Energy Absorption Analysis
J. Todd Mitchell, Naum Derzhi, Eugene Lichman, Eric N. Lanning
Seismic attenuation, presumably related to the presence of gas in a channel sand, was detected using a seismic analysis program called EAA (Energy Absorption Analysis). The program extracts frequency information from a cascading series of small time windows along the seismic trace, then employs a simple series of steps to compare the spectra in successive time windows to detect anomalous loss of high frequency energy as a function of time. The algorithm uses a method to minimize the effect of homogeneous energy decay, and generates anomalous absorption values only when energy decay exceeds background levels. The computation of the absorption attribute is demonstrated using seismic data crossing the producing field.
Seismic attenuation can be reduced to a simple concept: when a seismic wave moves through a body of rock in the subsurface, some portion of the wave energy may be converted to heat within the rock body itself. The conversion of wave energy to heat represents a net loss of energy for the propagating wave.
Extensive work has been done in laboratory settings to measure energy attenuation in rocks under a variety of conditions, and the result is a large body of literature that documents the phenomenon. Numerous mechanisms are proposed. One mechanism is based on the principle that the seismic wave induces an interaction between the rock matrix and the pore fluid, such as fluid flow between adjacent pore spaces, which generates friction. The physical properties of the rock matrix and the composition of the fluids within the rock matrix determine the degree to which energy is dissipated, and possibly the frequency range in which the dissipation principally occurs. Other studies show attenuation varying in response to changes in water saturation, clay content, porosity, pore geometry, permeability, micro-fracturing, and pressure. There is strong evidence that partial gas saturation increases the attenuating properties of water, independent of any interaction with a rock matrix. Studies in this area focus on the interaction between liquid and gas in response to seismic energy, as well as compressibility of gas.
Extracting some measure of attenuation from seismic data has great potential for reservoir characterization and direct detection of hydrocarbons, especially natural gas. Studies show that attenuation is frequency selective – seismic energy loss typically occurs preferentially in the high frequency end of the spectrum – which means that signal processing algorithms should be constructed that target anomalous high frequency energy loss.
There are, however, obstacles that have slowed the use of attenuation detection as an exploration tool. First, most petro-physical laboratory studies have been conducted at sonic and ultrasonic frequencies, because of limitations of laboratory equipment. Extrapolating from higher frequency laboratory measurements is probably inadequate for understanding attenuation at seismic frequencies. As a result, the specific petrophysical conditions which cause energy attenuation at seismic frequencies are not completely understood. Research in this area is active. Obstacles to extracting seismic attenuation data include seismic acquisition limitations (the data need to have an adequate frequency range to target the loss of high frequency energy); contamination of data in seismic processing (AGC, spectral whitening, deconvolution, and other processes can alter frequency content); and signal processing limitations (conventional approaches have difficulty generating reliable frequency spectra in small time windows).
Nevertheless, published cases, of which two are mentioned in the next section, indicate that energy attenuation can be detected in seismic data. Algorithms such as the one described here attempt to overcome some of the signal processing limitations, and should find increasing use in exploration and exploitation geophysics.
Published examples of field seismic data demonstrate the potential usefulness of attenuation for exploration and development. Dilay and Eastwood (Leading Edge, November 1995) document an empirical relation between partial gas saturation and attenuation at seismic frequencies in a time-lapse 3D study of a steam flood. During the steam injection cycle gas saturation is close to zero but increases to greater than 5% around wellbores during the oil production cycle. (The increase in free gas during the production cycle is attributed to lower reservoir pressures near the well bore.) The authors noted a pronounced loss of high frequencies during the oil production cycle in the analysis window below the reservoir. This effect is attributed to intrinsic attenuation, a result of the interaction of gas with other pore fluids in a high porosity matrix, during times of elevated gas saturation in the oil production phase.
Russian geophysicists have published numerous cases showing energy attenuation as a direct hydrocarbon indicator. Rappoport (in Technical Program Expanded Abstracts, 1994 Society of Exploration Geophysicists Annual Meeting) documents energy attenuation as a method for predicting reservoir quality in a Siberian oil and gas field. The technique which he describes derives Q from VSP data, calibrates the VSP-derived Q with an attenuation attribute computed from coincident 2D seismic data, then extrapolates the attenuation value regionally across a seismic grid. The study finds that the locations of commercial wells-those that produced at high initial volumes-correspond to areas of high energy absorption at the producing horizon, while non-commercial or dry wells correspond to areas of low energy absorption. It is particularly interesting to note that the attenuation attribute helps to document the stratigraphic nature of the trap, and explains why the wells drilled on the structural crest did not encounter the optimal reservoir conditions.
Notwithstanding the occasional example, for the most part there are few published cases of energy attenuation used as a seismic attribute for hydrocarbon exploration. A systematic study needs to be undertaken on 2D and 3D data, in a variety of geologic settings, calibrated to known well log and core data, to test the effectiveness of analysis techniques such as the one described here.
Method Energy Absorption Analysis (EAA) is a program which runs within a commercial seismic analysis package. The EAA algorithm is designed to detect a sudden increase in the rate of exponential decay in the relatively higher frequency portion of the spectrum.
EAA analyzes a seismic trace in a series of small time windows along the trace. EAA works on a trace by trace basis by computing spectra from cascading analysis windows at a user-defined increment. The increment can be as small as the sampling rate. The length of the analysis window, also user defined, is kept small (30-70 ms). In a typical computation, the discrepancy between the analysis window length (e.g., 40 ms) and the analysis increment (e.g., 4 ms) creates an overlap of analyses that increases the resolution of the process (Figure 3). There is no averaging across traces.
In order to obtain a single value of absorption corresponding to a certain reflection time, we select a window around this reflection time – it should be a window of the smallest reasonable size – and compute the amplitude spectrum. In the portion of the spectrum which is affected by absorption, we fit an exponential function. It is a function of form exp (-aw), so that a, or alpha, is the absorption coefficient parameter that we are interested in. This absorption coefficient is now associated with the center of that time window. The time window is moved by the increment chosen for the analysis and the procedure is repeated. The entire seismic trace is processed in this fashion, yielding alpha as a function of time.In order to obtain a single value of absorption corresponding to a certain reflection time, we select a window around this reflection time – it should be a window of the smallest reasonable size – and compute the amplitude spectrum. In the portion of the spectrum which is affected by absorption, we fit an exponential function. It is a function of form exp (-aw), so that a, or alpha, is the absorption coefficient parameter that we are interested in. This absorption coefficient is now associated with the center of that time window. The time window is moved by the increment chosen for the analysis and the procedure is repeated. The entire seismic trace is processed in this fashion, yielding alpha as a function of time.
A complicating factor in our computation is attributable to background energy decay. Even a hypothetically homogeneous subsurface – lacking in any stratal variations that introduce local, anomalous absorption – will absorb seismic energy. Furthermore, the energy loss will be most pronounced in the higher frequencies. If we simply displayed alpha as the attribute, there would be a steady increase in high absorption values as a function of distance from the source. But we are interested in anomalous absorption, that is, absorption which is much higher than that in the surrounding intervals. Therefore, our computations have to compensate for background energy decay. Assuming that the background absorption changes slowly from layer to layer, we remove it by subtracting vertically (time) successive alpha values. The difference in alpha between two successive time windows on a single trace is the number that is then generated and displayed at the center of each analysis time window.
The goal of the EAA algorithm is to produce information that is of sufficiently high resolution to be useful at the scale of the geology. This requires small time windows for the analysis (generally in the range of 30-70 ms). But small time windows contain very few samples for computing the complex spectra. If we were to assume seismic data with a 4 ms sampling interval, there would be only 11 samples within a 40 ms time window. This suggests the need to increase the number of samples within the time window by some form of interpolation of the original data. Extreme care must be taken to use an interpolation method that does not add any new information into the signal while increasing the sampling rate.
This can be accomplished by taking the complex spectrum of the original seismic trace and extending the Nyquist limit using zeroes in the new high frequency positions. This new complex spectrum has exactly the same frequency content as the original, but now, when we take the inverse transform back to the time domain, we have a new seismic time series (trace) which has the desired (much smaller) sampling interval. This simple procedure provides a sound, stable method for increasing the sampling rate of the data without introducing any new information.
The case study field is located in the updip portion of the Yegua producing trend, onshore, Texas. The productive sand, at a depth of about 4,500 ft subsea, is a dip oriented Yegua channel. Wireline log curves indicated a 42 ft gross sand interval, including a 24 ft clean upper gas bearing zone. Core analysis yields porosity measurements from 25-27% and permeabilities from 150-300 md in the main producing interval. A 2D seismic line crosses the field in the dip direction. The top of the productive sand ties to a pronounced high amplitude seismic trough, followed by a equally distinct seismic peak (top curtain).
After stacking the data, the EAA process was applied. In (bottom curtain), the stacked seismic wiggle trace data overlays the EAA output. At the producing interval an energy absorption anomaly is present as a “bull’s eye” that has its highest amplitude at roughly the center point of the seismic high amplitude trough. A well was drilled based on the superposition of multiple direct hydrocarbon indicators – the data showed an AVO signature as well – and was completed and put on production at a rate of 700 MCF/D.
We extracted a common offset panel from the prestack data, in this case the eighth trace from every gather, across the gas field. We then used this data set to re-run the EAA program. Our analysis parameters included an analysis window length of 50 ms, and a window propagation increment of 4 ms. Figure 5 shows the energy absorption anomaly generated on this common offset panel, occurring in the same location as in the stacked data set. Although EAA is commonly run on stacked data, we analyzed prestack data in this case to demonstrate that the absorption response was not introduced by stacking.
To demonstrate the computation of the EAA algorithm across the field pay, we display in the location of five selected analysis windows from a trace that is coincident with the gas reservoir. In Figure 6, we display the extracted amplitude spectra from each selected time window (5A matches 6A, 5B matches 6B, etc.). The series of analysis windows chosen for exhibit begin above the reservoir then progresses through and below the reservoir. For graphical purposes, the increment between each displayed window is 20 ms, which is five times greater than the increment actually used to calculate the absorption attribute. The length of each analysis window in this case is 40 ms.
Progressing from 5A to 5C, one observes a steepening of the associated energy decay curves, with the most dramatic steepening occurring between 5B and 5C. The observed energy decay may represent the increasing attenuating effect of the gas charged reservoir, with the highest alpha value centered in the seismic trough (negative amplitude) that marks the gas reservoir. Below the reservoir, in windows D and E, the energy decay slopebecomes progressively less steep, but more importantly exhibits relatively little change between the two windows, and consequently the Energy Absorption Analysis attribute value (change in alpha) diminishes. The EAA algorithm outputs a value that is the difference in alpha between vertically successive windows. In this case, the greatest value would occur between 5B and 5C, and that value would be placed at the center of the 5C analysis window. This is in fact the “bull’s eye” of the absorption anomaly.
Observations and Pitfalls
We have processed numerous data sets using the Energy Absorption Analysis program, and can make some general observations. The process is not a gas indicator per se, nor does it deliver a quantitative Q value. Rather, the process detects local areas where high frequency energy has been rapidly lost over a small vertical distance. It should be thought of as a qualitative way of detecting intervals of anomalous energy attenuation in the subsurface. Because numerous petrophysical mechanisms cause energy attenuation, gas hydrocarbons should be only one of several possible mechanisms considered by the interpreter. Nevertheless, we have seen numerous data sets in which absorption anomalies were coincident with gas reservoirs, and in many cases, the absorption attribute is diagnostic while other seismic attributes (e.g., amplitude, AVO) are not. We are encouraged to pursue EAA as a reservoir characterization attribute in high velocity plays. We find that the absorption anomalies in these consolidated geologic sections tend to be distinct and coherent, and are often positioned where the seismic amplitude response is unremarkable.
Words of caution are appropriate. The EAA process detects rapid high frequency energy loss in the data, and non-geological effects must be considered. For example, poor NMO due to inadequate velocity analysis may severely affect the frequency character of the final stack. Another concern is frequency variation due to tuning or thin-bed effects, which may have no connection with intrinsic attenuation in the reservoir. Improved modeling techniques must be developed for predicting high frequency seismic energy loss, whether attributable to attenuation, tuning, scattering, or other mechanisms.
There are other pitfalls. Acquiring a broad frequency range during seismic acquisition, and then preserving the frequency character during processing, are essential to generating a meaningful absorption analysis. It is important to be aware of the processing steps that affect the frequency content of the data. Spectral whitening, spectrum balancing, AGC, and certain deconvolution procedures can all have deleterious effects on the frequency character of the data. We recommend the style of true amplitude processing that has become familiar in AVO analysis.
We believe that modern seismic acquisition technology, careful prestack processing, and high resolution analysis algorithms eliminate the most substantial barriers to detecting energy attenuation in reflection seismic data. Current work to investigate attenuation at seismic frequencies will improve our understanding of the link between subsurface rock properties and the attenuation responses computed from reflection seismic data. A systematic effort is needed to create and apply signal processing techniques to assess the full potential of energy attenuation as a seismic attribute for reservoir characterization.