Modern oil and gas exploration depends on a variety of geophysical prospect tools. One of them is reflection seismology that allows to obtain interwell information of sufficient resolution economically. This exploration method collects reflection seismic data on the surface of an area of prospect interest and then uses them to build seismic images of the subsurface. All imaging approaches can be divided into two groups: wave equation-based methods and integral schemes. Kirchhoff migration, which belongs to the second group, is an indispensable tool in seismic imaging due to its flexibility and relatively low computational cost. Unfortunately, the classic formulation of this method images only a part of the surface data, if so-called multipathing is present in it. That phenomenon occurs in complex geologic settings, such as subsalt areas, when seismic waves travel between a subsurface point and a surface location through more than one path. The quality of imaging with Kirchhoff migration in complex geological areas can be improved if multiple paths of ray propagation are included in the integral. Multiple arrivals can be naturally incorporated into the imaging operator if it is expressed as an integral over subsurface take-off angles. In this form, the migration operator involves escape functions that connect subsurface locations with surface seismic data values through escape traveltime and escape positions. These escape quantities are functions of phase space coordinates that are simply related to the subsurface reflection system. The angle-domain integral operator produces output scattering- and dip-angle image gathers, which represent a convenient domain for subsurface analysis. Escape functions for angle-domain imaging can be simply computed with initial-value ray tracing, a Lagrangian computational technique. However, the computational cost of such a bottom-up approach can be prohibitive in practice. The goal of this work was to construct a computationally efficient phase space imaging framework. I designed several approaches to computing escape functions directly in phase space for mapping surface seismic reflection data to the subsurface angle domain. Escape equations have been introduced previously to describe distribution of escape functions in the phase space. Initially, I employed these equations as a basis for building an Eulerian numerical scheme using finite-difference method in the 2-D case. I show its accuracy constraints and suggest a modification of the algorithm to overcome them. Next, I formulate a semi-Lagrangian approach to computing escape functions in 3-D. The second method relies on the fundamental property of continuity of these functions in the phase space. I define locally constrained escape functions and show that a global escape solution can be reconstructed from local solutions iteratively. I validate the accuracy of the proposed methods by imaging synthetic seismic data in several complex 2-D and 3-D models. I draw conclusions about efficiency by comparing the compute time of the imaging tests with the compute time of a well-optimized conventional initial-value ray tracing. / text

The mode of tectonics by which early Archean proto-continents were deformed was investigated in the Pilbara Craton in Western Australia, which has not been substantially tectonically deformed since ~3.2 Ga. The craton consists of a unique dome and keel structure where vertical, low-grade metamorphism basaltic greenstone keels surround large granitic (TTG) domes. The dominant model for 3.5-3.2 Ga deformation in the Pilbara is gravity-driven vertical tectonics, or partial convective overturn in a hot crust. In this model, the granitic bodies rose upward as solid-state diapirs, and the greenstones "sagducted" downward around the granitic bodies. Australian scientists acquired deep seismic reflection data crossing a granitoid-greenstone boundary. Their processing did not image the geologically mapped steep dip of the boundary because standard methods limit the maximum dip. A 37-km section of these data were reprocessed using 2D Kirchhoff prestack depth migration to include vertical dips. The western half of the migrated section images a granitoid dome with weak to no reflectivity that extends deeper than 4 km. The eastern half images 2-3 km of layered volcanic rocks of the Fortescue Group overlying the greenstones. Seismic velocity models created using travel-time tomography suggest a thin weathering layer overlying slightly fractured crystalline rocks. These fractures close within 200-300 m depth, and velocity reaches bedrock speeds consistent with expected values of granitoids to the west and volcanic rocks of the Fortescue Group to the east. The best migrated image contains several reflections with dips (~45-55˚) cross-cutting each other from both directions at the location of the expected granitoid-greenstone boundary. This strongly suggests the presence of steep dips in the upper ~1.5 km but does not provide a definitive image. This inconclusive result is due to strong surface-wave noise, the crooked 2D seismic line, and the 3D nature of the geologic boundary at the seismic line. A very small seismic velocity gradient within the crystalline bedrock limits the maximum depth to which vertical features can be imaged. / Master of Science / The Pilbara craton is one of the few exposed and intact pieces of continents that were formed ~3.2 billion years ago. This research analyzes how these early land masses were deformed. There are two methods by which early land masses evolved—vertical tectonics (a more rudimentary, gravity-driven form of plate movement) or horizontal tectonics (which is closer to modern-day tectonics and requires many stages of deformation). This area has a unique dome-and-keel structure where greenstones (metamorphosed volcanics) are vertically wrapped around large granitic domes. Studying the vertical features of the greenstones will allow us to ascertain how tectonics evolved in the area. A seismic survey was conducted in 2018 in the area. These data were reprocessed to include steep dips to extract the exact location of the steeply dipping boundary between the dome and keel structure at depth. The resulting image contains inconclusive evidence due to the physical limitations of the geology and the sharp bend in the seismic line. Further studies need to be done to determine if the Pilbara Craton was formed by vertical tectonics.