岩石內部傳遞的超音波除了與組成礦物的彈性模數有關外，與岩石內部裂隙的分佈狀況也有相對關係。為利於層狀材料波速之量測，實有需要針對層狀材料之超音波波速變化加以研究。
本文模式根據Snell’s law，推導多相層狀試體之不同層厚比、波速比於不同角度之超音波波速預測模式。軟體方面使用Tomograph 2D，此程式以Fermat’s principle為基礎，利用離散的方法搜尋最小走時路徑，以此路徑與走時求得層狀材料之波速。本文模式與Tomograph 2D計算結果相當一致。本文模式為解析解，相對於軟體具有計算快速、層狀數量不受限制的優點。
為探討本文模式之正確性，本研究以壓克力、紙張和鋼片堆疊成不同層厚比之層狀試體，進行不同角度之超音波量測。試驗結果於θ=0度之波速為最高，相當接近波速最高材料之波速，且波速隨角度之增加而遞減，至θ=90度時波速達最小值。其餘角度波速可利用鏡射與對稱方式求得。試驗結果顯示與本文模式及Tomograph 2D計算結果相當一致。並以不同厚度之壓克力堆疊成不同界面間距之層狀試體，於相同接觸應力下，界面間距越小，波速異向性越明顯，隨著接觸壓力增加，層狀材料會逐漸趨於等向性。

The ultrasonic transfer within the rock is not only related to the elastic modulus of mineral compostion, but also the cracks distribution of the rock. It is needed to study the change of P-wave velocity.
In this paper, predictions are all based on Snell’s law. This study derives different layer thickness ratio of multiphase layered models and different wave velocity ratio at different angle-prediction model. Tomograph 2D is used as computation program. It is based on Fermat’s principle using discrete way to search the minimum travel time path. Therefore, wave velocity is obtained by path and traveltime. The model found in this article is very consistence with the result from Tomograph 2D. Analytical solution is found and its advantages are quick computation and unrestricted by the number of the layers.
In order to examine the accuracy of the model, the acrylics, papers and steels are applied to stack into interlayer model of the different layer thickness ratio. In addition the P-wave velocity at different angles is measured. The results showed that the P-wave velocity was fastest at θ=0°, quite close to the velocity of the material which has maximum. The minimum of the P-wave velocity appeared at θ=90°. The velocity at other angles can be obtained from mirroring and symmetric ways. As a result, under the same contact force, the less the layer spacing, the more obvious the velocity anisotropy. With the increasing of contact force, the interlayer material will become more like isotropic material.

(1).田永銘、王仲宇、王仁正、賴逸少，人造異向性岩體製作及其力學性質(I)，行政院國家科學委員會專題研究計畫成果報告，NSC-84-2611-E-008-004(1995)。
(2).田永銘、許宗傑、陳慶洪，人造異向性岩體製作及其力學性質(II)，行政院國家科學委員會專題研究計畫成果報告，NSC 85-2211-E-008-036(1996)。
(3).胡廷秉，「超音波儀器之組裝及異向性岩石之超音波特性」，碩士論文，國立交通大學土木工程系，新竹(1995)。
(4).馬正明，「單軸壓力對岩石材料波傳速度的影響」，碩士論文，國立台灣大學土木工程系，台北(1987)。
(5).黃宗義，「人造互層岩體之組成率及破壞準則」，碩士論文，國立中央大學土木工程系，中壢(1994)。
(6).黃純夫，品質檢測技術與校正實務非破壞檢測應用，中華民國品質管制學會，台北(1996)。
(7).陳志賢，「RC構件之三維斷層掃描與理論驗證」，碩士論文，國立中央大學土木工程系，中壢(2005)。
(8).陳永增、鄧惠源，非破壞檢測，全華科技圖書股份有限公司，台北，(2004)。
(9).馮若，超聲手冊，南京大學出版社，南京(1999)。
(10).游漢輝、劉叔平、焦修理、周其宇，實用普通物理，台灣商務圖書館，台北(1975)。
(11).楊政穎，「鋼筋混凝土構件掃瞄斷層掃描之顯像處理」，碩士論文，國立中央大學土木工程系，中壢(2003)。
(12).張家銘，「以熱探針法量測大地材料熱傳導係數之適用性」，碩甚論文，國立中央大學土木工程系，中壢(2006)。
(13).蕭弘典，「橫向等向性岩石熱傳導係數量測及誤差分析」，碩士論文，國立中央大學土木工程系，中壢(2008)。
(14).韓嵩、蔡美峰，「單軸荷載下裂隙岩體超聲波傳播速度研究」，採礦工程，第12期，第27卷，第35-39頁(2006)。
(15).Amadei, D., Rock Anisotropy and the Theory of Stress Mesasurement, Springer-Verlag, Heidelberg (1983).
(16).Asakawa, E., and Kawanaka, T., “Seismic ray tracing using linear traveltime interpolation,”Geophysical Prospecting, Vol. 41, pp. 99-111 (1993).
(17).Babuška, V., “Elastic anisotropy of igneous and metamorphic rocks,”Stud. Geph. Geod., Vol. 12, pp. 291-303 (1968).
(18).Barla, G. Rock anisotropy – Theory and laboratory testing. In: Műller L., editor. Rock mechanics, pp.131-169 (1974).
(19).Brich, F., “The velocity of compeessional waves in rocks to 10 kbrs: Part1,”J. Geophys., Res. 65, pp. 1083-1102 (1961).
(20).Habeher, C.C., and Wink, W.A., “Ultrasonic velocity measurements in the thickness direction og paper,”Journal of Applied Polymer Science, Vol. 32, pp. 4503-4540 (1986).
(21).Hakala, M., Kuula, H., and Hudson, J.A.,“Estimating the transversely isotropic elastic intact rock properties for in situ stress measurement data reduction: A case study of the Olkiluoto mica gnesiss, Finland,”International Journal of Rock Mechanics and Mining Sciences, Vol. 44, pp. 14-46 (2007).
(22).Holub, K., Jr, P.K., and Knejzlík, J.,“Investigation of the mechanical and physical properties of greywacke specimens,” International Journal of Rock Mechanics and Mining Sciences, Vol. 46, pp. 188-193 (2009).
(23).Kahraman, S., “A correlation between P-wave velocity, number of joints and Schmidt hammer rebound number,”International Journal of Rock Mechanics and Mining Sciences, Vol. 38, pp. 729-733 (2001).
(24).Kahraman, S., “Estimating the direct P-wave velovity value of intact rock from indirect laboratory measurements,”International Journal of Rock Mechanics and Mining Sciences, Vol. 39, pp. 101-104 (2002).
(25).Kahraman, S., and Yeken, T.,“Determination of physical properties of carbonate rocks from P-wave velocity,”Bull. Eng. Geol. Environ., Vol. 67, pp. 277-281 (2008).
(26).Lekhnitskii, S. G., Theory of elastic of an anisotropy elastic body, Translated by P.Fern, Holden-Day Inc., San Francisco (1963).
(27).Liao, J.J., Hu, T.B., and Chang, C.W., “Determination of dynamic elastic constants of transversely isotropic rocks using a single cylindrical specimen,”International Journal of Rock Mechanics and Mining Sciences, Vol. 34, pp. 1045-1054 (1997).
(28).Liu, H.H., James, R., and Berryman, J.G., “On the relationship between stress and elastic strain for porous and fractured rock,” International Journal of Rock Mechanics and Mining Sciences, Vol. 46, pp. 289-296 (2009).
(29).Vajdová, V., Přikryl, R., Pros, Z., and Klíma K., “The effect rock fabric on P-wave velocity distrubtion in amphibolites,”Physis of the Earth and Planetary Interiors, Vol. 114, pp. 39-47 (1999).
(30).Vasconcelos, G., Lourenço, P.B., Alves, C.A.S., and Pamplona, J.,“Ultrasonic evaluation of the physical and mechanical properties of granite,”Ultrasonics, Vol. 48, pp. 453-466 (2008).
(31).Vernik, L., and Nur, A., “Ultrasonic velocity and aisotropy of hydrocarbon source rocks,”Geophysics, Vol. 57, No. 5, pp. 727-735 (1992).
(32).Yasar, E., and Erdogan, Y., “Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks,” International Journal of Rock Mechanics and Mining Sciences, Vol. 41, pp. 871-875 (2004).