reflections added by the CDP method do not represent identical areas of the dipping bed. However, if the various reflection zones lie on an inclined plane, they are added in‐phase and assume the time of a reflection from a point on the plane.

Kenneth S. Cressman

Papers

How velocity layering and steep dip affect cdp