A new inversion method to estimate high-resolution amplitude-versus-angle attributes (AVA) attributes such as intercept and gradient from prestack data is presented. The proposed technique promotes sparse-spike reflectivities that, when convolved with the source wavelet, fit the observed data. The inversion is carried out using a hybrid two-step strategy that combines fast iterative shrinkagethresholding algorithm (FISTA) and a standard least-squares (LS) inversion. FISTA, which can be viewed as an extension of the classical gradient algorithm, provides sparse solutions by minimizing the misfit between the modeled and the observed data, and the l 1 -norm of the solution. FISTA is used to estimate the location in time of the main reflectors. Then, LS is used to retrieve the appropriate reflectivity amplitudes that honor the data. FISTA, like other iterative solvers for l 1 -norm regularization, does not require matrices in explicit form, making it easy to apply, economic in computational terms, and adequate for solving large-scale problems. As a consequence, the FISTA+LS strategy represents a simple and cost-effective new procedure to solve the AVA inversion problem. Results on synthetic and field data show that the proposed hybrid method can obtain highresolution AVA attributes from noisy observations, making it an interesting alternative to conventional methods.
Well-to-seismic tie and wavelet phase estimation are closely related steps that link geology and seismic data. Usually, these processes are solved separately or alternately, diminishing the quality of the well-tying procedure. Apart from trying different wavelets, the well-to-seismic tie involves shifting and, often, stretching and/or squeezing the synthetic data until the correlation with the observed trace is high. These operations, which are somewhat arbitrary and prone to human errors, may lead to unrealistic velocity models and undesired waveform deformations. The automatic tying method that we propose avoids these issues allowing us to simultaneously adjust the wavelet phase and the velocity log within a predefined tolerance. The problem is solved iteratively by perturbing the observed velocity log and the wavelet phase in a way that leads to an increase of the correlation coefficient between the seismic data and the synthetic seismogram. The velocity log is perturbed smoothly using a function defined by monotonic cubic splines, whereas the wavelet phase is assumed to be an unknown constant. We solve the resulting optimization problem by means of differential evolution, which allows us to have complete control over the allowable velocity changes and guarantees that the measured borehole observations are well-honored. By means of pseudosynthetic and field data examples, we found that our automatic well-to-seismic tying method leads to high correlation values between the synthetic and the observed traces, accurate wavelet phase estimations, and small departures from the observed velocity log. Because it is the time scale that is stretched and/or squeezed and not the synthetic trace itself, as opposed to other automatic and manual well-tying methods, the resulting trace preserves the wavelet shape, a feature that certainly improves seismic data interpretation.
Presentism is, roughly, the metaphysical doctrine that maintains that whatever exists, exists in the present. The compatibility of presentism with the theories of special and general relativity was much debated in recent years. It has been argued that at least some versions of presentism are consistent with time-orientable models of general relativity. In this paper we confront the thesis of presentism with relativistic physics, in the strong gravitational limit where black holes are formed. We conclude that the presentist position is at odds with the existence of black holes and other compact objects in the universe. A revision of the thesis is necessary, if it is intended to be consistent with the current scientific view of the universe.
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