Seismic Refraction Method: A Technique for Determining the Thickness of Stratified Substratum

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1 Amerian Journal of Applied Sienes 0 (8: , 0 ISSN: O. Anomohanran, his open aess artile is distributed under a Creatie Commons Attribution (CC-BY.0 liense doi:0.844/ajassp Published Online 0 (8 0 ( Seismi Refration Method: A ehnique for Determining the hikness of Stratified Substratum Ohuko Anomohanran Department of Physis, Faulty of Siene, Delta State Uniersity, Abraka, Delta State, Nigeria Reeied , Reised ; Aepted ABSRAC he seismi refration surey is a ery important geophysial tehnique used in the inestigation of subsurfae harateristis. his is why this study was arried out to emphasize the ability of the seismi refration method in determining the thikness of stratified layers of soil and rok. he results obtained are generalized expressions that relate trael time, offset distane, eloity and thikness of subsurfae layers. Keywords: Seismi Refration, Diret Arrials, Geophones, Seismograph. INRODUCION he seismi refration method is one geophysial tehnique whih is frequently used to determine the harateristis of soils and roks (Ugwu, 008; Ayolabi et al., 009. Seismi refration finds appliation in the determination of rok ompetene for engineering appliation, depth to bedrok, groundwater exploration, rustal struture and tetonis (Kilner et al., 005; Asokhai et al., 008; Varughese et al., 0; Chiemeke and Aboh, 0. he seismi refration method is based on the measurement of the trael time of seismi waes refrated at the interfaes between subsurfae layers of different eloity (Ayolabi et al., 009. he seismi signal is introdued into the subsurfae ia a shot point using explosies, hammer blow, dropped weight or an elasti wae generator (Igboekwe and Ohaegbuhu, 0. he energy generated either traels diretly through the upper layer (diret arrials, or trael down through the arious layers before returning to the surfae (refrated arrials. he energy is then deteted on surfae at a series of reeiers alled geophones spaed at regular interals (Anomohanran, 0. After a ertain distane from the shot point, known as the ross oer distane, the refrated signal is obsered as a first 857 arrial signal at the geophones (arriing before the diret arrial. Both ompressional waes (P-waes whih proide depth information of interfaes and Shear waes (S-waes whih proide additional data about engineering properties of the subsurfae media an be used in the seismi refration method (Ayolabi et al., 009; Igboekwe and Ohaegbuhu, 0; Gabr et al., 0. In seismi refration method, the signal from the shot returns to the surfae by refration at subsurfae interfaes and is reorded at distanes muh greater than the depth of inestigation (Igboekwe and Ohaegbuhu, 0. he method relies on the tendeny of aousti eloities to inrease with depth, whih sometimes makes it insensitie to low eloity layers in the subsurfae. Based on the analysis of the field data, the seismi sureyor draws a profile showing the thikness of the subsurfae and a good idea of what materials they onsist of (Ayolabi et al., 009; Okiongbo et al., 0; Igboekwe and Ohaegbuhu, 0; Varughese et al., 0; Gabr et al., 0. Seismi refration surey uses the proess of ritial refration to infer interfae depths and layer eloities. he data are usually presented as ross setional plots representing P-wae path, eloities and depths to arious interfaes. he reason for this study is to present the field and data analysis proedure of the seismi refration

2 Ohuko Anomohanran / Amerian Journal of Applied Sienes 0 (8: , 0 method and present its ability to determine the thikness of subsurfae layers of the earth. his study will obtain the mathematial expression relating time of arrial of the waes, distane between soure and geophones, eloity and depth of arious layers... Mathematial Consideration he refration surey gies rise to first arrial signals whose time are piked up from a seismogram and plotted as trael time ures (Igboekwe and Ohaegbuhu, 0. he interpretation of the seismi signal is therefore set to determine the interfae depths and layer eloities. his will be arried out in stages... wo Layered Subsurfae Here we onsider a two layer horizontal stratified substratum as shown in Fig. where x is the offset distane from the energy soure to the geophone. is the thikness of the first layer, V is the signal eloity in the first layer and V is the signal eloity in the seond layer. he path of the energy signal is defined as SABG (Fig. Using Fig., we onsider the wae SA whih hits the layer boundary at the ritial angle θ. he total trael time for the refration signal to trael from the soure S to the geophone G is expressed as Equation : SA + AB + BG ( Whih an also be expressed as Equation : SA AB BG + + ( z From Fig., we dedue that SA BG os θ and AB x tan θ Hene we write that Equation and 4: z x tanθ z + + osθ osθ z x tanθ + osθ his an be re-arranged to gie: x sinθ + osθ osθ ( (4 (5 858 Aording to Snell s law, V sinθ V while the relations Sin θ + Cos θ. We an express Equation 5 as Equation 6: x + [ sin θ] osθ x osθ (6 + (7 Equation 7 represents the time taken by the wae to trael to the bedrok and bak to the geophone. he time distane ure produes two segments with different slopes as shown in Fig.. he trael time ures as shown in Fig. is used to determine the eloities of the two layers. From Fig., the slope of the first part gies / and the slope of the seond part gies /. he inerse of slopes gies us the eloities of the subsurfae (Igboekwe and Ohaegbuhu, 0. he ritial distane (x is the point on the surfae at whih the diret wae and the head wae arried simultaneously. Before the ritial distane, the diret waes arrie first while beyond the ritial distane, the head wae arries first. Aording to Fig., t is the interept of the seond segment of the straight line graph. With all the neessary information obtained from the plot, the depth of the first layer is obtained to be Equation 8: t.. hree Layered Subsurfae (8 he ase of a three layered horizontal subsurfae is as shown in Fig.. he interpretation of the three layered subsurfae is based on the understanding that: he time signals are the diret arrials in the first layer of thikness Critial refration with angle θ takes plae at top of the third layer We shall again onsider the wae whih leaes the shot point S and traelled through the path SA, AB, BC, CD and DG. he total trael time from the soure S to the geophone G is expressed as Equatin 9: SA + AB+ BC + CD + DG (9

3 Ohuko Anomohanran / Amerian Journal of Applied Sienes 0 (8: , 0 z Following from the fat that osθ and: SA z osθ AB We an dedue that: And: SA z DG osθ Fig.. A two layer horizontal stratified substratum AB z CD osθ Sine BC X tan θ - tan θ : BC X z tanθ z tanθ Hene Equation 0 beomes Equation and : z z X z sinθ z sinθ + + osθ osθ osθ osθ ( X z sinθ z sinθ + + osθ osθ ( Fig.. rael-ime graph for two layer surfae x + sinθ + θ osθ osθ ( Sine sin θ,sin θ and Sin θ + Cos θ Equation beomes: x z osθ z osθ + + (4 Fig.. A three layered horizontal stratified substratum Whih again is expressed as Equation 0: he plot of the trael time against the offset distane gies a straight line graph with three segments as shown in Fig. 4. he time interepts t and t as shown in Fig. 4 an be obtained and used to determine the thikness of the different layers of soil or rok. Using Equation 4, the time t and t are expressed as: SA AB BC CD DG (0 z osθ t 859

4 Ohuko Anomohanran / Amerian Journal of Applied Sienes 0 (8: , 0 he time signals are the diret arrials in the first layer of thikness Critial refration with angle θ also takes plae at top of the fourth layer We shall again onsider the wae whih leaes the shot point S and traelled through the path SA, AB, BC, CD, DE, EF and FG. he total trael time from the soure S to the geophone G is expressed as Equation 9: SA + AB + BC + CD + DE + EF + FG (9 Whih again is expressed as Equation 0: Fig. 4. rael-time graph for three layered subsurfae And: z osθ t Whih transforms to gie Equation 5 and 6 respetiely: / z ( t (5 And: / z ( t (6 SA AB BC CD DE EF FG (0 V V V V V V V 4 Following the same steps as in the ase of the three layers subsurfae, we hae Equation to : z z z x osθ osθ osθ 4 z sinθ z sinθ z sinθ osθ osθ osθ x z sinθ z sinθ 4 osθ 4 osθ z sinθ osθ 4 ( ( Using Equation 5 and 6, the thikness of the different layers are determined as Equation 7 and 8: t / ( (7 X z V z + sinθ + V V os V V os 4 θ 4 θ sinθ + sinθ 4 osθ 4 ( t / (.4. Four Layered Subsurfae (8 he ase of a four layered horizontal surfae is as shown in Fig. 5. he interpretation of the four layered subsurfae is based on the understanding that: 860 Whih redues to Equation 4: X osθ osθ osθ (4 V4 V V V he plot of the trael time against the offset distane gies a straight line graph with four segments as shown in Fig. 6.

5 Ohuko Anomohanran / Amerian Journal of Applied Sienes 0 (8: , 0 Fig. 5. A four layered horizontal stratified substratum / ( (8 / ( (9 4 / (4 (0 Fig. 6. rael-ime graph for three layered subsurfae he time interepts t, t and t are read from the plot and their alues used to determine the thikness of the subsurfae layers. he mathematial expressions are written as Equation 5 to 7: / z (V V t (5 V V / z (V V t (6 V V / z (V4 V t (7 V V 4 Hene the thikness of the subsurfae beomes Equation 8 to 0: Multi-Layered Subsurfae he multi-layered subsurfae is onsidered as a many plane horizontal layer as shown in Fig. 7. he ray shown is refrated ritially at the top of the n th layer with speed V n. herefore, in determining the total trael time for a multi-layered subsurfae, we onsider the expressions in Equations 7, 4 and and generalize the interfae trael time Equation as: X osθ n i i + ( Vn i Vi Where: n he number of layers, θ i he angle of inidene at the i th interfae i he depth at the base of a layer of eloity V i he generalized depth equation of the subsurfae layers is also obtained after onsidering Equation 8, 7, 8, 8, 9 and 0 as Equation : i i i + i / (Vi +! V i (

6 Ohuko Anomohanran / Amerian Journal of Applied Sienes 0 (8: , 0 Fig. 7. A multi-layered horizontal stratified substratum. CONCLUSION his study has highlighted the mathematial relations inoled in determining the thikness of the arious subsurfae in a seismi refration surey. A generalized equation for the determination of both the total trael time and thikness of the subsurfae layers were obtained in this study. he results obtained are useful expressions of the physial parameters in the refration interpretation.. REFERENCES Anomohanran, O., 0. Geophysial interpretation of seismi refletion data obtained from Umureute and Amiynaibo area of Delta state. Nigeria, Nigerian J. Si. Eniron., : Asokhai, M.B., J.C. Egbai and E.C. Okolie, 008. Using shallow refletion seismology for mapping bedroks. Nigeria J. Si. Eniron., 7: Ayolabi, E.A., L. Adeoti, N.A. Oshinlaja, I.O. Adeosun and O.I. Idowu, 009. Seismi refration and resistiity studies of part of Igbogbo township, south-west Nigeria. J. Sient. Res. De., : 4-6. Chiemeke, C.C. and H.O. Aboh, 0. Delineation of aquiferous layers within the basement omplex using joint inersion of seismi refration tomography and high resolution D seismi refletion surey. Arh. Applied Si. Res., 4: Gabr, A., A. Murad, H. Baker, K. Bloushi and H. Arman et al., 0. he use of seismi refration and eletrial tehniques to inestigate groundwater aquifer, Wadi Al-ain, United Arab Emirates (UAE. Proeedings of the International Conferene on Water Resoures and Wetlands Sept. 4-6, ulea-romania, pp: Igboekwe, M.U. and H.E. Ohaegbuhu, 0. Inestigation into the weathering layer using up-hole method of seismi refration. J. Geol. Min. Res., : Kilner, M., L.J. West and. Murray, 005. Charaterisation of glaial sediments using geophysial methods for groundwater soure protetion. J. Applied Geophys., 57: DOI: 0.06/j.jappgeo Okiongbo, K.S., E. Akpofure and E. Odubo, 0. Determination of aquifer protetie apaity and orrosiity of near surfae materials in Yenagoa ity, Nigeria. Res. J. Applied Si., Eng. eh., : Ugwu, S.A., 008. Determination of depth to bedrok in Afikpo synline of the Benue rough, Nigeria, using seismi refration methods. Sient. Afr. Varughese, A., P. Kumar and N. Kumar, 0. Seismi refration surey a reliable tool for subsurfae haraterisation for hydropower projets. Proeedings of Indian Geotehnial Conferene, De. 5-7, Kohi, pp:

Pre-Critical incidence

Pre-Critical incidence Seismi methods: Refration I Refration reading: Sharma p58-86 Pre-Critial inidene Refletion and refration Snell s Law: sin i sin R sin r P P P P P P where p is the ray parameter and is onstant along eah