Intelligent sequence stratigraphy through a wavelet-based decomposition of well log data

Identification of sequence boundaries is an important task in geological characterization of gas reservoirs. In this study, a continuous wavelet transform (CWT) approach is applied to decompose gamma ray and porosity logs into a set of wavelet coefficients at varying scales. A discrete wavelet transform (DWT) is utilized to decompose well logs into smaller frequency bandwidths called Approximations (A) and Details (D). The methodology is illustrated by using a case study from the Ilam and upper Sarvak formations in the Dezful embayment, southwestern Iran. Different graphical visualization techniques of the continuous wavelet transform results allowed a better understanding of the main sequence boundaries. Using the DWT, maximum flooding surface was successfully recognised from both highest frequency and low frequency contents of signals. There is a sharp peak in all A&D corresponding to the maximum flooding surface (MFS), which can specifically be seen in fifth Approximation (a5), fifth Detail (d5), fourth Detail (d4) and third Detail (d3) coefficients. Sequence boundaries were best recognised from the low frequency contents of signals, especially the fifth Approximation (a5). Normally, the troughs of the fifth Approximation correspond to sequence boundaries where higher porosities developed in the Ilam and upper Sarvak carbonate rocks. Through hybridizing both CWT and DWT coefficient a more effective discrimination of sequence boundaries was achieved. The results of this study show that wavelet transform is a successful, fast and easy approach for identification of the main sequence boundaries from well log data. There is a good agreement between core derived system tracts and those derived from decomposition of well logs by using the wavelet transform approach

Well Log Segmentation in Spectral Domain

Classic well log interpretation involves direct horizon mapping using log signature, attributes cross plot, etc to produce lithologic section for the delineation, exploration and production of hydrocarbon in oil and gas fields. The methods operate on recorded lithologic logs without adequate calibration. These result in interpretational ambiguities because of relatively poor resolution of well log owing to its recording in time, under sampling and coarse processing. In this paper, a new technique and algorithm for segmenting well log using discrete Fourier transform in the interpretation of well data obtained from the Niger Delta is presented. The aims and objectives of the study are to segment well logs into their constituent lithology in time domain, transform the well data from time to frequency domain and segment, and deduce viable diagnostic attributes such as magnitude, phase and frequency from the transform coefficients which could be used to identify the most probable zonation/contact in the well. The algorithm adopts Short time Fourier transform technique in the time to frequency transformation and is implementable on both standard and general seismic and well log interpretational platforms. It directly computes the spectral equivalent of the adopted lithologic log (Gamma-ray) and recovers hitherto lost frequency information. The results of the spectral decomposition of the well data yielded frequency (pseudo) logs that reveal subtle sub-well horizons and differences in lithology. By revealing masked horizons and better delineating and delimiting reservoirs, more hydrocarbons will be recovered and field development will be enhanced. Keywords: Fourier transform, Spectral decompositio

Geological stratigraphy and spatial distribution of microfractures over the Costa Rica convergent margin, Central America – a wavelet-fractal analysis

Identification of spatial distribution of lithology as a function of position and scale is a very critical job for lithology modelling in industry. Wavelet transform (WT) is an efficacious and powerful mathematical tool for time (position) and frequency (scale) localization. It has numerous advantages over Fourier transform (FT) to obtain frequency and time information of a signal. Initially continuous wavelet transform (CWT) was applied on gamma ray logs for identification of lithofacies distribution, and later discrete wavelet transform (DWT) was applied on density logs to identify the fracture zones. In this study the data were taken from two different well sites (well 1039 and well 1043) of the Costa Rica convergent margin, Central America. The CWT analysis provides four major sedimentary layers terminated with a concordant igneous intrusion passing through both the wells. In addition, the wavelet-based fractal analysis (WBFA) technique was applied on identified sedimentary successions, and fractal-dimension (FD) values were calculated for every succession to know the presence and distribution of fractures. We found that the second and third successions have a high FD value, whereas the first and fourth successions have a low FD value. These high values may be due to the presence of abundant shale content and low-energy environments in the sedimentary successions

Elastic and shear moduli of coal measure rocks derived from basic well logs using fractal statistics and radial basis functions

Gamma ray, density, sonic and core logs obtained from two boreholes drilled over a longwall panel in Southwestern (SW) Pennsylvania were analyzed for formation boundaries, log-derived porosities and densities and for rock elastic properties from sonic transit times. Gamma ray (GR) and density logs (DL) were analyzed using univariate statistical techniques and fractal statistics for similarity and ordering of the log data in depth. A Fourier transformation with low-pass filter was used as a noise elimination (filtering) technique from the original logs. Filtered data was tested using basic univariate and fractal statistics, rescaled range (R/S) and power spectrum (PS) analysis to compare the information characteristics of the filtered logs with the original data. The randomness of log data in depth was analyzed for fractional Gaussian noise (fGn) or fractional Brownian motion (fBm) character. A new prediction technique using radial basis function (RBF) networks was developed to calculate shear and Young\ue2\u20ac\u2122s moduli of the formations when sonic logs are not available. For this approach, the filtered logs were used as input to an RBF based upon a combination of supervised and unsupervised learning. The network was trained and tested using rock elastic properties calculated from the sonic log of one of the boreholes. The network was used to predict the elastic and shear moduli of the coal-measure rocks over a longwall coal mine in SW Pennsylvania. This approach demonstrated that it could be used for prediction of elastic and shear moduli of coal-measure rocks with reasonable accuracy

SEISMIC DATA MULTI-SPECTRAL ANALYSIS, ATTENUATION ESTIMATION AND SEISMIC SEQUENCE STRATIGRAPHY ENHANCEMENT APPLIED TO CONVENTIONAL AND UNCONVENTIONAL RESERVOIRS

Seismic data are an essential resource for interpretation, providing abundant information about geological structures, sedimentation, stratigraphy and reservoir quality. Geophysicists have dedicated tremendous efforts in fully utilizing the information content in seismic data. Time series analysis and frequency (spectral) analysis are the two most common tools used to characterize seismic data. Multi-spectral analysis highlights geological features at different scales. The spectral sensitivity is not only from the tuning effects, but also from the geological structures and rock properties, including attenuation. To analyze the additional information in the spectral components rather than in the broad-band data, I begin by examining the spectrally limited coherence responses of multiple stages of incised valleys of Red Fork formation, Anadarko Basin, Oklahoma. Later, I combine covariance matrices for each spectral component, add them together, and compute multi-spectral coherence images. Spectral ratio and frequency shift methods are traditional attenuation estimation methods. However, the assumptions of each method introduce errors and instabilities into the results. I propose a modified frequency shift method to estimate attenuation (the reciprocal of the quality factor, Q), that relaxes some of these assumptions. Synthetic and field applications show robust and accurate results. Thin-bed layering also modifies the spectra, causing simple attenuation estimation to be inaccurate. To address this limitation, I use well logs based impedance inversion results to calculate a spectral correction for elastic variability in the spectra prior to estimating the inelastic attenuation contribution. The spectral correction can be viewed as a pre-conditioning step, following which both spectral ratio and frequency shift methods can produce better results. xix Traditional attenuation estimation methods work well in high porosity and high permeability gas sands. However, the well accepted squirt model does not apply to low permeability shale reservoirs. Rather, micro-cracks generate strong geometric or scattering attenuation, which combined with the intrinsic attenuation produced by TOC (total organic carbon) result in complicated spectral responses. Rather than estimating Q, I evaluate a suite of attenuation attributes. Even though the mechanism underlying may be unknown, these attenuation attributes can be statistically linked to the production and geology. Using the classic Fourier transform, the available spectral band often falls between 10 and 80 Hz. Nevertheless, interpreters observe lower frequency patterns in the data, for example, a 200 ms thick (5 Hz) pattern of low reflectivity sandstone and a 400 ms thick (2.5 Hz) pattern of high reflectivity responses (e.g. sabkhas or cyclothems). I introduce an adaptive intrinsic mode decomposition method called variational mode decomposition to analyze the “rhythm” in the seismic data. The intrinsic modes are defined as combinations of AM modulated signals, which are analyzed in the frequency domain with carrier frequencies (that fall within the 10-80 Hz limit), to characterize the buried stratigraphy information seen in the longer wavelength patterns. Because intrinsic modes are able to model seismic signals, but unable to model the noise component, the random noise lies within the residual of the intrinsic mode decomposition. Unlike filtering methods with predefined parameters, I develop a fully data-driven denoising method to suppress random noise, thereby enhancing the data quality

Electromagnetic reflections inside ice sheets

When radio echo sounding polar ice sheets weak stratified reflections are visible deep inside the ice sheets. These reflections are often called internal layers. Previously it has been suggested as a result of glacier flow models that these reflections can be treated as surfaces of equal age. In order for a reflection to be related to a single age feature in an ice sheet a one dimensional wave model must be adequate to model the propagation of a wavelet down to the feature and back to the surface. In this thesis four different one dimensional models are constructed each including different physics. It is shown that for the frequencies of interest to radio echo sounding it is sufficient to use the non-dispersive high frequency values of permittivity and conductivity for the ice in the models. The models are used on data from two drill sites. The first site is Berkner Island where I constructed an instrument to measure the electrical conductivity of the 181 metre long ice core. The second site is the Greenland Ice Core Project (GRIP) site at Summit of length 3028 metres. For both sites permittivity and conductivity profiles inside the ice sheet are calculated and put into the models with an estimate of the transmitted wavelet to produce expected radio echo profiles at the sites. For Berkner despite altering many parameters no match between model result and radar data was obtained. For GRIP a satisfactory match was obtained between model result and radar data. It is concluded that the weak, specular (plane like), st Ratified reflections at depth can be treated as isochrones. The strong reflections at shallow depths are a result of a combination of spherical reflection surfaces and interference between many closely spaced layers and cannot necessarily be treated as isochrones

AN INVESTIGATION OF SEISMIC ATTENUATION IN MARINE SEDIMENTS

There have been relatively few investigations into the attenuation properties of unconsolidated sediments using marine surface seismic data. Several methods of measuring attenuation were assessed for reliability in a noise-free case and with the addition of noise using a set of synthetically absorbed and dispersed wavelets. Wavelet modelling proved to be superior to the other techniques, followed by spectrum modelling and the spectral ratios method. Complex trace analysis using the analytical signal proved to be unreliable for non-sinusoidal wavelets, whilst the risetime method was found to be very susceptible to noise for practical purposes. Numerical modelling was carried out to assess the spectral effects of layering on a propagating pulse. The thin layer / peg-leg phenomenon has varying filtering effects on the propagating pulse. In particular, layers which are less than the "tuning thickness" of the propagating pulse have a low-pass effect. The quality factor, Q, was measured in two case studies. In the first, the mean Q was determined from wavelet and spectrum modelling and found to be 60 for fine sands and 47 for coarse sands in the 1 kHz to 3 kHz frequency band. In the second, Q was determined as 59 for poorly sorted sandy diamicts in the 100 Hz to 240 Hz frequency band. The close fit between synthesised spectra and wavelets and observed data showed that a constant- Q mechanism would account for the spectral changes between the seabed and the deeper target reflection events in the two case studies. The spectra of the target reflection events in both case studies were lacking in low frequencies which is likely to be due to low-pass filtering from composite reflection events due to thin bed layering. For practical purposes, the determination of Q from a mean normalised seismic trace yielded the same result as measuring a mean Q from individual traces. In a third case study, the seabed multiple was compared to the seabed reflection using wavelet and spectrum modelling. A lack of low frequencies in the seabed multiple showed that the seabed can act as a low-pass filter to an incident pulse. As the numerical methods rely on the seabed as having a white reflection and transmission response, the low-pass effect will result in erroneous estimates of the quality factor, Q

Statistical and wavelet analysis of density and magnetic susceptibility data from the Bushveld Complex, South Africa

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2015The Bushveld Complex (BC) is the largest known layered intrusion. This suite of rock crop out in northern South Africa to form the Western, Eastern and Northern Limbs. Most research carried out focuses on the mineralized horizons in the Rustenburg Layered Suite (RLS) of the BC. This study presents a large database of wireline geophysical logs across a substantive part of the stratigraphy of the RLS. These consist of density and magnetic susceptibility datasets sampled at 1 cm. The major lithologies of the RLS intersected in the boreholes presented are gabbro, gabbronorite, norite and anorthosite whose density histograms reveal that they are predominantly normally distributed, with density averages of 2.86-2.91 g/cm3. The lithologies consist of mainly two minerals, pyroxene and plagioclase. In general, the average density increases with an increase in pyroxene. The distribution of the magnetic susceptibility for these lithologies has a large variation from SI to 13.2 SI, which is typical of layered intrusions. Susceptibility distributions are also multi-modal, asymmetric and not normally distributed, which makes the average magnetic susceptibilities less representative of the lithologies. Cross-correlation plots between density and magnetic susceptibility for several boreholes show that the above-mentioned lithologies form clusters (circular to elliptical), which typically overlap. This has been further investigated using k-means classification, to automatically detect these clusters in the cross-correlation plots and to compare these with those created by lithologies. The comparison shows some degree of correlation, implying that physical properties can be used to identify lithologies. This is particularly true for the Eastern Limb. However the classification has not been effective in all of the boreholes and often becomes complicated and an inaccurate representation of lithology log. This occurs in boreholes in which there is an overlap in the physical properties of the abovementioned lithologies. Analysis on the density and magnetic susceptibility data has also been carried out using wavelet analysis at individual locations across the BC. This has revealed multi-scale cyclicity in all of the boreholes studied, which is attributed to subtle layering created by variations in modal proportions between plagioclase and pyroxene. In addition to this, since layering is generally ubiquitous across layered intrusions, this cyclicity can be assumed to be present across the entire BC. This technique may become increasingly important should the cyclicity in physical property data correlate with reversals in fractionation trends since this may suggest zones of magma addition, whose thickness or III volumes can be quantified using wavelet analysis. This could be an important contribution since the current perspective on magma addition in the RLS is that four major additions have formed this 8 km thick suite of rocks, as opposed to smaller periodic influxes of magma. Wavelet-based semblance analysis has been used to compare the wavelengths at which the cyclicity occurs across boreholes. A comparison of wavelengths of this cyclicity shows that boreholes in the northern Western Limb show positive correlation in the density data at wavelengths >160 m and 20-60 m, while those further south show correlations at wavelengths of 120-200 m and 60-80 m. Boreholes of the Eastern Limb show positive correlation in the density and magnetic susceptibility data at wavelengths of 10-20 m, 20-30 m and 5m. These positive correlations across boreholes in density and magnetic susceptibility respectively, may imply that cyclicity may be produced by a chamber-wide process for several kilometres of the BC