ESTIMATION OF QUALITY FACTORS FROM CMP RECORDS AND VSP DATA

Djeddi Mbk and Mender M.*

Laboratory of Earth Physics, M’Hamed Bougara University, Boumerdes, Algeria

If you use data from this work you need to quote the reference in the bibliography as follows:

DJEDDI Mabrouk and MENDER M: Estimation of quality factoring from CMP records and VSP data. 13pp, 12 figures. Laboratory of Physics of the Earth, University M'Hamed Bougara , Boumerdes - Algeria, 2013  http://djeddimabrouk.fr.gd/

Abstract

During its propagation through a medium, the elastic energy associated with the seismic wave is gradually absorbed by the medium due to internal friction, eventually ending up as heat energy. This is known as absorption (or inelastic attenuation) and will eventually cause the total disappearance of the seismic wave. The rate of inelastic attenuation itself contains additional information about the lithology and reservoir conditions such as porosity, saturation and pore pressure so it can be used as a useful reservoir characterization tool and as an absorption compensation factor to enhance seismic data resolution in seismic data processing. The absorptive property of a medium can be described by a quality factor Q, which determines the energy decay and a velocity dispersion relationship. The quality factor and the velocity conduct the propagation of seismic energy in the earth.

To compensate for absorption, were quires an estimation of the quality factor (Q). Methods for estimating Q-factor from surface seismic data are not well developed .However; some research has been published concerning the estimation of Q-factor from vertical seismic profile (VSP) and cross well data.

This paper presents a synthesis of the most important methods used to estimate the Q-factor directly from common midpoint (CMP) gathers by assuming that the amplitudes spectrum of the seismic source signature may be modelled by that of a Ricker wavelet, we derive an analytical relation between Q-factor and seismic data peak frequency variation both along offset and vertical time direction. The Q-factor is estimated from CMP gathers using a layer-stripping approach. And for the vertical seismic profile (VSP) one technique we have employed for Q estimation is the spectral ration method. Our VSP-derived Qp curve shows an inverse linear relationship with the VSP-derived Vp/Vs curve. Finally, the bulk value of Qp, Vp/Vs and Vp are estimated for three main geological formations in the oilfield part.

Key words: Quality factor, Vertical seismic profiling, Amplitude decay, analytical signal, absorption.

INTRODUCTION

1

In seismic exploration, the propagation of seismic waves in the earth is affected by the anisotropic and the heterogeneity of the medium. Therefore, the visco-elasticity of the earth materials causes seismic energy dissipation, and thus decreases the amplitude and modifies the frequency content of propagating waves. This phenomenon of wave energy dissipation is called seismic absorption or seismic attenuation. Otherwise, the effect of attenuation is a relative loss of high-frequency components of a propagating wave. As a result, a seismic wave propagating in an attenuating medium will become richer in low frequencies, thus changing shape, in addition to suffering an overall amplitude reduction. The seismic attenuation property of a medium is usually described bya quality factor designated by Q. Many algorithms to estimate Q values have been published. And the most popular is the spectral ratio method (Tonn, 1991). The objectives of Q estimation can be grouped into two categories, one is for Q compensation, and another one is for reservoir description. For Q compensation, generally, we only require absorptive information for major layers. For reservoir characterisation, we require Q information of higher resolution for the study affine layers. In reservoir description, characterised by porous rocks saturated with fluid, generally, a strong attenuation can be observed. In a medium, shear and compressional waves travel at different velocities. They could show different attenuation on their wave-paths depending on the fluid contenting rock fractures. Many scientists have investigated the characteristics of shear wave attenuation in seismic data.

Seismic attenuation is usually categorized into scattering attenuation and intrinsic attenuation. Scattering attenuation is generally caused by three dimensional heterogeneities in the subsurface that distribute wave energy in arbitrary directions. Intrinsic attenuation is caused by internal friction among grains in the rock matrix, and the relative movement between the solid rock matrix and the pore fluid, when a seismic wave travels through loosely consolidated or porous media. Internal friction and fluid flow are considered directly related to rock porosity, permeability and the fluid content in the empty space.

In this paper we start by showing the development of analytical formula that can be used to estimate Q from a CMP gather, and also from a stacked seismic trace. Attenuation of the received signal sis only determined by the interval Q-factor sand travel times in each layer by assuming that the amplitude spectrum of a seismic wavelet is like Ricker one. Interval Q-factors can be computed directly from the variation of the peak frequency of a spectrum as a function of time. Results show that the relationship determines interval Q-factor values with reasonable accuracy. Then we use the spectral ration method to estimate interval quality factor from zero-offsets VSP data. We calculate Vp and Vs values from the direct arriving energy in the VSP. The VSP-derived attenuation (1/Qp) shows a quasi-linear relationship with the Vp/Vs values. Finally, the bulk values of Qp, Vp, and Vp/Vs are estimated for three major geological intervals in the oilfield zone. The VSP data used in this paper is of two type of source: a vertical vibrator for P-wave generation and a horizontal vibrator for S-wave generation. There are 130 3-component geophone levels ranging from 198 m to 1165 m at 7.5 m depth spacing.

Definition of Q-factor The seismic quality factor Q, which is an intrinsic property of rocks. Formally, Q is defined as a dimensionless measure of the inelasticity and is given by:

2

Q =−2π EΔE

Where is the fraction of energy lost per cycle. And the amplitude A of a wave at a particular frequency is proportional to √E (Aki and Richards, 1980), thus

Where is the amplitude at the start of a cycle and represents the amplitude decay in a cycle.We can rewrite A as a function of distance A(z) and,

Designing by λ the wavelength given in terms of frequency and phase velocity by

Combining the three equations above we can obtain

Estimation Q-factor from CMP gathers

Peak Frequency Variation and Quality factor estimation from surface seismic data

In seismic processing, the inverse Q-factor filtering is often used to remove the absorption effect. Therefore, to estimate Q from seismic data is, at first to examine the variation of a seismic wavelet with time, and then calculate a Q value from the variation of the wavelet shape or spectrum. By assuming that the amplitude spectrum of a seismic wavelet is like that of a Ricker wavelet, this part of the paper derives an analytical formula which allows a Q value to be calculated from the spectral peak frequency variation. The time domain and frequency domain methods are illustrated in Fig.1

There are two well-known methods based on frequency shift method to estimate quality factor. Centred frequency shift (CFS) method (Quan& Harris 1997) and Peak frequency shift method (PFS) (Zhang &Ulrych 2002). PFS method satisfied low Q condition and far target wavelet but dissatisfied high Q condition and near target wavelet. Meanwhile, the CFS method gives high accuracy in high Q condition but will not concur for deeper targets.

The spectrum of Ricker wavelet can be expressed by :

(1)

3

Figure 1. Time domain and frequency domain methods

EΔE

Q =−πA0ΔA

A0 ΔA

Where fm is a dominant frequency, fp the peak frequency and f is frequency content. After travelling time, the Ricker wavelet will be:

(2)

H (f,t) is the absorption filter in which the frequency spectral is given by

Where the integral is evaluated along ray path l. And,

Where:

Quality factor and velocity

Q-factor is assumed to be independent of frequency. By considering a half space the amplitude spectrum of the recorded signal is

(3)

Including all Q-factor unrelated functions into an amplitude term, the amplitude spectrum can be written as (4)

Where M(t) is an amplitude factor independent of frequency and absorption. And the peak frequency fp can be determined by equating the derivative of the spectrum, with respect to frequency, to zero:

(5)

Also for the Ricker wavelet:

. (6)

By inserting this expression into equation (5), the peak frequency at time t is :

... (7)

From here :

. (8)

We can notice that if the dominant frequency fm is known, the Q-factor can be computed from the peak frequency at only one time location.

Generally, we do not know the initial fm. So, designating the peak frequencies at times t1

and t2 by fp1 and fp2, respectively, we have

4

Thus,

(9)

Combining the equations (8) and (9) we obtain

(10)

This relation allows us to determine the absorption property of a layer if an event in the layer is observed at two different time locations.Two layer case characterised by Q1 and Q2

Consider first the case of two layers with quality factors Q1 and Q2 and travel times t1 and t2 in each layer, respectively, using equation (4), the amplitude spectrum after t = t1 + t2 is:

If Q1 and the dominant frequency fm of the source wavelet are known. The expression of Q2 is

With

Multi-layer case

For multi-layer media, we may write the amplitude attenuation equation (4) as:

...... (11)

Where Qi and Δti are t he quality factor and the travel time in layer, respectively. Taking an approach from velocity estimation, we assume straight ray paths and assume that quality factors and travel times in layers above layer N are known. Now we can calculate quality factor QN as

. (12)

Where,

5

The Q-factor values can now be calculated layer by layer by means of layer stripping. Since a straight ray path approximation is used, the computed QN is not the actual interval quality factor. Analogous toRMS velocities, we refer to such Q values as RMS Q values using a relation similar to Dix formula.

(13)

Where Qi is the average of the calculated Q values at different offsets for layer i, and t0(i) is the zero-offset arrival time of reflection i when the raypath is assumed to be straight across interfaces. Moreover, values of Qint are derived from RMS Q values, they are apparent values.

Application of the Analytical Formula to a Prestack and Poststack data Prestack

To estimate Q from CMP gathers, suppose that the arrival times for the main reflection events are known. Then we calculate the Fourier transforms in a window for each offsets, then each amplitude spectrum is fitted with ricker spectrum of 60 Hz and the peak frequency spectrum is estimated.To calculate the Q’s values layer by layer using peak frequency variation. Figure 2 shows a synthetic CMP gather with two events. The Q values in the two layers are 10 and 20 respectively. The desired and estimated Q curves are shown in Figures 2b and 2c respectively. The two curves are almost the same, because the estimated Q values are close to the actual values. The corresponding dominant frequency is estimated as 60.67 Hz. The agreement between the corresponding values shows that the method works well for ideal synthetic data.

The variation of peak frequencies with offset is shown in Figure 3. Peak frequency variation with offset of the first event is shown in black and the variation of the second event is shown in red.

6

Figure 2: (a) A synthetic CMP gather (b) Values of input qualityfactors. (c) Computed quality factors.

Figure 3: Variation of peak frequency of the two reflections

The effect of Q-factor compensation in term of resolution an exemple showing the effect of inverse Q-filtering on a prestack CMP gather using obtainedQ-factor values is illustrated in Figure 4. The two above events are clearly separated after apllication the inverse Q-filtering (c).

7

Figure 4: The effect of inverse Q-filtering.

PoststackTo apply the analytical formula to poststack data, we should assume each trace in a stacked section is zero offset.

Figure 4(a) shows a real stacked seismic trace, (b) shows a windowedtime-variant spectrum of this trace in which the trend of the spectral variation is indicated. Picking the peak amplitude. The calculted quality factor from each line segment for the main events are shown in (c).we use windowed time-variant spectral analysis applied on a narrow window to the inputtrace and calculates the conventional Fourier spectrum of the windoweddata. The window is then translated and widened successively with timealong the trace and the Fourier transform is calculated for each new position window.

8

Figure 5: Q estimation from a real stacked data. (b) Windowed time-variant spectrum. (c) Inverse of estimated Q-factor

Figure 6 shows the effect of application Q compensation on the stacked seismic data.

Figure 6 (a) before Q compensation (b) after Q compensation

9

Estimation Q-factor from VSP data

The spectral-ratio method is widely used to determine an attenuation or Q factor from zero-offset VSP data. The calculation proceeds as follows: for two downholereceivers at depths Z1 and Z2,

(14)

ω= 2 πf and A(z) the amplitude spectrum, v1 and v2 the average velocities for Z1 and Z1 respectively. Expressed in time, equation (14) becomes:

(15)

Where t1 and t2 are travel times at depths z1 and z2.

By taking the logarithm of equation (15) we obtain

(16)

Equation (16) is of the form Y = mX +C, where m =

Δt2Q is the slowness. By using least square

technique we can estimate the Q-factor values.

VSP data preparation

In this part, the data used for the Q calculation are the zero-offset downgoing wavefield traces. For the Psource vertical-component data, after aligning the first arrival times, a median filter is used to separate the downgoing wavefield from the total wavefield.For the S-source horizontal-component data, the radial component traces are then flattened at the first breaktime (Figure 7), and the same median filter is applied as for P-source data to extract thedowngoing shear wavefield (Figure 8).

Figure 7: P-source vertical S-source radial

10

A ( z2)A (z1)

=

A02 .exp [− ωz22ν2Q ]

A01 .exp [− ωz12ν1Q ]

=A02A01

exp [− ω2Q ( Z2V 2 −

Z1V 1 )]

A ( z2)A ( z1)

=A02A01exp [− ω

2Q ( t2 − t1) ]

ln ( A ( z2 )A ( z1 ) ) − ln ( A02A01 )=− ω

2Q (t2−t1) =− Δt2Q

.ω

Figure 8: Aligned down going P wave field Aligned down going S wave field

We can observe in Figure 8 that the S-wave amplitude decays faster than the P-wave, and has less high-frequency components.

Q estimation

By using the spectral ratio method and set the surface as the reference level. The spectral ratio between any trace and thesurface sweep is used to calculate a Qave instead of Qint. The benefit of this approach is that thesurface sweep is relatively constant and designed to have a largely flat spectrum across a givenband. Figure 9 displays the spectra of the defined surface sweep, a shallow station (220m) and adeep station (1157m) for both P-wave and S-wave.

Figure 9: the amplitude spectrums: P-source S-source.

11

Now, Qp_ave and Qs_ave curve for the whole interval are calculated and plotted against depth (Figure 10). It’s noted that Qp_ave and Qs_ave have different trends.

Figure 10: Average QP (blue) and average QS (red) curve.

Qp and Vp/VsGenerally, the Vp/Vs ration is commonly used as a lithology indicator. Figure 11 displays the interval Qp derived from VSP , Vp from sonic log and Vs/Vp fromVSP. Generally, the three curves are following the similar trend and tracking each other. QPshows a linear inverse proportional relation with Vp/Vs : higher Vp/Vs correspondsto lower Qp (more attenuation) and vice versa. It’s more obvious in the crossplot of Qp with Vpand Vs, respectively, and the crossplot of Qp with Vp/Vs which gives us Qp = -40.3924(Vp/Vs) +144.1752 by linear regression (Figure 12).

Figure 11: Qp, Vp, Vp/Vs curves

Figure 12: Cross plot of Qp with Vp and Vs

12

CONCLUSION

The subsurface lithology is characterized by its speed, density and quality factor. The latter has an effect on the amplitude and the frequency content of the signal.

We have shown an analytical approach for estimating the quality factor of the surface data for prestack and post stack data based on the assumption that the source wavelet has an amplitude spectrum similar to that of a Ricker wavelet. Furthermore, to estimate Q-factor from a prestack CMP gather, variation of a wavelet spectrum of an event is analyzed along offset. To obtain spectral peak frequency variation from a post stack trace, we can use windowed time-variant spectral analysis.

We have used the spectral ratio method to calculate Q values from VSP data. A reliable continuous interval Qp curve from about 450m to 1050m has been derived from a zero-offset VSP by this approach.

The Qp curve derived from VSP shows an inverse linear relationship with the Vp/Vs curve. Finally, the bulk value of Qp, Vp/Vs and Vp are estimated for the reservoir formations.

References

- Changjun Zhang 2008, Seismic Absorption Estimation and Compensation.- Changjun Zhang¤ and Tadeusz J. Ulrychz, Estimation of quality factors from CMP records,

GEOPHYSICS, VOL. 67, NO. 5 (SEPTEMBER-OCTOBER 2002)- Mohammad Bigdeli Tabar, Shoorangiz Shams Shamsabad Farahani, Mehdi Nikzad,

HossainTourang, Mehdi Ghasemi Naraghi, A Study of Relations between Velocity Ratio and Seismic Quality Factors Ratio, Journal of Basic and Applied Scientific Research

- Chuandong (Richard) Xu*, Robert Stewart, Seismic Attenuation (Q) Estimation from VSP Data- Zhang, C. Ulrych, T.J., 2002. Estimation of Q from CMP records. Geophysics 67, 1542-1547.

13