Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates

The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is computationally expensive for large data sets. In this paper we present a new method for fast computation of the hyperbolic Radon transforms. It is based on using a log-polar sampling with which the main computational parts reduce to computing convolutions. This allows for fast implementations by means of FFT. In addition to the FFT operations, interpolation procedures are required for switching between coordinates in the time-offset; Radon; and log-polar domains. Graphical Processor Units (GPUs) are suitable to use as a computational platform for this purpose, due to the hardware supported interpolation routines as well as optimized routines for FFT. Performance tests show large speed-ups of the proposed algorithm. Hence, it is suitable to use in iterative methods, and we provide examples for data interpolation and multiple removal using this approach.Comment: 21 pages, 10 figures, 2 table

Spatial distribution of Pleistocene/Holocene warming amplitudes in Northern Eurasia inferred from geothermal data

International audienceWe analyze 48 geothermal estimates of Pleistocene/Holocene warming amplitudes from various locations in Greenland, Europe, Arctic regions of Western Siberia, and Yakutia. The spatial distribution of these estimates exhibits two remarkable features. (i) In Europe and part of Asia the amplitude of warming increases toward the northwest and displays clear asymmetry with respect to the North Pole. The region of maximal warming is close to the North Atlantic. A simple parametric dependence of the warming amplitudes on the distance to the warming center explains 91% of the amplitude variation. The Pleistocene/Holocene warming center is located northeast of Iceland. We claim that the Holocene warming is primarily related to the formation (or resumption) of the modern system of currents in the North Atlantic. (ii) In Arctic Asia, north of the 68-th parallel, the amplitude of temperature change sharply decreases from South to North, reaching zero and even negative values. These small or negative amplitudes could be attributed partially to a joint influence of Late Pleistocene ice sheets. Using a simple model of the temperature regime underneath the ice sheet we show that, depending on the relationship between the heat flow and the vertical ice advection velocity, the base of the glacier can either warm up or cool down. Nevertheless, we speculate that the more likely explanation of these observations are warm-water lakes thought of have formed in the Late Pleistocene by the damming of the Ob, Yenisei and Lena Rivers

Neural Eikonal Solver: improving accuracy of physics-informed neural networks for solving eikonal equation in case of caustics

The concept of physics-informed neural networks has become a useful tool for solving differential equations due to its flexibility. There are a few approaches using this concept to solve the eikonal equation which describes the first-arrival traveltimes of acoustic and elastic waves in smooth heterogeneous velocity models. However, the challenge of the eikonal is exacerbated by the velocity models producing caustics, resulting in instabilities and deterioration of accuracy due to the non-smooth solution behaviour. In this paper, we revisit the problem of solving the eikonal equation using neural networks to tackle the caustic pathologies. We introduce the novel Neural Eikonal Solver (NES) for solving the isotropic eikonal equation in two formulations: the one-point problem is for a fixed source location; the two-point problem is for an arbitrary source-receiver pair. We present several techniques which provide stability in velocity models producing caustics: improved factorization; non-symmetric loss function based on Hamiltonian; gaussian activation; symmetrization. In our tests, NES showed the relative-mean-absolute error of about 0.2-0.4% from the second-order factored Fast Marching Method, and outperformed existing neural-network solvers giving 10-60 times lower errors and 2-30 times faster training. The inference time of NES is comparable with the Fast Marching. The one-point NES provides the most accurate solution, whereas the two-point NES provides slightly lower accuracy but gives an extremely compact representation. It can be useful in various seismic applications where massive computations are required (millions of source-receiver pairs): ray modeling, traveltime tomography, hypocenter localization, and Kirchhoff migration.Comment: The paper has 14 pages and 6 figures. Source code is available at https://github.com/sgrubas/NE

Surface temperature trends in Russia over the past five centuries reconstructed from borehole temperatures

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94976/1/jgrb13614.pd

Hybrid Kinematic-Dynamic Approach to Seismic Wave-Equation Modeling, Imaging, and Tomography

Estimation of the structure response to seismic motion is an important part of structural analysis related to mitigation of seismic risk caused by earthquakes. Many methods of computing structure response require knowledge of mechanical properties of the ground which could be derived from near-surface seismic studies. In this paper we address computationally efficient implementation of the wave-equation tomography. This method allows inverting first-arrival seismic waveforms for updating seismic velocity model which can be further used for estimating mechanical properties. We present computationally efficient hybrid kinematic-dynamic method for finite-difference (FD) modeling of the first-arrival seismic waveforms. At every time step the FD computations are performed only in a moving narrowband following the first-arrival wavefront. In terms of computations we get two advantages from this approach: computation speedup and memory savings when storing computed first-arrival waveforms (it is not necessary to make calculations or store the complete numerical grid). Proposed approach appears to be specifically useful for constructing the so-called sensitivity kernels widely used for tomographic velocity update from seismic data. We then apply the proposed approach for efficient implementation of the wave-equation tomography of the first-arrival seismic waveforms

The study of the relationship between thermal conductivity and porosity, permeability, humidity of sedimentary rocks of the West Siberian Plate

The determination of correlation between thermal conductivity and structural parameters (porosity, permeability, humidity) of sedimentary rocks is a very urgent task. This article analyzes and compares the results of measurements of these parameters for ~300 samples of Mesozoic sandstones and siltstones from the core of 18 wells drilled in the north-eastern and southern regions of the West Siberian plate. The thermal conductivity of all samples was measured in the dry state and some (90 samples) – after saturation with water. Porosity and permeability are determined for 280 and 230 samples, respectively. The obtained data are used to establish linear correlation connections between thermal conductivity, porosity and permeability. The most interesting are rather stable dependences of thermal conductivity of dry and water-saturated samples between themselves and with porosity. The established correlation dependences are interesting in practical terms. Some of them can be used to approximate the thermal conductivity of water-saturated rocks by measurements of dry rocks or even only by the porosity value. The relationship between the thermal conductivity of sedimentary rocks and porosity can be used for rapid assessment of porosity of rocks on advanced measurements of thermal conductivity of a full-size core. It is obvious that the revealed correlation connections require further clarification

Geomechanic modeling of seismic emission due to fracture growth - connection to microseismic source mechanisms

We present an approach to study the rock failure mechanisms due to fracture growth or activation. Our approach includes a series of numerical geomechanic simulations of an incremental rock failure (fracture growth) accounting for elastic wavefield generation and propagation. We then record these wavefields and perform their seismic moment-tensor inversion. We then try to establish connections between seismic moment-tensor solutions and different geomechanic scenarios of the fracture growth with possible applications in monitoring hydraulic fracturing, reservoir development, and local tectonic stress analysis. Our results show that in most cases the amplitudes of generated P-and S-waves can be reasonably well approximated by a moment-tensor point source. When the fracture hits the pre-existing crack then we observe stronger seismic emission compared to the case of the fracture growth in continuous medium. Thus our geomechanic modeling confirms the concept that the most noticeable microseismicity may come from activating the existing natural fractures rather than from the main fracture growth. We also note that the S-wave radiation pattern may be asymmetric (does not correspond to any ideal moment tensor) radiating more energy forward when the fracture hits long pre-existing cracks. Finally, our examples show that the moment tensors may give misleading idea about the direction of the fracture growth (advancement). This result should be kept in mind when interpreting microseismic data in the hydrofrac monitoring applications