Mirko van der Baan

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization, and the automatic estimation of network size and architecture.

Seismic anisotropy in exploration and reservoir characterization: An overview

Recent advances in parameter estimation and seismic processing have allowed incorporation of anisotropic models into a wide range of seismic methods. In particular, vertical and tilted transverse isotropy are currently treated as an integral part of velocity fields employed in prestack depth migration algorithms, especially those based on the wave equation. We briefly review the state of the art in modeling, processing, and inversion of seismic data for anisotropic media. Topics include optimal parameterization, body-wave modeling methods, P-wave velocity analysis and imaging, processing in the τ-p domain, anisotropy estimation from vertical-seismic-profiling (VSP) surveys, moveout inversion of wide-azimuth data, amplitude-variation-with-offset (AVO) analysis, processing and applications of shear and mode-converted waves, and fracture characterization. When outlining future trends in anisotropy studies, we emphasize that continued progress in data-acquisition technology is likely to spur transition from t...

Time-varying wavelet estimation and deconvolution by kurtosis maximization

Phase mismatches sometimes occur between final processedsectionsandzero-phasesyntheticsbasedonwelllogs, despite best efforts for controlled-phase acquisition and processing. The latter are often based on deterministic corrections derived from field measurements and physical laws.A statisticalanalysisofthedatacanrevealwhetheratime-varying nonzero phase is present. This assumes that the data should be white with respect to all statistical orders after proper deterministic corrections have been applied. Kurtosis maximizationbyconstantphaserotationisastatisticalmethod that can reveal the phase of a seismic wavelet. It is robust enough to detect time-varying phase changes. Phase-only corrections can then be applied by means of a time-varying phase rotation.Alternatively, amplitude and phase deconvolution can be achieved using time-varying Wiener filtering. Time-varyingwaveletextractionanddeconvolutioncanalso be used as a data-driven alternative to amplitude-only inverse-Qdeconvolution.

The robustness of seismic attenuation measurements using fixed- and variable-window time-frequency transforms

Frequency-based methods for measuring seismic attenuation are used commonly in exploration geophysics. To measure the spectrum of a nonstationary seismic signal, different methods are available, including transforms with time windows that are either fixed or systematically varying with the frequency being analyzed. We compare four time-frequency transforms and show that the choice of a fixed- or variable-window transform affects the robustness and accuracy of the resulting attenuation measurements. For fixed-window transforms, we use the short-time Fourier transform and Gabor transform. The S-transform and continuous wavelet transform are analyzed as the variable-length transforms. First we conduct a synthetic transmission experiment, and compare the frequency-dependent scattering attenuation to the theoretically predicted values. From this procedure, we find that variable-window transforms reduce the uncertainty and biasof the resulting attenuation estimate, specifically at the upper and lower ends of th...

Hydraulic Fracturing and Seismicity in the Western Canada Sedimentary Basin

The development of most unconventional oil and gas resources relies upon subsurface injection of very large volumes of fluids, which can induce earthquakes by activating slip on a nearby fault. During the last 5 years, accelerated oilfield fluid injection has led to a sharp increase in the rate of earthquakes in some parts of North America. In the central United States, most induced seismicity is linked to deep disposal of coproduced wastewater from oil and gas extraction. In contrast, in western Canada most recent cases of induced seismicity are highly correlated in time and space with hydraulic fracturing, during which fluids are injected under high pressure during well completion to induce localized fracturing of rock. Furthermore, it appears that the maximum-observed magnitude of events associated with hydraulic fracturing may exceed the predictions of an often-cited relationship between the volume of injected fluid and the maximum expected magnitude. These findings have far-reaching implications for assessment of inducedseismicity hazards.

Local singular value decomposition for signal enhancement of seismic data

Singular value decompositionSVD is a coherency-based technique that provides both signal enhancement and noise suppression. It has been implemented in a variety of seismic applications — mostly on a global scale. In this paper, we use SVD to improve the signal-to-noise ratio of unstacked and stacked seismic sections, but apply it locally to cope with coherent events that vary with both time and offset. The local SVD technique is compared with f-x deconvolution and median filtering on a set of synthetic and real-data sections. Local SVD is better than f-x deconvolution and median filtering in removing background noise, but it performs less well in enhancing weak events or events with conflicting dips. Combining f-x deconvolution or median filtering with local SVD overcomes the main weaknesses associated with each individual method and leads to the best results.

Spectral estimation—What is new? What is next?

Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

Estimating anisotropy parameters and traveltimes in the τ-p domain

The presence of anisotropy influences many aspects of seismic wave propagation and has therefore implications for conventional processing schemes. To estimate the anisotropy, we need both forward modelling and inversion tools. Exact forward modelling in anisotropic media is generally done by raytracing. However, we present a new and fast method, using the τ‐p transform, to calculate exact P and SV reflection moveout curves in stratified, laterally homogeneous, anisotropic media which requires no ray tracing. Results are exact even if the SV‐waves display cusps. In addition, we show how the same method can be used for parameter estimation.Since inversion for anisotropic parameters is very nonunique, we develop expressions requiring only a reduced number of parameters. Nevertheless, predictions using these expressions are more accurate than Taylor series expansions and are also able to handle cusps in the SV traveltime curves. In addition, layer stripping is a linear process. Therefore, both effective (aver...

Robust wavelet estimation and blind deconvolution of noisy surface seismics

Robust blind deconvolution is a challenging problem, particularly if the bandwidth of the seismic wavelet is narrow to very narrow; that is, if the wavelet bandwidth is similar to its principal frequency. The main problem is to estimate the phase of the wavelet with sufficient accuracy. The mutual information rate is a general-purpose criterion to measure whiteness using statistics of all orders. We modified this criterion to measure robustly the amplitude and phase spectrum of the wavelet in the presence of noise. No minimum phase assumptions were made. After wavelet estimation, we obtained an optimal deconvolution output using Wiener filtering. The new procedure performs well, even for very band-limited data; and it produces frequency-dependent phase estimates.

Microseismic Monitoring Developments in Hydraulic Fracture Stimulation

The last decade has seen a significantly increased interest in microseismic monitoring by the hydrocarbon industry due to the recent surge in unconventional resources such as shale-gas and heavy-oil plays. Both hydraulic fracturing and steam injection create changes in local pore pressures and in situ stresses and thereby brittle failure in intact rock plus additional slip/shearing in naturally fractured rock. Local rock failure or slip yields an acoustic emis‐ sion, which is also known as a microseismic event. The microseismic cloud represents thus a volumetric map of the extent of induced fracture shearing, opening and closing. Microseis‐ mic monitoring can provide pertinent information on in situ reservoir deformation due to fluid stimulation, thus ultimately facilitating reservoir drainage. This paper reviews some of the current key questions and research in microseismicity, ranging from acquisition, proc‐ essing to interpretation.