ergey Fomel

Bio: ergey Fomel is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Regularization (mathematics) & Tikhonov regularization. The author has an hindex of 1, co-authored 3 publications receiving 4 citations.

daptive multiple subtraction using regularized nonstationary regression

Abstract: Stationary regression is the backbone of seismic data-processing algorithms including match filtering, which is commonly applied for adaptive multiple subtraction. However, the assumption of stationarity is not always adequate for describing seismic signals. I have developed a general method of nonstationary regression and that applies to nonstationary match filtering. The key idea is the use of shaping regularization to constrain the variability of nonstationary regression coefficients. Simple computational experiments demonstrate advantages of shaping regularization over classic Tikhonov’s regularization, including a more intuitive selection of parameters and a faster iterative convergence. Using benchmark synthetic data examples, I have successfully applied this method to the problem of adaptive subtraction of multiple reflections.

haping regularization in geophysical-estimation problems

Abstract: Regularization is a required component of geophysical-estimation problems that operate with insufficient data. The goal of regularization is to impose additional constraints on the estimated model. I introduce shaping regularization, a general method for imposing constraints by explicit mapping of the estimated model to the space of admissible models. Shaping regularization is integrated in a conjugate-gradient algorithm for iterative least-squares estimation. It provides the advantage of better control on the estimated model in comparison with traditional regularization methods and, in some cases, leads to a faster iterative convergence. Simple data interpolation and seismic-velocity estimation examples illustrate the concept.

Local seismic attributes

Abstract: Local seismic attributes measure seismic signal characteristics not instantaneously, at each signal point, and not globally, across a data window, but locally in the neighborhood of each point. I define local attributes with the help of regularized inversion and demonstrate their usefulness for measuring local frequencies of seismic signals and local similarity between different data sets. I use shaping regularization for controlling the locality and smoothness of local attributes. A multicomponent-image-registration example from a ninecomponent land survey illustrates practical applications of local attributes for measuring differences between registered images.

Adaptive overburden elimination with the multidimensional Marchenko equation

Abstract: Iterative substitution of the multidimensional Marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process. In so-called Marchenko imaging, a macro velocity model of the subsurface is required to meet this objective. The model is used to back-propagate the data during the first iteration and to truncate integrals in time during all successive iterations. In case of an erroneous model, the image will be blurred (akin to conventional imaging) and artifacts may arise from inaccurate integral truncations. However, the scheme is still successful in removing artifacts from internal multiple reflections. Inspired by these observations, we rewrote the Marchenko equation, such that it can be applied early in a processing flow, without the need of a macro velocity model. Instead, we have required an estimate of the two-way traveltime surface of a selected horizon in the subsurface. We have introduced an approximation, such that adaptive subtracti...

Unveiling the signals from extremely noisy microseismic data for high-resolution hydraulic fracturing monitoring

Abstract: Microseismic method is an essential technique for monitoring the dynamic status of hydraulic fracturing during the development of unconventional reservoirs. However, one of the challenges in microseismic monitoring is that those seismic signals generated from micro seismicity have extremely low amplitude. We develop a methodology to unveil the signals that are smeared in the strong ambient noise and thus facilitate a more accurate arrival-time picking that will ultimately improve the localization accuracy. In the proposed technique, we decompose the recorded data into several morphological multi-scale components. In order to unveil weak signal, we propose an orthogonalization operator which acts as a time-varying weighting in the morphological reconstruction. The orthogonalization operator is obtained using an inversion process. This orthogonalized morphological reconstruction can be interpreted as a projection of the higher-dimensional vector. We first test the proposed technique using a synthetic dataset. Then the proposed technique is applied to a field dataset recorded in a project in China, in which the signals induced from hydraulic fracturing are recorded by twelve three-component (3-C) geophones in a monitoring well. The result demonstrates that the orthogonalized morphological reconstruction can make the extremely weak microseismic signals detectable.