Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency-time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time-frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale-translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive-source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet-based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.

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Frequency‐time decomposition of seismic data using wavelet‐based methods

Seismic bright spots are commonly interpreted to mark fluid concentrations, but their nature (melt or aqueous) is usually inferred only from circumstantial evidence of the geologic setting. A band of bright spot reflections has been imaged by Project INDEPTH (International Deep Profiling of Tibet and the Himalayas) at about 15 km depth along 150 km of the northern Yadong-Gulu rift, southern Tibet. We use INDEPTH three-component wide-angle seismic data to measure seismic velocities at the bright spot reflector, and theoretical rock physics bounds to constrain the nature of the fluids. Merging of data from multiple bright spots allows us to use a one-dimensional approximation. Travel time modeling yields average P and S velocities for the upper crust above the bright spots of 5.3±0.2 and 3.2±0.2 km s−1, respectively. Reflection-amplitude variation with offset (AVO) modeling constrains the P and S velocities of the bright spots to 3.0±0.8 and 1.6±0.8 km s−1, respectively. Multiple modeling procedures suggest these velocities are not model dependent. Our results imply that of the order of 10% volume of free aqueous fluids in the Tibetan middle crust produces the observed bright spot reflections. The presence of relatively large quantities of free aqueous fluids, presumably mostly saline supercritical H2O, does not preclude the presence of melt but does constrain the maximum temperature at the bright spots to the wet granite solidus (about 650°C) and thus the maximum surface heat flow to ≤110 mW m−2. The observed bright spots can alternatively be explained as a result of transient flow of aqueous fluids through a lower temperature and lower heat flow southern Tibetan crust.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JB900074

Measuring the seismic properties of Tibetan bright spots: Evidence for free aqueous fluids in the Tibetan middle crust

Progress in seismic methodology and ambitious large-scale seismic projects are enabling high-resolution imaging of the continental crust. The ability to constrain interpretations of crustal seismic data is based on laboratory measurements on rock samples and calculations of seismic properties. Seismic velocity calculations and their directional dependence are based on the rock microfabric, which consists of mineral aggregate properties including crystallographic preferred orientation (CPO), grain shape and distribution, grain boundary distribution, and misorientation within grains. Single-mineral elastic constants and density are crucial for predicting seismic velocities, preferably at conditions that span the crust. However, high-temperature and high-pressure elastic constant data are not as common as those determined at standard temperature and pressure (STP; atmospheric conditions). Continental crust has a very diverse mineral composition; however, a select number of minerals appear to dominate seismic properties because of their high-volume fraction contribution. Calculations of microfabric-based seismic properties and anisotropy are performed with averaging methods that in their simplest form takes into account the CPO and modal mineral composition, and corresponding single crystal elastic constants. More complex methods can take into account other microstructural characteristics, including the grain shape and distribution of mineral grains and cracks and pores. Dynamic or active wave propagation schemes have recently been developed, which offer a complementary method to existing static averaging methods generally based on the use of the Christoffel equation. A challenge for the geophysics and rock physics communities is the separation of intrinsic factors affecting seismic anisotropy, due to properties of crystals within a rock and apparent sources due to extrinsic factors like cracks, fractures, and alteration. This is of particular importance when trying to deduce crustal composition and the state of deformation from seismic parameters.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016RG000552

Seismic properties and anisotropy of the continental crust: Predictions based on mineral texture and rock microstructure

Since their introduction in early 1970`s seismic attributes have become one of the most commonly used and powerful interpretation tools. In earlier applications they were considered as a management display tool. This view has changed rapidly as their use in interpretation expanded. Results were analyzed in a qualitative manner. Recently, as evidenced from increasing number of papers, attribute use finally became more quantitative through calibration with well bore measurements. In this paper the authors will present a review of basic attributes, their recently introduced derivatives and their expected significance. They will also classify them with respect to their computation and their end use. They define all seismically driven parameters as the Seismic Attributes. They can be velocity, amplitude, rate of change of any of them with respect to time or space and so on. They can be computed from pre-stack or post stack data sets. Some of the attributes computed from complex traces such as envelope, phase and etc. correspond to the various measurements of the propagating wave-front. They will call those the physical Attributes. These attributes may be used for prediction or extrapolation of lithological or reservoir characteristics. Others are computed from the reflection configurations and continuity. They willmore » call these Geometric Attributes. These are used in structural and stratigraphic interpretation. In this paper they will confine themselves to the classification and definition of the attributes and their possible uses. They will give examples from different geological settings.« less

Seismic Attributes Revisited

SUMMARY In this paper, attenuation values are obtained from seismic data using instantaneousfrequency matching and spectral ratios. To obtain differential t* values using instantaneous-frequency matching, a near offset reference pulse is attenuated until the resulting instantaneous frequency matches the observed value at the receiver. Prior to matching, filtering can be applied to each trace in order to reduce the effects of noise on the calculated instantaneous frequencies. In the second method, the spectral ratio between a receiver pulse and a reference pulse is used to obtain differential t* values. To obtain an unbiased estimate, a variable spectral bandwidth is used depending on the noise level of the data. The two methods are tested using synthetic traces and then applied to crustal refraction data from the 1986 PASSCAL Ouachita experiment. Results show that the differential t* values obtained using filtered, instantaneousfrequency matching are consistent with and have less scatter than those obtained from spectral ratios with a variable bandwidth.

/pdf/seismic-attenuation-values-obtained-from-instantaneous-4g42gki28r.pdf

Seismic attenuation values obtained from instantaneous‐frequency matching and spectral ratios

Robertson and Nogami (1984) have shown that the instantaneous frequency at the peak of a zero‐phase Ricker wavelet is exactly equal to that wavelet’s average Fourier spectral frequency weighted by its amplitude spectrum. Bodine (1986) gave an example which shows this is also true for constant‐phase bandpass wavelets. Here I prove that this holds for any constant‐phase wavelet. I then develop an equation expressing this quantity as a function of propagation time through an attenuating medium. A corresponding equation is derived for the amplitude of the envelope peak. Taken together, these may aid in the analysis of seismic data as suggested by Robertson and Nogami (1984), Bodine (1986), and Robertson and Fisher (1988).

Instantaneous frequency and amplitude at the envelope peak of a constant-phase wavelet

SUMMARY Two high-amplitude reflections, or ‘bright spots’, occur on COCORP (Consortium for Continental Reflection Profiling) line Georgia 16 at a record time of 5.9s, corresponding to nearly 16 km depth. They are significant because bright spots often mark great contrasts in subsurface physical properties. The first is the ‘Surrency Bright Spot’ (SBS), an exceptionally bright antiformal reflection, and the second is the ‘Reedy Creek Reflection’ (RCR), which lies 5 km to the south and resembles the south half of a diffraction. The RCR is also imaged on a crossline, Georgia 18, as a relatively symmetric antiformal reflection. These reflections coincide with the Brunswick magnetic anomaly, thought to mark the late Palaeozoic Alleghanian suture. The SBS and the RCR are reflections from bodies that lie within the plane of Georgia 16. Migration and 2-D seismic modelling show the aniformal SBS is from a synformal reflector with a buried focus while the RCR is from a relatively small body. The inferred geometry of the SBS reflector, with its flat portion corresponding to the deepest part of the reflector, argues that it does not represent fluids. These results, combined with recent evidence that the SBS is a reflection from a high-velocity thin layer, suggest that the SBS and the RCR might be reflections from ultramafic slices emplaced within the Alleghanian suture zone during collision or from mafic sheets intruded into the suture zone during subsequent rifting. The brightness of the SBS is attributed to a large impedance contrast, constructive interference, good data quality, and a relatively large reflector size with respect to the Fresnel zone and neighbouring reflectors.

/pdf/a-study-of-two-mid-crustal-bright-spots-from-southeast-84ob94lcll.pdf

Arthur E. Barnes

Papers

Instantaneous frequency and amplitude at the envelope peak of a constant-phase wavelet

A study of two mid-crustal bright spots from southeast Georgia (USA)