Satish Sinha

Spectral decomposition of seismic data with continuous-wavelet transform

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the timefrequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

Instantaneous spectral attributes using scales in continuous-wavelet transform

Instantaneous spectral properties of seismic data — center frequency, root-mean-square frequency, bandwidth — often are extracted from time-frequency spectra to describe frequency-dependent rock properties. These attributes are derived using definitions from probability theory. A time-frequency spectrum can be obtained from approaches such as short-time Fourier transform (STFT) or time-frequency continuous-wavelet transform (TFCWT). TFCWT does not require preselecting a time window, which is essential in STFT. The TFCWT method converts a scalogram (i.e., time-scale map) obtained from the continuous-wavelet transform (CWT) into a time-frequency map. However, our method includes mathematical formulas that compute the instantaneous spectral attributes from the scalogram (similar to those computed from the TFCWT), avoiding conversion into a time-frequency spectrum. Computation does not require a predefined window length because it is based on the CWT. This technique optimally decomposes a multiscale signal. F...

Time‐frequency attribute of seismic data using continuous wavelet transform

A time-frequency decomposition that can provide higher frequency resolution at lower frequencies and higher time resolution at higher frequencies is desirable for analyzing seismic data. This is because the hydrocarbons in the reservoir are diagnostic at lower frequencies and thin beds can be resolved with enhanced time resolution at higher frequencies. In this paper we present a new method to compute the time-frequency spectrum using wavelet as a window that achieves this objective. Time-frequency spectrum is commonly used to compute various frequency attributes of seismic signal like single frequency, dominant frequency, center frequency and so forth. The conventional approach is to use short time Fourier transform (STFT) to obtain a time-frequency spectrum. Time-frequency resolution in the STFT is limited by the choice of a window length. The proposed time-frequency spectrum using CWT (TFCWT) in this work has the ability to adapt with the frequency content of the signal. The flexibility of not having to choose a window is an advantage of our method. We present two applications of TFCWT to real data sets in this paper. In the first example, we use TFCWT to enhance low frequency shadows caused by hydrocarbon reservoirs. In the second example, we apply the time frequency spectrum in interpreting time slices from a 3D seismic volume in frequency space to identify thin beds below tuning thickness.

Markov random field-based method for super-resolution mapping of forest encroachment from remotely sensed ASTER image

Forest encroachment (FE) is a problem in Andaman and Nicobar Islands (ANI) in India for environment and planning. Small gaps created in the forest slowly expand its periphery disturbing the biodiversity. Therefore, intrusion of poachers, slash and burn and other factors causing FE must be carefully detected and monitored. Remote sensing offers a great opportunity to accomplish this task because of its synoptic view. Conventional classification methods with remotely sensed images are problematic because of small size of FE and mixed landcover composition. This study presents an application of super-resolution mapping (SRM) based on Markov random field for detection of FE using ASTER (15 m) images. The SRM results were validated using multispectral IRS LISS-IV (5.8 m) image. Non-contiguous FE patches of various sizes and shapes are characterized using the spatial contextual information. The novelty of this approach lies in the identification and separability of small FE pockets which could not be achieved with pixel-based maximum likelihood classifier (MLC). The SRM parameters were optimized and found comparable to previous studies. Classification accuracy obtained with SRM at scale factor 3 is κ = 0.62 that is superior to accuracy of MLC (κ = 0.51). SRM is a promising tool for detection and monitoring of FE at Rutland Island in ANI, India.

Scale Attributes From Continuous Wavelet Transform

Average instantaneous attributes of time-frequency decompositions are useful in revealing the time varying spectral properties of seismic data. In the continuous wavelet transform (CWT), a time signal is decomposed into a time-scale spectrum or a scalogram; unlike a timefrequency spectrum or a spectrogram from the short time Fourier transform (STFT). Although there are various approaches of converting a time-scale spectrum into a timefrequency spectrum we introduce new mathematical formulas to calculate spectral attributes from the scalogram. In this process, we bypass the conversion of a scalogram into a time-frequency spectrum and provide average spectral attributes based on scale. The attributes are: center frequency, dominant frequency, and spectral bandwidth. Since these attributes are based on the CWT, computation of these attributes avoids subjective choice of a window length.

Forest encroachment mapping in Baratang Island, India, using maximum likelihood and support vector machine classifiers

Abstract. Maximum likelihood classifier (MLC) and support vector machines (SVMs) are commonly used supervised classification methods in remote sensing applications. MLC is a parametric method, whereas SVM is a nonparametric method. In an environmental application, a hybrid scheme is designed to identify forest encroachment (FE) pockets by classifying medium-resolution remote sensing images with SVM, incorporating knowledge-base and GPS readings in the geographical information system. The classification scheme has enabled us to identify small scattered noncontiguous FE pockets supported by ground truthing. On Baratang Island, the detected FE area from the classified thematic map for the year 2003 was ∼202  ha, and for the year 2013, the encroachment was ∼206  ha. While some of the older FE pockets were vacated, new FE pockets appeared in the area. Furthermore, comparisons of different classification results in terms of Z-statistics indicate that linear SVM is superior to MLC, whereas linear and nonlinear SVM are not significantly different. Accuracy assessment shows that SVM-based classification results have higher accuracy than MLC-based results. Statistical accuracy in terms of kappa values achieved for the linear SVM-classified thematic maps for the years 2003 and 2013 is 0.98 and 1.0, respectively.

P-wave And Converted-waves Anisotropy Due to Multiple Fracture Sets

P and S waves velocity characteristics of hydrocarbon reservoirs are altered by hydraulically induced fractures. In the case where a reservoir is fractured at various stages, a complex fracture network is formed within the reservoir. In this abstract, the reflectivity method is used to compute reflection coefficients for PP, PS1 and PS2 waves at an interface of two initially VTI (vertically transverse isotropic) half-spaces (shales) and four vertical fracture sets are introduced in the lower half space at 0, 30, 60 and 90 degrees successively. Schoenberg and Sayers’ method is utilized to calculate the effective elastic constants of the fractured medium. Two shear waves in general anisotropic media are tracked based on the continuity of their polarization vectors instead of their velocities. This technique is important while tracing the continuity of reflection coefficients in the critical and supercritical zones. Fracture modeling suggests that velocity anisotropy in conjunction with AVAZ (Amplitude variation with Angle and Azimuth) response should be utilized to understand fractured media. It is observed that as the number of fracture sets increases, critical angle moves towards higher angle.

Acoustic reflections in the water column of Krishna-Godavari offshore basin, Bay of Bengal

Seismic oceanographic studies from various oceans worldwide have indicated that the acoustic reflections are mostly observed along thermal boundaries within the water column. However, the authors present a case study of seismic data from Krishna-Godavari Basin which shows that salinity variations also play an important role in the occurrence of water column reflections. The observed reflection is modeled using the reflectivity series derived from the salinity and temperature profiles from a nearby Conductivity-Temperature-Depth (CTD) location. Sensitivity analysis of temperature and salinity on soundspeed shows that the effect of salinity cannot be ignored for modeling acoustic reflections. The synthetic seismogram matches well with the observed reflection seismic data. Remarkable similarities between the reflection seismic and the salinity profile in the upper thermocline suggest the importance of salinity variations on the water column reflection. Furthermore, impedance inversion of the reflectivity data reveals several thermohaline structures in the water column. The origin of these thermohaline structures is largely unaddressed and may be attributed to the fresh water influx coming from Himalayan and Peninsular rivers or due to the presence of different water masses in the Indian Ocean which warrants a detailed study using concurrent seismic and CTD data.

Predicting S-Wave Anisotropy from P-Wave Anisotropy

Summary The developed method in this paper uses P-wave phase velocity to calculate the 21 independent elastic constants that define a general anisotropic medium. In this method we seek a solution close to a reference body and compute the deviation from the reference. Having calculated the elastic constants, we predict S-wave anisotropy. Forward modeling promises good results and we attribute this performance on the number of velocity measurements and the choice of a reference body. We inverted P-wave velocity measurements of the mantle rocks for stiffnesses in the frame work of a vertical transversely isotropic (VTI) medium and found these stiffnesses to be in good agreement with the published data based on mineralogy. We implemented this idea on 3D reflection seismic data that was processed for P-wave anisotropy. The predicted Swave anisotropy follows the P-wave anisotropy.

AVO Amplitude Calibration Without Well Control

When well-defined petrophysical relationships between compressional and shear-wave velocities and density exist for layers within a reference window above a target of interest, it is often possible to calibrate target amplitude variation with offset (AVO) in such a way that meaningful inversions for petrophysical parameters at the target level can then be obtained. We have developed an amplitude calibration algorithm that utilizes (1) inverted compressional wave impedance profiles from zero-offset sections, (2) corresponding pre-stack seismic models to predict the “correct” reference AVO response, (3) measurement of amplitude-versus-offset for selected reference events or time windows on the synthetic and real data, and (4) correction of the real gather by application of the resulting offset-dependent scalar. Tests on synthetic and real data show that the method can be effective when the underlying assumptions are valid.