Elastic properties of transversely isotropic rocks containing aligned cracks and application to anisotropy measurement*
Xu Song 1,2,3, Su Yuan-Da 1,2,3, and Tang Xiao-Ming 1,2,3
1. Key Laboratory of Deep Oil and Gas, China University of petroleum, Qingdao 266580, China.
2. School of Geosciences, China University of Petroleum, Qingdao 266580, China.
3. China Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology,Qingdao 266071, China.
Abstract Currently, most rock physics models, used for evaluating the elastic properties of cracked or fractured media, take into account the crack properties, but not the background anisotropy. This creats the errors of in the anisotropy estimates by using field logging data. In this work, based on the scattered wavefield theory, a sphere-equivalency method of elastic wave scattering was developed to accurately calculate the elastic properties of a vertical transversely isotropic solid containing aligned cracks. By setting the scattered wavefield due to a crack equal to that due to an equivalent sphere, an effective elastic stiff ness tensor was derived for the cracked medium. The stability and accuracy of the approach were determined for varying background anisotropy values. The results show that the anisotropy of the eff ective media is affected by cracks and background anisotropy for transversely isotropic background permeated by horizontally aligned cracks, especially for the elastic wave propagating along the horizontal direction. Meanwhile, the crack orientation has a significant influence on the elastic wave velocity anisotropy. The theory was subsequently applied to model laboratory ultrasonic experimental data for artificially cracked samples and to model borehole acoustic anisotropy measurements. After considering the background anisotropy, the model shows an improvement in the agreement between theoretical predictions and measurement data, demonstrating that the present theory can adequately explain the anisotropic characteristics of cracked media.
This work was supported by the National Natural Science Foundation of China (No. 41821002), the Fundamental Research Funds for the Central Universities (Nos. 18CX02065A, 20CX06046A), the Young Elite Scientist Sponsorship Program by the China Association for Science and Technology, Major Scientific and Technological Projects of CNPC (No. ZD2019-183- 004), Qingdao Postdoctoral Applied Research Project (No. qdyy20190079), and China Postdoctoral Science Foundation (No. 2020M672171).
Corresponding Authors: Su Yuan-da (Email: syuanda@sina.com).
E-mail: syuanda@sina.com
About author: Xu Song, fi rst author, selected in Young Elite Scientist S p o n s o r s h i p P r o g r a m b y t h e China Association for Science and Technology, received his Ph.D.,Sc.D., and B.S. degrees from China Petroleum University (East China) in 2019, 2015, and 2012, respectively. He performed research at the University of Texas at Austin as a joint Ph.D. student. He is currently working at the China University of Petroleum (East China) and is primarily engaged in the study of borehole acoustic logging theory, methodology, and fi eld data processing; rock physics theory; and other aspects of research. Email: xusongupc@sina.com
Cite this article:
. Elastic properties of transversely isotropic rocks containing aligned cracks and application to anisotropy measurement*[J]. APPLIED GEOPHYSICS, 2020, 17(2): 182-191.
2020, Vol. 17 
