From the Hagedoorn imaging technique to Kirchhoff migration and inversion

The seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique – a 'string construction' or 'ruler and compass' method – for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave-equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle-dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two.     

Aerosols: A limitation on the determination of ozone from BUV observations

Summary Recent satellite experiments have measured the radiance of the earth at ultraviolet wavelengths and the data thus obtained has been used to determine atmospheric ozone concentrations. It is pointed out in this paper that in the presence of significant concentrations of aerosols at high altitudes, it is not possible from observations of backscattered ultraviolet radiation to separate the effects of aerosols from those attributable to ozone.The earth's daytime horizon was scanned on several occasions between 1963 and 1967 from an altitude of 80 km. For at least one of the flights analyzed we interpret the data to indicate the existence of an aerosol layer at 50 km. This observation, in combination with related observations of other experimenters, implies a limitation on the ability of the backscattered ultraviolet technique to determine ozone concentrations, particularly at altitudes in the region between 35 and 50 km. This limitation may be overcome by altering the viewing geometry and making observations of the earth's horizon. Data thus obtained may be used to deduce the concentrations of both ozone and aerosols.     

The alkali-extraction test as a reliable method of detecting oxidized metallurgical coal

Because oxidized coal is known to have an adverse effect on bulk-density control and coal handling in the coke plant, and on coke quality, U.S. Steel has developed the alkali-extraction test as a means to identify oxidized (weathered) coal in coal blends. In the test, coal is boiled in a caustic solution so that oxidized coal dissolves and darkens the solution. The solution is then tested for light transmittance, with the solution transmittance decreasing as the coal oxidation increases. A transmission value less than 80% indicates that the coal is too oxidized for metallurgical use. This rejection limit corresponds to 8 to 12% microscopically recognizable oxidized coal. Petrographic determinations of oxidized coal in four ranks of metallurgical coal show a linear relationship (0.964 correlation coefficient) with corresponding transmission values and a detection limit of three percent oxidized coal for the test. In addition, the oxygen content and infrared-band intensities of these coals also show a linear trend with transmission values. The study indicates that the alkali-extraction test is a reliable test for detecting oxidized coal in metallurgical coal blends and is superior to the Free-Swelling Index for setting mining limits in stripping operations. U.S. Steel is presently using the test to monitor captive and purchased coals for acceptance as metallurgical coal.     

On the least-squares fit of small and great circles to spherically projected orientation data

Given the direction cosines a _i ^′ = (a ₁ ⁱ , a ₂ ⁱ , a ₃ ⁱ )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x₁, x₂, x₃, x₄)for the angular radius x₄,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking x_j+1 = x_j + Δxwhere x_j is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.     

Cataclasites along the Saltville thrust,U.S.A. and their implications for thrust-sheet emplacement

Cataclasis and frictional wear are the primary bulk deformation mechanisms along steeply dipping portions of the Saltville thrust in the southern Appalachian foreland zone, U.S.A. Fault character ranges from a single discrete sliding surface with negligible gouge, to a zone of several discrete sliding surfaces or a zone (up to 0.3 m thick) of pervasive cataclasite. Marked fracturing occurs up to 20 m above the fault, whereas minimal deformation is found in the footwall rocks. Hanging wall dolomites range from crush breccias (less than 5% matrix) to ultracataclasites (with 90% matrix), although cataclasites (50–70% matrix) are predominant. Foliated cataclasites occur where dolomite is thrust over shale. Progressive development of cataclastic fabrics is due to comminution by fracturing and grinding along intersecting fractures. Continued frictional grinding results in complete disruption of the original fabric to produce cataclasite and minor ultracataclasite. Grain alignment occurs by rigid body rotation with subsequent local enhancement by pressure-solution. Microstructural relations of the fault gouge suggest periodic fluctuations in fluid pressure, where λ_v (ratio of fluid to overburden pressure) probably ranged between 0.45 and 1. The Saltville thrust-sheet emplacement must have occurred in a caterpillar-like fashion involving aseismic and seismic shear. Shear stresses accompanying fault motion as determined from dolomite twin lamellae are in the order of 65 mPa.     

Interrelations of mesoscopic structures and strain across a small regional fold,Virginia Appalachians

Small regional folds, such as the Clover Hollow anticline of the Narrows thrust-sheet in southwest Virginia, U.S.A., are considered to be large buckle folds expressing lateral shortening above a subsurface décollement. Cleavage, mesoscopic and regional folds, and contraction faults have developed in these rocks under anchimetamorphic conditions, in a single, protracted deformation during thrust-sheet emplacement. The contraction faults dominate the structure at all scales. Three fault associations (isolated contraction faults, contraction faults in series and complex fault zones with intense folding) determine the pattern and intensity of local structures. Regional displacement transfer of strain along and across faults has produced local variations in structural style. Duplex-like systems of second-order faults terminate laterally into zones of intense folding and third-order faulting. Fold tightness, cleavage intensity, strain magnitude and total longitudinal strain (ε_T) are maximum in these regions. Contraction faults in this thrust-sheet have propagated along zones of high strain rate associated with mesoscopic folding and intense cleavage. Regional hinge migration, and greater structural complexity along the southeast limb of the Clover Hollow anticline, are considered to be due to emplacement of the adjacent thrust-sheet.     

Crenulation cleavage differentiation: implications of solution-deposition processes

Metamorphic differentiation associated with cleavage development in crenulated anisotropic rock fabrics is commonly due to a redistribution of mineral phases within a certain volume of the fabric. Such a volume redistribution can be explained by solution transfer of soluble minerals from sites of high chemical potential, fold limbs, to sites of low chemical potential, fold hinges. The processes involved are dissolution, diffusional transfer via grain-boundaries and redeposition. The driving force for the diffusion, differences in chemical potential, is relatable to stress and fabric variations around the microfolds. The rate of transfer is influenced by the initial solubility of the mineral grains, the kinetics of grain-boundary diffusion, the nature of grain contacts and the microfold wavelength. The sense of migration of dissolved species is dependent on spatial variations in the magnitudes of normal stress and mean stress combined with grain shape and grain orientation changes around the microfolds.     

Investigations on the mechanical significance of crenulation cleavage

Measurements of total, incremental and progressive strains associated with the development of small scale crenulation cleavage in some low-grade metamorphic rocks from Australia and Switzerland are applied to a discussion of the mechanical significance of the cleavage.Limits are placed on the amount of incremental and total slip or simple shear possible along the cleavage by the observation that the XY principal plane trace of bulk total crenulation strain coincides within 4° of the crenulation cleavage trace in all cases where this strain has been measured or estimated. The measurements are made on eight specimens using deformed porphyroblasts, crystal fibres in pressure-shadows around pyrite and flattened folds and include deformations with coaxial and non-coaxial histories.Further measurements derived from pressure-shadow fibres (eight specimens) show that the style and orientation of incremental deformation are essentially independent of the crenulation cleavage, except for a limit (43°) to the obliquity of the principal incremental extension axis during a given cleavage episode. The only special deformation related to the cleavage is the coaxial one. An indication of passive cleavage behaviour at high strain is shown by the progressive strain history of one specimen. Evidence for passive rotation of a transected axial plane is shown by another. A model is proposed to account for these observations, especially the conditions necessary for initiation and continued development of a new cleavage fabric.Some further applications of existing strain measurement techniques are described: of the R_f/Ø_f method to heterogeneously superposed tectonic strains and of an improved procedure of t′_α/α flattening analysis.