A Matlab code package for 2D/3D local slope estimation and structural filtering

Local slope is an important attribute that can help distinguish seismic signals from noise. Based on optimal slope estimation, many filtering methods can be designed to enhance the signal-to-noise ratio (S/N) of noisy seismic data. We present an open-source Matlab code package for local slope estimation and corresponding structural filtering. This package includes 2D and 3D examples with two main executable scripts and related sub-functions. All code files are in the Matlab format. In each main script, local slope is estimated based on the well-known plane wave destruction algorithm. Then, the seismic data are transformed to the flattened domain by utilizing this slope information. Further, the smoothing operator can be effectively applied in the flattened domain. We introduce the theory and mathematics related to these programs, and present the synthetic and field data examples to show the usefulness of this open-source package. The results of both local slope estimation and structural filtering demonstrate that this package can be conveniently and effectively applied to the seismic signal analysis and denoising.

A Novel Method for Estimating the Intrinsic Magnetic Field Spectrum of Kinetic-Range Turbulence

Understanding plasma turbulence below the ion characteristic scales is one of the key open problems of solar wind physics. The bulk of our knowledge about the nature of the kinetic-scale fluctuations comes from the high-cadence measurements of the magnetic field. The spacecraft frame frequencies of the sub-ion scale fluctuations are frequently around the Nyquist frequencies of the magnetic field sampling rate. Thus, the resulting ‘measured’ time series may significantly differ from the ‘true’ ones. It follows that second-order moments (e.g., power spectral density, PSD) of the signal may also be highly affected in both their amplitude and their slope. In this paper, we focus on the estimation of the PSD slope for finitely sampled data and we unambiguously define a so-called local slope in the framework of Continuous Wavelet Transform. Employing Monte Carlo simulations, we derive an empirical formula that assesses the statistical error of the local slope estimation. We illustrate the theoretical results by analyzing measurements of the magnetic field instrument (MFI) on board the Wind spacecraft. Our analysis shows that the trace power spectra of magnetic field measurements of MFI can be modeled as the sum of PSD of an uncorrelated noise and an intrinsic signal. We show that the local slope strongly depends on the signal-to-noise (S/N) ratio, stressing that noise can significantly affect the slope even for S/N around 10. Furthermore, we show that the local slopes below the frequency corresponding to proton inertial length, 5≳kλpi>1, depend on the level of the magnetic field fluctuations in the inertial range (Pin), exhibiting a gradual flattening from about −11/3 for high Pin toward about −8/3 for low Pin.

Pre-stack diffraction separation by parameterizing the reflection local slope

Diffracted waves provide the opportunity to detect small-scale subsurface structures because they give wide illumination direction of geological discontinuities such as faults, pinch-outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometrical amplitude losses and are generally weaker than reflections. To retain more diffracted waves, a pre-stack diffraction separation method is proposed based on the local slope pattern and plane-wave destruction method. Generally, it is difficult to distinguish between the hyperbolic reflections and hyperbolic diffractions using the data-driven local slope estimation in the shot domain. Therefore, we transfer the slope estimation in the shot domain to the velocity analysis in the common midpoint domain and the ray parameter calculation in the stack domain. The connection between the local slope and the normal move-out velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of the hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the plane-wave destruction (PWD) method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of the proposed pre-stack diffraction separation method.

Non-stationary local slope estimation via forward-backward space derivative calculation

The local slope estimated from seismic images has a variety of meaningful applications. Slope estimation based on the plane-wave destruction (PWD) method is one of the widely accepted techniques in the seismic community. However, the PWD method suffers from its sensitivity to noise in the seismic data. We propose an improved slope estimation method based on the PWD theory that is more robust in the presence of strong random noise. The PWD operator derived in the Z-transform domain contains a phase-shift operator in space corresponding to the calculation of the first-order derivative of the wavefield in the space domain. The first-order derivative is discretized based on a forward finite difference in the traditional PWD method, which lacks the constraint from the backward direction. We propose an improved method by discretizing the first-order space derivative based on an averaged forward-backward finite-difference calculation. The forward-backward space derivative calculation makes the space-domain first-order derivative more accurate and better anti-noise since it takes more space grids for the derivative calculation. In addition, we introduce non-stationary smoothing to regularize the slope estimation and to make it even more robust to noise. We demonstrate the performance of the new slope estimation method by several synthetic and field data examples in different applications, including 2D/3D structural filtering, structure-oriented deblending, and horizon tracking.

A deep learning network for estimation of seismic local slopes

The local slopes contain rich information of the reflection geometry, which can be used to facilitate many subsequent procedures such as seismic velocities picking, normal move out correction, time-domain imaging and structural interpretation. Generally the slope estimation is achieved by manually picking or scanning the seismic profile along various slopes. We present here a deep learning-based technique to automatically estimate the local slope map from the seismic data. In the presented technique, three convolution layers are used to extract structural features in a local window and three fully connected layers serve as a classifier to predict the slope of the central point of the local window based on the extracted features. The deep learning network is trained using only synthetic seismic data, it can however accurately estimate local slopes within real seismic data. We examine its feasibility using simulated and real-seismic data. The estimated local slope maps demonstrate the successful performance of the synthetically-trained network.

Estimating local slope in the time-frequency domain: Velocity-independent seismic imaging in the near surface

Seismic reflection processing for multicomponent data is very time consuming. To automatically streamline and shorten this process, a new approach for estimating the local event slope (local static shift) in the time-frequency domain is proposed and tested. The seismic event slope is determined by comparing the local phase content of Stockwell transformed signals. This calculation allows for noninterfering arrivals to be aligned by iteratively correcting trace by trace. Alternatively, the calculation can be used in a velocity-independent imaging framework with the possibility of exporting the determined time and velocities for each common midpoint gather, which leads to a more robust moveout correction. Synthetic models are used to test the robustness of the calculation and compare it directly to an existing method of local slope estimation. Compared to dynamic time warping, our method is more robust to noise but less robust to large time shifts, which limits our method to shorter geophone spacing. We apply the calculation to near-surface shear-wave data and compare it directly to semblance/normal-moveout processing. Examples demonstrate that the calculation yields an accurate local slope estimate and can produce sections of better or equal quality to sections processed using the conventional approach with much less user time input. It also serves as a first example of velocity-independent processing applied to near-surface reflection data.

Oriented pre-stack inverse Q filtering for resolution enhancements of seismic data

SUMMARY Seismic attenuation is one of the main factors responsible for degradation of the resolution of seismic data. During seismic wave propagation in attenuation medium, the energy of signal components seriously decreases, especially those with higher frequencies. The seismic attenuation and resolution reduction are generally compensated for with inverse Q filtering in the frequency or time domain. However, the implementation of pre-stack inverse Q filtering is challenging because the traveltime in each layer is not easy to obtain for the pre-stack seismic gather, unless the accurate velocity model is known. In this study, we propose an inverse Q filtering method for the pre-stack seismic gather that uses the local slope and warped mapping to determine the propagation path, and Taylor-expansion-based division is used to stabilize the inversion. The local slope can determine the reflection events with the same ray path, and the inverse warped mapping can transform the attenuation factor from the ${t_0} - p$ (zero-offset traveltime to ray parameter) domain to the $t - x$ (traveltime and offset) domain. The attenuation factor in the ${t_0} - p$ domain is easy to calculate because the traveltimes and Q values in each layer are known. The proposed oriented pre-stack inverse Q filtering method is velocity-independent and suitable for a depth varying Q model. The synthetic and real data examples demonstrated that the method can effectively correct the attenuation and dispersion of seismic waves, and can obtain pre-stack seismic gathers with high resolution.

Deblending of simultaneous source data using a structure-oriented space-varying median filter

SUMMARY In seismic data processing, the median filter is usually applied along the structural direction of seismic data in order to attenuate erratic or spike-like noise. The performance of a structure-oriented median filter highly depends on the accuracy of the estimated local slope from the noisy data. When local slope contains significant error, which is usually the case for noisy data, the structure-oriented median filter will still cause severe damages to useful energy. We propose a type of structure-oriented median filter that can effectively attenuate spike-like noise even when the local slope is not accurately estimated, which we call structure-oriented space-varying median filter. A structure-oriented space-varying median filter can adaptively squeeze and stretch the window length of the median filter when applied in the locally flattened dimension of an input seismic data in order to deal with the dipping events caused by inaccurate slope estimation. We show the key difference among different types of median filters in detail and demonstrate the principle of the structure-oriented space-varying median filter method. We apply the structure-oriented space-varying median filter method to remove the spike-like blending noise arising from the simultaneous source acquisition. Synthetic and real data examples show that structure-oriented space-varying median filter can significantly improve the signal preserving performance for curving events in the seismic data. The structure-oriented space-varying median filter can also be easily embedded into an iterative deblending procedure based on the shaping regularization framework and can help obtain much improved deblending performance.

Sedimentologi Batugamping Formasi Jayapura di Sepanjang Lintasan Dewarebru, Mamei-Waibron, Jayapura

The Pleistocene of the Jayapura Formation limestones well cropped out at Dewarebru Section, Mamey-Waybron, Jayapura Regency. Detailed descriptions of rock outcrops and petrography analysis of selected limestone samples is used to find out the limestone sedimentology characters. This Jayapura limestone was divided onto four limestone facies, including lithoclastic rudstone, bioclastic packstone, bioclastic grainstone and bioclastic wackesone rock facies. The rocks was deposited in a fore slope talus forming submarine alluvial fan, furthermore the rocks was deposited in a local slope on the back reef environment.Keywords: Limestone, petrography, stratigraphy, sedimentology, Jayapura