Hoda Rashedi

2D FINITE-DIFFERENCE SIMULATIONS: EFFECTS OF PATH, SOURCE

AND ANELASTIC ANISOTROPY ON MICROSEISMIC WAVEFORMS

Hoda Rashedi* and David Eaton

Department of Geoscience, University of Calgary, AB, Canada

Work Flow: Theory, Methodology and Inputs

In this research, microseismic synthetic data produced in order toinvestigate the effect of moment tensor, velocity model, anisotropy andattenuation on the waveforms. This data generated by 2D acousticfinite-difference modeling program which originally developed byBoyd[3].

These realistic synthetic data provide an effective way to benchmarkprocessing and interpretation algorithms. An excellent example isprovided by the Marmousi dataset created by IFP[2] a shown in Figure1.

Therefore, realistic suite of syntheticmicroseismograms for a scenario inwhich the source location, mechanismand background model are known andthe complete wavefield containingmultiples, guided waves etc, is accuratelysimulated.

Figure1: Prestack FD dataset created by IFP in 1988

Understand the effects of moment tensor on the waveforms Investigate the wave propagation pattern in different medium with

or without anisotropy

Study the impact of various degrees of attenuation during propagation on waveform

Produce a suite of synthetic data to be used for benchmarking and calibration

SUMMARY

Figure2: Sample realistic velocity model, Central Alberta Velocity model.

Vs Vp

Equation of motion

(,), =

Step 1 : Solve it using FINITE DIFFERENCE

Step 2 : Assign properties of medium into Stiffness Tensor

ISOTROPIC

Shear modulus: K bulk modulus:

VTI (Vertically Transverse Isotropic)

Thomsen Parameters:

Souce: Moment tensors with various focal mechanism

Realistic Velocity Model Attenuation(Anelastic Medium)

=

.

N: Damping FactorC: Stiffness Tensor Matrix: Angular FrequencyQ: Quality Factor Matrix

ISOTROPIC

13 = 3333 255

33 2553355

VTI

12 = 1111 266

11 2661166

5 independent elements2 independent elements

Double Couple Tensile Crack Opening

ISOTROPIC ISOTROPICVTI ISOTROPIC& ANELASTIC

VTI & ANELASTIC VTI ISOTROPIC& ANELASTIC

VTI & ANELASTIC

=0 0 10 0 01 0 0

P-Wave Radiation pattern S-Wave Radiation pattern

=1 0 00 1 00 0 3

S-Wave Radiation patternP-Wave Radiation pattern

CONCLUSION

REFERENCES

RESULTS

Anelastic attenuation refers to amplitude losses due to conversion ofelastic strain energy to other types of energy, such as heat. The effectsof attenuation are often approximated using a constant, isotropic Qmodel. On the other hand, anisotropy refers to the dependence ofelastic properties on propagation and polarization directions. Here,these phenomena are combined to evaluate the potential effects ofattenuation anisotropy for microseismic recordings.Finite-difference simulations are used to investigate the changes on thewaveforms. This will provide a valuable data that model the wavepropagation in realistic media due to various rock behavior duringhydraulic fracturing with different moment tensors.

INTRODUCTION

SCIENTIFIC OBJECTIVE

Case studies of finite-difference simulations involving various source types and positions incorporating varying degrees of anisotropy establishes a tool to study thebehaviour of waves. On the other hand, simulations involving attenuation anisotropy are scarce in microseismic monitoring, , hence, synthetic data can provide valuableinsights for an interpretation of microseismic wave propagation and waveforms. This approach enables analysis and identification of wave-field elements such as headwaves, post-critical reflections and guided waves. Imperfect absorbing boundaries create artifacts that require model dimensions to be extended to ensure that artifacts donot interfere with desired signals.The effects of strong anisotropy are evident. The main goal of this study is to build a series of synthetic data including attenuation anisotropy for both isotropic and verticallytransverse isotropic medium and investigate the wave-field elements and the effect of the attenuation to them.

[1] Arts, R. J., and P. N. J. Rasolofosaon, 1992: Approximation of velocity and attenuation in general anisotropic rocks: 62nd Annual International Meeting: SEG, Expanded abstract, 640- 643.[2] Bourgeois, A. M. Bourget, P. Lailly, M. Poulet, P. Ricarte, and R. Versteeg. Marmousi, model and data. Proceedings of the 1990 EAGE workshop on Practical Aspects of Seismic Data Inversion: Eur. Assoc. Expl. Geophys, 5-16, 1991.[3] Boyd, O., 2006, An efficient MATLAB script to calculate heterogeneous anisotropically elastic wave propagation in three dimensions: Comp.Geoscince, 32, 32, 259-264.[4] Carcine, J. M., 2001: Wavefields in real media: Wave propagation in anisotropic, anelastic and porous media: Nature, 277:528-531.[5] Hosten, B., M. Deschamps, and B. R. Tittmann, 1987: Inhomogeneous wave generation and propagation in lossy anisotropic solids: Application to the characterization of viscoelastic composite materials: Journal of the Acoustical Society of America, 82, 1763-1770.[6] Tao, G., and M. S. King, 1990: Shear-wave velocity and Q anisotropy in rocks: A laboratory study: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 27, 353- 361.[7] Thomsen, L., 1986: Weak elastic anisotropy: GEOPHYSICS, VOL. 51, NO 10, (October 1986); P.1954-1966.[8] Toksoz, M. N., Johnston, D. H., and Timur, A., 1979: Attenuation of seismic waves in dry and saturated rocks: I. laboratory measurements: Pergamon Press, Inc.

[9] Tsvankin, I., 1997: Anisotropic parameters and P-wave velocity for orthorhombic media: GEOPHYSICS, VOL. 62, NO.4, (July-August 1997); P.1292-1309.[10] Sinha, S., Abaseyev, S. and Chesnokov, E., 2007: Full waveform synthetics and its spectral characteristics in multilayered anisotropic attenuating media: SEG 2007 Annual Meeting.[11] Winkler, K. and Nur, A., 1979: Pore fluids and seismic attenuation in rocks: GEOPHYSICS, Res,Lett., VOL 6, P. 1-4.[12] Winkler, K., Nur, A., and Gladwin, M., 1979: Friction and seismic attenuation in rocks: Nature, 277:528-531.[13] Zhu, Y and Tsvankin, I., 2006: Plane-wave propagation in attenuative transversely isotropic media: GEOPHYSICS, VOL.71, NO 2, (March-April 2006); P. T17-T30.

VTIAttenuating Attenuating

VTI VTIAttenuating

Attenuating

VTI

P-wave

S-wave

P-S conversion

Velocity Dispersion

P-wave

S-wave

Artifacts