AVO inversion is a seismic exploration methodology used to predict the earth’s elastic parameters and thus rocks and fluid properties. It is built up on elastic theory and does not consider the seismic dispersion in real strata. Recent experiments and theory of rock physics have shown that in hydrocarbon-bearing rocks, especially in gas-bearing ones, the change of seismic velocity with frequency may be pretty remarkable for fluid flow in pore space. Some scholars proposed methods about seismic dispersion, such as frequency-dependent AVO inversion, to forecast oil and gas reservoirs underground. In this paper, we demonstrate an improved scheme of frequency-dependent AVO inversion, which is based on conventional Smith-Gidlow’s AVO equation, to extract seismic dispersion and predict the hydrocarbon underground. A simple model with gas-bearing reservoir is devised to validate the inversion scheme, and further analysis indicates that our scheme is more accurate and reasonable than the previous scheme. Our new scheme applied to the tight gas reservoirs in Fenggu area of western Sichuan depression of China finds that regions with high dispersion gradients correlate well with regions with prolific gas. Analysis and case studies show that our scheme of frequency-dependent AVO inversion is an efficient approach to predict gas reservoirs underground.
The amplitude versus offset (AVO) is one of the most widely used geophysical techniques to predict oil and gas reservoirs [
AVO approaches mentioned above are based on the assumption that subsurface rocks are elastic. However, recent developments in seismic rock physics theory and practical studies have revealed that underground strata are viscoelastic, and seismic wave always has noticeable dispersion and attenuation for fluid flow in pore space of rocks [
In rocks bearing oil, gas, or water, the seismic velocity is dependent on frequency. Especially in those bearing abundant gas, there may be remarkable seismic dispersion. The more fluid the rocks hold, the greater the seismic wave disperses at seismic frequency band. Therefore, seismic velocity dispersion may be used to identify the fluid in porous rocks underground. This has attracted some researchers to study and apply dispersion in hydrocarbon exploration. Chapman et al. [
In this paper, we develop an improved scheme of frequency-dependent AVO inversion to predict tight gas reservoirs. Analysis and case studies show that the new frequency-dependent AVO inversion scheme is more reasonable and accurate than the previous scheme.
In this part, Wilson’s scheme of frequency-dependent AVO is briefly introduced first. Then, our improved scheme is derived in detail and analytical comparison between two schemes is made. Finally, a signal decomposition technique, which is used to obtain seismic records at different frequencies in frequency-dependent AVO inversion, is illustrated.
AVO inversion is a seismic exploration methodology used to predict the earth’s elastic parameters and thus rocks and fluid properties. Zoeppritz derived the formulations of reflectivity and transmissivity when a plane wave impinges on an interface of different strata underground and developed the theoretical work for AVO theory. Assuming the difference of elastic parameters across an interface is small, Aki and Richards [
The Smith-Gidlow’s equation has been widely used in geophysics. But it is based on elasticity, and it does not consider the seismic dispersion in real rocks.
Considering the seismic velocity is dependent on frequency in rocks, Wilson et al. [
In equation (
Although some cases of success have been reported by Wilson’s frequency-dependent AVO inversion, there are some problems in the equation. The item
In this paper, we derive an improved scheme of frequency-dependent AVO inversion without the unreasonable assumption in Wilson’s scheme. The following is the derivation process of the improved one.
First, the Smith-Gidlow’s equation (
Generally P-wave reflection coefficient
Expanding equation (
Because there is a relationship as
Equation (
From the equation of (
It is should be noted that there is reference frequency
Our scheme of frequency-dependent AVO inversion is inspired by Wilson’s scheme, but it is improved. First, there is no unreasonable assumption that
Obtaining seismic records at different frequencies is an important step of frequency-dependent AVO inversion. Many methods can decompose seismic data into parts in different frequency bands, such as Fourier transform, short-time Fourier transform (STFT) and wavelet transform etc. Here, a signal decomposition technique named smoothed pseudo Wigner-Ville distribution (SPWVD) is introduced. The comparison between SPWVD and other methods, such as STFT and wavelet transform, is also made to test the accuracy of SPWVD.
Wigner-Ville distribution (WVD) is one of the most effective approaches to decompose nonstationary signal on the time-frequency plane via an energy distribution function. The time-frequency decomposition of a signal
For a synthetic or a seismic trace, the magnitudes of decomposed components at different frequencies are different for two factors. One is different reflection coefficients at different frequencies, which is caused by dispersion. The other is the different magnitude of wavelet components. Frequency-dependent AVO inversion considers the reflection coefficients at different frequencies. So, the effects of the wavelet must be removed before frequency-dependent AVO inversion. An efficient spectrum balance technique [
In the following frequency-dependent AVO inversion, the SPWVD technology is used to obtain seismic records at different frequencies.
In this part, a simple model with horizontal layers is devised to test our scheme of frequency-dependent AVO inversion. Comparison of results by Wilson’s scheme and ours is also made for the model.
The simple model is composed by three horizontal layers as shown in Figure
A horizontally layered medium model. The top two layers are nonreservoir and are regarded as elastic medium. The bottom layer is gas-bearing reservoir and poroelastic medium is adopted to represent it.
The parameters of layered medium model.
Layer 1 | 4500 | 2700 | 2.4 | — | — | — |
Layer 2 | 4800 | 3200 | 2.6 | — | — | — |
Layer 3 | 3458 | 2100 | 2.3 | 0.08 | 0.4 | 0.6 |
Reflection coefficients at the interface between layer 1 and layer 2 can be computed easily by Aki-Richard’s equation or Smith-Gidlow’s equation. Then, corresponding synthetics can be obtained by convolution between the coefficients and wavelet. But the synthetics at the interface between layer 2 and layer 3 are more difficult to get because the seismic velocity is dependent on frequency. We first compute the seismic velocities at different frequencies on patchy model [
Figure
The prestacked synthetics at different incidence angles for layered medium model. The peak at 0.1 s coincides with the interface across the top two elastic nonreservoir layers. The trough at 0.2 s coincides with the interface between the elastic nonreservoir and poroelastic gas-reservoir layers.
SPWVD technique is used to decompose the synthetics. Figure
(a) Decomposed synthetic at 6° incidence for layered medium model by SPWVD. (b) The balanced results of the decomposed synthetic. The effects of seismic wavelet at different frequency are eliminated by spectrum balance technique. The remaining energy differences with various frequencies at 0.2 s are caused by seismic dispersion.
Figure
The inversion results by our scheme and Wilson’s scheme. (a) P-wave dispersion gradients
Since the mixed dispersion gradient has similar characters with that of P-wave dispersion gradient, in following application, we only employ P-wave dispersion gradient
In this part, we first introduce the geology background of Fenggu area briefly. Then, our scheme of frequency-dependent AVO inversion is applied to predict the gas reservoirs in this area.
The Fenggu structure is located in eastern end of the Xiaoquan-Hexingchang-Xinchang-Fenggu structural zone in western Sichuan depression, China (Figure
Location of Fenggu area and tectonic divisions of western Sichuan Basin [
Developing feature of strata in Xujiahe formation, Fenggu area [
In Upper Triassic Xujiahe formation, Fenggu area, T3x4 member is considered highly prospective for gas. The favorable sedimentary include plain river, frontal mouth bar of fan deltas, and meandering stream deltas facies. Rock physics tests show that reservoir porosity is primarily composed of secondary corrosion pores, remaining intergranular pores and developed micro fracturing. Since the average porosity and permeability are low, the reservoirs in T3x4 member of Xujiahe formation are tight gas reservoirs. In the following, we will detect gas reservoirs in T3x4 member.
The scheme (
Figure
P-wave dispersion gradient of T3x4 member in the Xujiahe formation, Fenggu area. The color bar represents the amplitude of P-wave dispersion gradient.
Figure
The inversion profile through well cf175. The region marked by the purple ellipse is a good conventional gas reservoir. It has big value of P-wave dispersion gradient. Our inversion results match the well tests in this domain.
Figure
The inversion profile through well cf563. The three domains marked by ellipses are fractured or conventional gas reservoirs. These regions have big value of P-wave dispersion gradient. The inversion results match the well tests in these domains.
Figure
Time–slice of P-wave dispersion gradient along the first set sand of T3x4 member. Inversion results show that the west and the southeast of the area is the favorable zone of gas reservoirs for the high value of P-wave dispersion gradient.
In the object area, five wells reaching the bottom of T3x4 member have been drilled, and Table
Logging results of the first set sand of T3x4 member.
Fg22 | Cf175 | Cf125 | Cf563 | Fg21 | |
---|---|---|---|---|---|
Test result | Mudstone | Poor gas reservoir | Poor gas reservoir | Gas reservoir | Poor gas reservoir |
Comparison of P–wave’s dispersion and the well tests in Table
Frequency-dependent AVO inversion by Wilson’s scheme is also done on seismic data of Fenggu area. Figure
The inversion profile through well cf563 by Wilson’s scheme. The prediction by Wilson’s scheme matches the well test at location 2. But at the locations 1 and 3, the values of P-wave dispersion gradient are not high while they are good conventional and fractured gas reservoirs. The predictions by Wilson’s scheme mismatch with well tests at the two locations.
Figure
Inversion profile through well cf125 by the new scheme (a) and Wilson’s (b). Two P–wave’s dispersion gradients at the location marked by red ellipse are low, and well test indicates the place is a poor gas reservoir (white block). Two inversion results match well test. But comparison shows that result by our scheme has better continuity and more contrast than that by Wilson’s.
Dispersion is related to porous fluid when seismic wave propagates in reservoirs. In regions where porous fluid is abundant, the seismic dispersion is always great at seismic frequency band, especially in gas reservoirs. Frequency-dependent AVO inversion is indeed a method to extract P-wave dispersion gradient from prestack angle gathers. Further prediction of oil and gas reservoirs can be made by inverted dispersion gradient.
In this paper, we derived a scheme of frequency-dependent AVO inversion. It is motivated by Wilson’s scheme, but is improved. The comparison between inversion results for a layered model by two different schemes shows that our scheme is more reasonable. Further practical application in Fenggu area is made on our inversion scheme. The predictions of gas reservoirs by our scheme of frequency-dependent AVO inversion match well tests. That verifies the effectiveness of our inversion scheme in prediction of gas reservoirs.
There is a point to be noted that the Gardner’s equation about density and P-wave velocity is employed in the derivation of our inversion scheme. Since it is just an empirical equation, it may need modification for special regions, and the scheme of frequency-dependent AVO needs corresponding modification too. By this treatment, better inversion results can be expected. This task will be undertaken in our future work.
All model data during this study are listed in this manuscript; researchers can replicate the analysis. But the real seismic data in the application section, which is very large, are not available because they involve business secrets.
The authors declare that they have no conflicts of interest.
This study is financially supported by National Science and Technology Major Project (Grant no. 2017ZX05005-004-002) and NSFC and Sinopec Joint Key Project (U1663207). We also acknowledge Miss Jie Li for her patient editing.