Embedded Wavelet

Key Takeaways

• Wavelet extraction methods for estimating the embedded wavelet from seismic data fall into two categories: statistical methods that make assumptions about the earth reflectivity (typically that it is white or random over a broad frequency band, so that the autocorrelation of the trace is dominated by the wavelet autocorrelation) and deterministic methods that use well log data to calibrate the wavelet by comparing the observed seismic trace to a synthetic seismogram computed from the well log: statistical wavelet extraction is performed by computing the autocorrelation of the seismic trace (or the power spectrum, which is the Fourier transform of the autocorrelation) and extracting the minimum-phase or zero-phase wavelet whose autocorrelation matches the trace autocorrelation; this approach is valid only if the earth reflectivity is truly white (random), which is approximately true for many geological sequences at seismic frequencies but breaks down in strongly periodic sequences (such as cyclic carbonates or evaporites) where the autocorrelation of the reflectivity has systematic peaks that add to the wavelet autocorrelation and bias the estimated wavelet; deterministic wavelet extraction computes the wavelet as the filter (cross-equalization operator) that converts the synthetic seismogram computed from the well log acoustic impedance profile into the actual seismic trace at the well location, using least-squares optimization over a time window around the reservoir of interest; the deterministic method does not require the white reflectivity assumption but is limited by the well log quality, the accuracy of the depth-to-time conversion, and the lateral variability of the wavelet between the well location and the prospect to be inverted.
• Zero-phase versus mixed-phase wavelet character of the embedded wavelet affects how the seismic trace relates to the geological reflectivity, with zero-phase wavelets providing the simplest and most intuitive relationship: a zero-phase wavelet is symmetric about its peak, meaning that the maximum amplitude of the wavelet-filtered reflectivity series occurs at the same time as the actual reflection coefficient, so that a positive reflection coefficient from a hard layer (positive acoustic impedance contrast) produces a central peak in the seismic trace that is centered at the time of the reflector; this alignment of wavelet peak with reflector time makes geological interpretation of zero-phase seismic data straightforward because the interpreter can directly relate amplitude peaks and troughs to geological boundaries; most modern seismic processing sequences attempt to convert the acquired data to zero phase as a standard processing step (using either minimum-phase to zero-phase conversion based on the measured or estimated minimum-phase source wavelet, or phase-matching using a well-log synthetic as reference), but residual phase errors of 20-30 degrees are common and can cause systematic misties (time differences between the seismic trace amplitude and the well log synthetic at the same depth) that complicate inversion and interpretation; mixed-phase embedded wavelets (which have a non-symmetric shape with both leading and trailing energy) are harder to interpret because the relation between the wavelet peak and the reflector time depends on the phase, and incorrect phase assumptions in the interpretation lead to systematic depth errors in the interpreted horizons.
• Wavelet consistency across the seismic volume is a critical quality control issue in 3D seismic data because the embedded wavelet must be spatially invariant (or at least slowly varying) for seismic inversion, amplitude interpretation, and AVO analysis to produce reliable results: the wavelet embedded in the data varies spatially because the source wavelet may change with shooting direction (azimuthal variation from directional array effects), the near-surface attenuation varies laterally (causing frequency-dependent absorption that changes the wavelet shape from one area to another), and the processing applied to correct for these effects may not perfectly remove the spatial variations; the practical test for wavelet consistency is to extract the wavelet at multiple well locations distributed across the seismic survey area and compare the extracted wavelets, with good consistency (similar amplitude spectrum, phase spectrum, and temporal shape across the wells) indicating that the processing has achieved adequate wavelet uniformity for inversion purposes, and significant variation indicating that local wavelet correction (applying spatially varying filters to match the wavelet to a target shape) is needed before inversion; the spatial variation of the wavelet is particularly important for AVO analysis, where the angle-dependent amplitude variation interpreted as hydrocarbon indicators can be corrupted by angle-dependent wavelet changes caused by near-surface effects, source directivity, or processing artifacts.
• Seismic inversion dependence on the embedded wavelet makes the wavelet estimation step the most uncertainty-prone part of the inversion workflow, because errors in the extracted wavelet propagate directly into the inverted acoustic impedance model and cannot be distinguished from geological variation in the impedance after the inversion: the sensitivity of the inversion result to wavelet errors can be tested by running the inversion with multiple wavelets (perturbing the extracted wavelet in both amplitude and phase) and comparing the resulting impedance models, with the range of outputs providing an uncertainty envelope on the inverted impedance; a well-constrained inversion with multiple control wells and a consistent wavelet extraction will have a narrow uncertainty envelope, while an inversion with a single control well and uncertain wavelet extraction may produce an impedance model that appears geologically reasonable but has sufficient wavelet-induced uncertainty to prevent reliable discrimination between porous reservoir and tight non-reservoir facies; the fundamental data quality requirement for any model-based or simultaneous seismic inversion is that the extracted wavelet reproduces the observed seismic trace when convolved with the well-derived reflectivity, verified by the synthetic-to-seismic mistie at the control wells, which should be less than 5-10 milliseconds systematic phase error and less than 10-15% amplitude error for a well-constrained inversion.
• Tuning effects from the embedded wavelet complicate the interpretation of thin reservoir zones where the wavelet length is comparable to or greater than the two-way travel time through the reservoir layer, causing the reflections from the top and base of the layer to interfere constructively or destructively depending on the layer thickness and the wavelet character: the tuning thickness (approximately a quarter wavelength of the dominant frequency of the embedded wavelet) is the layer thickness at which constructive interference between the top and base reflections produces the maximum amplitude, and thicknesses below tuning cannot be resolved as separate reflectors but appear as a single composite amplitude response that is a complex function of the wavelet shape and the layer thickness; knowing the embedded wavelet dominant frequency and shape is essential for predicting and correcting tuning effects in thin reservoir interpretation, because the apparent amplitude anomaly from a thin gas sand below tuning thickness depends on both the actual gas saturation (which affects the true reflection coefficient) and the layer thickness relative to the tuning thickness (which affects the interference between top and base reflections); wedge model analysis, which computes the expected seismic response of a reservoir with known acoustic impedance and varying thickness using the extracted embedded wavelet, is the standard tool for predicting tuning behavior and designing the amplitude extraction approach (time-window versus horizon-based versus model-based extraction) that best captures the reservoir signal for a specific target geometry.