A hybrid strategy based on fast iterative shrinkage-thresholding algorithm and very fast simulated annealing: application to the prestack seismic inverse problem

With the purpose of characterizing the Earth subsurface, one of the objectives of the inversion of prestack seismic data is to determine contrasts between rock properties from the information contained in the variation of the amplitudes of the reflected compressional waves with the angle of incidence. This amplitude-versus-angle (AVA) variation can be described by various approximations to the so-called Zoeppritz equations, a set of non-linear equations that depend on the physical characteristics of the medium at each side of the interface where the compressional wave strikes. The coefficients of such approximations constitute AVA attributes that may provide important information about fluid content, a key issue for the characterization of hydrocarbon reservoirs. In this work we present a new inversion strategy to estimate efficiently and accurately high-resolution AVA attributes from prestack data. The proposed technique promotes sparse-spike reflectivities that, when convolved with the source wavelet, fit the observed data. Sparse solutions are desirable because they can be used to characterize significant and close reflectors more accurately than using conventional solutions. The inversion is carried out using a hybrid two-step strategy than combines Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and Very Fast Simulated Annealing (VFSA). FISTA provides sparse solutions by minimizing both the misfit between the modeled and the observed data, and the l1-norm of the solution. VFSA is an stochastic computational algorithm to finding near-optimal solutions to hard optimization problems. At the first stage, FISTA sparse-solutions provide an estimate of the location in time of the main reflectors, information that is subsequently used as an initial guess for the second stage, where accurate reflectivity amplitudes are estimated by solving a more stable overdetermined inverse problem. The second stage also involves the use of VFSA for tuning the location in time of the main reflectors and the source wavelet. FISTA does not require the inversion of matrices in explicit form. At each iteration only matrix-vector multiplications are involved, making it easy to apply, economic in computational terms, and adequate for solving large-scale problems. As a result, the FISTA+VFSA strategy represents a simple and cost-effective new procedure to solve the high-resolution AVA inversion problem. Results on synthetic data show that the proposed hybrid method can obtain high-resolution AVA attributes from noisy observations, even when the number of reflectors is not known a priori and the utilized wavelet is inaccurate, making it an interesting alternative to conventional methods.Facultad de Ciencias Astronómicas y Geofísica

Numerical analysis of wave-induced fluid flow effects on seismic data: Application to monitoring of CO2 storage at the Sleipner field

In this work we analyze how patchy distributions of CO2 and brine within sand reservoirs may lead to significant attenuation and velocity dispersion effects, which in turn may have a profound impact on surface seismic data. The ultimate goal of this paper is to contribute to the understanding of these processes within the framework of the seismic monitoring of CO2 sequestration, a key strategy to mitigate global warming. We first carry out a Monte Carlo analysis to study the statistical behavior of attenuation and velocity dispersion of compressional waves traveling through rocks with properties similar to those at the Utsira Sand, Sleipner field, containing quasi-fractal patchy distributions of CO2 and brine. These results show that the mean patch size and CO2 saturation play key roles in the observed wave-induced fluid flow effects. The latter can be remarkably important when CO2 concentrations are low and mean patch sizes are relatively large. To analyze these effects on the corresponding surface seismic data, we perform numerical simulations of wave propagation considering reservoir models and CO2 accumulation patterns similar to the CO2 injection site in the Sleipner field. These numerical experiments suggest that wave-induced fluid flow effects may produce changes in the reservoir's seismic response, modifying significantly the main seismic attributes usually employed in the characterization of these environments. Consequently, the determination of the nature of the fluid distributions as well as the proper modeling of the seismic data constitute important aspects that should not be ignored in the seismic monitoring of CO2 sequestration problems.Facultad de Ciencias Astronómicas y Geofísica

A hybrid strategy based on fast iterative shrinkage-thresholding algorithm and very fast simulated annealing: application to the prestack seismic inverse problem

With the purpose of characterizing the Earth subsurface, one of the objectives of the inversion of prestack seismic data is to determine contrasts between rock properties from the information contained in the variation of the amplitudes of the reflected compressional waves with the angle of incidence. This amplitude-versus-angle (AVA) variation can be described by various approximations to the so-called Zoeppritz equations, a set of non-linear equations that depend on the physical characteristics of the medium at each side of the interface where the compressional wave strikes. The coefficients of such approximations constitute AVA attributes that may provide important information about fluid content, a key issue for the characterization of hydrocarbon reservoirs. In this work we present a new inversion strategy to estimate efficiently and accurately high-resolution AVA attributes from prestack data. The proposed technique promotes sparse-spike reflectivities that, when convolved with the source wavelet, fit the observed data. Sparse solutions are desirable because they can be used to characterize significant and close reflectors more accurately than using conventional solutions. The inversion is carried out using a hybrid two-step strategy than combines Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and Very Fast Simulated Annealing (VFSA). FISTA provides sparse solutions by minimizing both the misfit between the modeled and the observed data, and the l1-norm of the solution. VFSA is an stochastic computational algorithm to finding near-optimal solutions to hard optimization problems. At the first stage, FISTA sparse-solutions provide an estimate of the location in time of the main reflectors, information that is subsequently used as an initial guess for the second stage, where accurate reflectivity amplitudes are estimated by solving a more stable overdetermined inverse problem. The second stage also involves the use of VFSA for tuning the location in time of the main reflectors and the source wavelet. FISTA does not require the inversion of matrices in explicit form. At each iteration only matrix-vector multiplications are involved, making it easy to apply, economic in computational terms, and adequate for solving large-scale problems. As a result, the FISTA+VFSA strategy represents a simple and cost-effective new procedure to solve the high-resolution AVA inversion problem. Results on synthetic data show that the proposed hybrid method can obtain high-resolution AVA attributes from noisy observations, even when the number of reflectors is not known a priori and the utilized wavelet is inaccurate, making it an interesting alternative to conventional methods.Facultad de Ciencias Astronómicas y Geofísica

High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy

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 l1-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 l1-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.Facultad de Ciencias Astronómicas y Geofísica

Fast and automatic microseismic phase-arrival detection and denoising by pattern recognition and reduced-rank filtering

We have developed a fast method that allowed us to automatically detect and denoise microseismic phase arrivals from 3C multichannel data. The method is a two-step process. First, the detection is carried out by means of a pattern recognition strategy that seeks plausible hyperbolic phase arrivals immersed in noisy 3C multichannel data. Then, the microseismic phase arrivals are denoised and reconstructed using a reduced-rank approximation of the singular value decomposition of the data along the detected phase arrivals in the context of a deflation procedure that took into account multiple arrivals and/or phases. For the detection, we have defined an objective function that measured the energy and coherence of a potential microseismic phase arrival along an apex-shifted hyperbolic search window. The objective function, which was maximized using very fast simulated annealing, was based on the energy of the average signal and depended on the source position, receivers geometry, and velocity. In practice, the detection process did not require any a priori velocity model, leading to a fast algorithm that can be used in real time, even when the underlying velocity model was not constant. The reduced-rank filtering coupled with a crosscorrelation-based synchronization strategy allowed us to extract the most representative waveform for all the individual traces. Tests using synthetic and field data have determined the reliability and effectiveness of the proposed method for the accurate detection and denoising of 3C multichannel microseismic events under noisy conditions. Two confidence indicators to assess the presence of an actual phase arrival and the reliability of the denoised individual wave arrivals were also developed.Facultad de Ciencias Astronómicas y Geofísica

Fast and automatic microseismic phase-arrival detection and denoising by pattern recognition and reduced-rank filtering

We have developed a fast method that allowed us to automatically detect and denoise microseismic phase arrivals from 3C multichannel data. The method is a two-step process. First, the detection is carried out by means of a pattern recognition strategy that seeks plausible hyperbolic phase arrivals immersed in noisy 3C multichannel data. Then, the microseismic phase arrivals are denoised and reconstructed using a reduced-rank approximation of the singular value decomposition of the data along the detected phase arrivals in the context of a deflation procedure that took into account multiple arrivals and/or phases. For the detection, we have defined an objective function that measured the energy and coherence of a potential microseismic phase arrival along an apex-shifted hyperbolic search window. The objective function, which was maximized using very fast simulated annealing, was based on the energy of the average signal and depended on the source position, receivers geometry, and velocity. In practice, the detection process did not require any a priori velocity model, leading to a fast algorithm that can be used in real time, even when the underlying velocity model was not constant. The reduced-rank filtering coupled with a crosscorrelation-based synchronization strategy allowed us to extract the most representative waveform for all the individual traces. Tests using synthetic and field data have determined the reliability and effectiveness of the proposed method for the accurate detection and denoising of 3C multichannel microseismic events under noisy conditions. Two confidence indicators to assess the presence of an actual phase arrival and the reliability of the denoised individual wave arrivals were also developed.Facultad de Ciencias Astronómicas y Geofísica

Establishing a sub-sampling plan for waste-derived solid recovered fuels (SRF): Effects of shredding on representative sample preparation based on theory of sampling (ToS)

The uncertainty arising from laboratory sampling (sub-sampling) can compromise the accuracy of analytical results in highly inherent heterogeneous materials, such as solid waste. Here, we aim at advancing our fundamental understanding on the possibility for relatively unbiased, yet affordable and practicable sub-sampling, benefiting from state of the art equipment, theoretical calculations by the theory of sampling (ToS) and implementation of best sub-sampling practices. Solid recovered fuel (SRF) was selected as a case of a solid waste sample with intermediate heterogeneity and chlorine (Cl) as an analyte with intermediate variability amongst waste properties. ToS nomographs were constructed for different sample preparation scenarios presenting the trend of uncertainty during sub-sampling. Nomographs showed that primary shredding (final d90 ≤ 0.4 cm) can reduce the uncertainty 11 times compared to an unshredded final sub-sample (d ≈ 3 cm), whereas cryogenic shredding in the final sub-sample can decrease the uncertainty more than three times compared to primary shredding (final d90 ≤ 0.015 cm). Practices that can introduce bias during sub-sampling, such as mass loss, moisture loss and insufficient Cl recovery were negligible. Experimental results indicated a substantial possibility to obtain a representative final sub-sample (uncertainty ≤ 15%) with the established sub-sampling plan (57–93%, with 95% confidence), although this possibility can be considerably improved by drawing two final sub-samples instead (91–98%, with 95% confidence). The applicability of ToS formula in waste-derived materials has to be investigated: theoretical ToS calculations assume a poorer performance of the sub-sampling plan than evidenced by the experimental results

Estudio comparativo de dos normas de simplicidad para la deconvolución sísmica

Se estudian comparativamente dos criterios de deconvoluclón de trazas sísmicas, a loe que se designarán MED (Deconvoluclón por mínima entropía) y MEDLN (versión logarítmica del MED). Ambos criterios pertenecen a una familia de normas descrlptas en el presente trabajo. Dichas normas se maximlzan cuando son evaluadas sobre una serie de Impulsos aislados, por lo que su maximlzaclón conduce a un operador lineal capaz de realizar la deconvoluclón. Complementando las consideraciones teóricas ss presentan ejemplos sintéticos con diferentes niveles de ruido.This paper concerns with the comparative study of two deconvolution criteria, named MED (Minlmun Entropy Deconvolution) and MEDLN. Both procedures are members of a family of norms described in this paper. When these norms are evaluatsd over a sparse spike series their maximum value is reached. Thus a linear operator capable of carrying out the deconvolution is obtained. Not only considerations about the theoretical approach are studied, but also many synthetic examples displaying different levels of nolee.Asociación Argentina de Geofísicos y Geodesta

Numerical analysis of wave-induced fluid flow effects on seismic data: Application to monitoring of CO2 storage at the Sleipner field

In this work we analyze how patchy distributions of CO2 and brine within sand reservoirs may lead to significant attenuation and velocity dispersion effects, which in turn may have a profound impact on surface seismic data. The ultimate goal of this paper is to contribute to the understanding of these processes within the framework of the seismic monitoring of CO2 sequestration, a key strategy to mitigate global warming. We first carry out a Monte Carlo analysis to study the statistical behavior of attenuation and velocity dispersion of compressional waves traveling through rocks with properties similar to those at the Utsira Sand, Sleipner field, containing quasi-fractal patchy distributions of CO2 and brine. These results show that the mean patch size and CO2 saturation play key roles in the observed wave-induced fluid flow effects. The latter can be remarkably important when CO2 concentrations are low and mean patch sizes are relatively large. To analyze these effects on the corresponding surface seismic data, we perform numerical simulations of wave propagation considering reservoir models and CO2 accumulation patterns similar to the CO2 injection site in the Sleipner field. These numerical experiments suggest that wave-induced fluid flow effects may produce changes in the reservoir's seismic response, modifying significantly the main seismic attributes usually employed in the characterization of these environments. Consequently, the determination of the nature of the fluid distributions as well as the proper modeling of the seismic data constitute important aspects that should not be ignored in the seismic monitoring of CO2 sequestration problems.Facultad de Ciencias Astronómicas y Geofísica