A model‐based data‐driven dictionary learning for seismic data representation

Planar waves events recorded in a seismic array can be represented as lines in the Fourier domain. However, in the real world, seismic events usually have curvature or amplitude variability, which means that their Fourier transforms are no longer strictly linear but rather occupy conic regions of the Fourier domain that are narrow at low frequencies but broaden at high frequencies where the effect of curvature becomes more pronounced. One can consider these regions as localised “signal cones”. In this work, we consider a space–time variable signal cone to model the seismic data. The variability of the signal cone is obtained through scaling, slanting, and translation of the kernel for cone‐limited (C‐limited) functions (functions whose Fourier transform lives within a cone) or C‐Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a non‐linear optimisation problem, which we address by a fixed‐point method that utilises a variable projection method with ?₁ constraints on the linear parameters and bound constraints on the non‐linear parameters. We observe that slow decay and oscillatory behaviour of the kernel for C‐limited functions constitute bottlenecks for the optimisation problem, which we partially overcome by the C‐Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity‐promoting curvelet decomposition, matching pursuit Fourier interpolation, and sparsity‐promoting plane‐wave decomposition methods.     

Well tie for broadband seismic data

The seismic industry is increasingly acquiring broadband data in order to reap the benefits of extra low‐ and high‐frequency contents. At the low end, as the sharp low‐cut decay gets closer to zero frequency, it becomes harder for a well tie to estimate the low‐frequency response correctly. The fundamental difficulty is that well logs are too short to allow accurate estimation of the long‐period content of the data. Three distinctive techniques, namely parametric constant phase, frequency‐domain least squares with multi‐tapering, and Bayesian time domain with broadband priors, are introduced in this paper to provide a robust solution to the wavelet estimation problem for broadband seismic data. Each of these techniques has a different mathematical foundation that would enable one to explore a wide range of solutions that could be used on a case‐by‐case basis depending on the problem at hand. A case study from the North West Shelf Australia is used to analyse the performance of the proposed techniques. Cross‐validation is proposed as a robust quality control measure for evaluating well‐tie applications. It is observed that when the seismic data are carefully processed, then the constant phase approach would likely offer a good solution. The frequency‐domain method does not assume a constant phase. This flexibility makes it prone to over‐fitting when the phase is approximately constant. Broadband priors for the time‐domain least‐squares method are found to perform well in defining low‐frequency side lobes to the wavelet.     

A study of the geophysical response of distributed fibre optic acoustic sensors through laboratory‐scale experiments

In the past few years, distributed acoustic sensing has gained great interest in geophysics. This acquisition technology offers immense improvement in terms of efficiency when compared with current geophysical acquisition methods. However, the fundamentals of the measurement are still not fully understood because direct comparisons of fibre data with conventional geophysical sensors are difficult during field tests. We present downscaled laboratory experiments that enabled us to characterise the relationship between the signals recorded by conventional seismic point receivers and by distributed fibre optic sensors. Interrogation of the distributed optical fibre sensor was performed with a Michelson interferometer because this system is suited to compact test configurations, and it requires only a very simple data processing workflow for extracting the signal outputs. We show acoustic data that were recorded simultaneously by both the fibre optical interferometer and conventional three‐component accelerometers, thus enabling the comparison of sensor performance. We present results focused on the directionality of fibre measurements, on the amplitude variation with angle of incidence, and on the transfer function that allows accelerometer signals to be transformed into optical fibre signals. We conclude that the optical fibre response matches with the array of the displacement differences of the inline accelerometers deployed along the fibre length. Moreover, we also analysed the influence of various types of coupling and fibre cable coating on the signal responses, emphasising the importance of these parameters for field seismic acquisitions when using the distributed fibre optic technology.     

Definitive superparamagnetic source identification through spatial,temporal, and amplitude analysis of airborne electromagnetic data

The aim of this paper is to add confidence to existing methods using decay shape analysis to detect superparamagnetic responses in airborne electromagnetic data. While expensive to acquire, vertical spatial gradient measurements of the electromagnetic signals can discriminate near‐surface superparamagnetic sources. This research investigated the use of horizontal spatial gradients and amplitude information as further indicators of superparamagnetic. High horizontal gradients were shown both theoretically and in field data to help discriminate superparamagnetic from deep mineral targets. Further, superparamagnetic responses have characteristically small amplitudes inconsistent with realistic mineral exploration targets at shallow depths.     

The Daily Erosion Project – daily estimates of water runoff,soil detachment,and erosion

Water runoff and sediment transport from agricultural uplands are substantial threats to water quality and sustained crop production. To improve soil and water resources, farmers, conservationists, and policy‐makers must understand how landforms, soil types, farming practices, and rainfall interact with water runoff and soil erosion processes. To that end, the Iowa Daily Erosion Project (IDEP) was designed and implemented in 2003 to inventory these factors across Iowa in the United States. IDEP utilized the Water Erosion Prediction Project (WEPP) soil erosion model along with radar‐derived precipitation data and government‐provided slope, soil, and management information to produce daily estimates of soil erosion and runoff at the township scale (93 km² [36 mi²]). Improved national databases and evolving remote sensing technology now permit the derivation of slope, soil, and field‐level management inputs for WEPP. These remotely sensed parameters, along with more detailed meteorological data, now drive daily WEPP hillslope soil erosion and water runoff estimates at the small watershed scale, approximately 90 km² (35 mi²), across sections of multiple Midwest states. The revisions constitute a substantial improvement as more realistic field conditions are reflected, more detailed weather data are utilized, hill slope sampling density is an order of magnitude greater, and results are aggregated based on surface hydrology enabling further watershed research and analysis. Considering these improvements and the expansion of the project beyond Iowa it was renamed the Daily Erosion Project (DEP). Statistical and comparative evaluations of soil erosion simulations indicate that the sampling density is adequate and the results are defendable. The modeling framework developed is readily adaptable to other regions given suitable inputs. © 2017 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Effect of thickness of planar nozzles on erosion depth of levee soils subjected to plunging water

In this study, the effect of the thickness of a planar jet on the erosion depth when the jet impinges on a surface composed of cohesive soil was analytically and numerically evaluated. The results showed that the erosion depth was practically independent of the nozzle thickness for erosion depths shallower than the potential core length (i.e. the region of the jet in which the central flow velocity is the same as the nozzle velocity). The relation between nozzle thickness and erosion depth was non-linear with continuously variable slope for erosion depths deeper than the potential core length. Finally, the relation was approximately linear when the erosion depth converged to the equilibrium erosion depth. The findings of this study indicate that direct and fast prediction of the erosion depth in the field is possible using the data from a small scale soil erosion test with similar flow velocities.     

Influence of IHSS Standard and Reference Materials on Copper and Mercury Toxicity to Vibrio fischeri

The reduction in light emission of the marine bacterium Vibrio fischeri used in the standard Microtox^® bioassay was measured for the metals copper and mercury. The concentration at which the light emission was reduced by 50% (EC₅₀) was determined to be (3.43 ± 0.83) μmol/L for Cu²⁺ and (0.66 ± 0.01) μmol/L for Hg²⁺. The reduction of the toxicity of these metals by humic and fulvic acids were studied using IHSS Standard and Reference Materials. Copper toxicity was reduced 17...20% by the soil and peat fulvic acids and 9...20% by the aquatic fulvic acids. While there appeared to be little difference in the reduction of Cu toxicity by fulvic acids from soils, peats, or aquatic systems, Hg toxicity was reduced 3.6...7.3% by the soils and peats, while aquatic fulvic acids reduced Hg toxicity 14...16%. Soil fulvic acids appear to have significantly less capacity to reduce Hg toxicity than Cu toxicity. Humic acids had much higher reductions of Cu toxicity (44...124%) compared to the fulvic acids, with little difference between aquatic and soil or peat humic acids, 44...124% and 67...100%, respectively. However, humic and fulvic acids, regardless of origin, had approximately the same effect on Hg toxicity with 3.5...16% reduction by fulvic acids and 8...20% reduction by humic acids. Unlike the fulvic acids, no clear trend was observed relative to origin of the humic acids. There was no correlation between percent reduction of Cu or Hg toxicity by the organic compounds and copper binding capacity (CuBC), C/N ratio, or carboxyl content of the materials. Examination of natural organic matter (NOM) isolated by reverse osmosis techniques from three water sources had reductions of both Cu and Hg toxicity that were most similar to the Suwannee River and Nordic fulvic acids.