1. Introduction. Lab 4 - Geophysics 424, October 29, One-dimensional Interpretation of Magnetotelluric Data

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1 Lab 4 - Gephysics 424, Octber 29, 2018 One-dimensinal Interpretatin f Magnettelluric Data Lab reprt is due by 5 p.m. Nvember 5, 2018 All late reprts require a valid reasn t be accepted. Include answers t all questins, required figures, and all MATLAB cdes. All wrk and MATLAB scripts shuld be yur wn riginal wrk. D nt cpy smene else's cde. D nt use MATLAB scripts frm ther classes in this curse, unless tld t d s. All lab material can be dwnladed frm the class webpage at: 1. Intrductin In this lab yu will be using the MATLAB cde yu wrte in Lab 3 t mdel and interpret bradband MT data which were cllected during field schl in 2010 (in suthern Alberta). Each statin was left t recrd fr abut 12 t 24 hurs. There are fur MT sundings yu will mdel. The shrtest perids sample the cnductive Western Canada Sedimentary Basin (WCSB), while the lngest perids sample electrical resistivities f the lithsphere and asthensphere bundary (LAB). The majrity f the perid range samples the lithsphere, the rigid prtin f the earth that sits abve the weaker asthensphere. The lithsphere belw suthern Alberta is part f the Nrth American cratn. The Nrth American cratn has been pieced tgether thrugh ancient subductin and cntinental cllisins, much f which ccurred in Precambrian times. The lcatin f these MT sundings, in suthern Alberta, sits abve a piece f Archean age cratn, pieced tgether during Paleprterzic times and the creatin f Laurentia. The crystalline prtin f the lithsphere in Suthern Alberta is hidden belw the relatively thin WCSB. The crystalline cratn belw the WCSB represents the extensin f the Canadian Shield frm the east, which cntinues t extend as far west as the Rcky Muntain Trench in B.C. In the MT sundings that yu will mdel, the Canadian Shield rcks cnstitute the tp f a layer whse electrical character is ften quite hmgenus dwn t the asthensphere (althugh this is nt always true). The Mh discntinuity is ften difficult t distinguish in the electrical sundings, but has been identified in places such as nrthern Canada (see Jnes & Fergusn, 2001 fr a discussin n the electric Mh). The electrical resistivity can be an indicatin f lithlgy, but since a small amunt f intercnnected fluids can change the bulk resistivity f a rck very significantly (ie: Archie s law), the fluid cntent is ften a larger cntrl n measured electrical resistivity. Remember that the lithsphere and asthensphere are defined n the basis f their mechanical prperties. The crust and mantle have different chemical cmpsitins. 1

2 Lab 4 - Gephysics 424, Octber 29, Describe tw assumptins in ne-dimensinal magnettellurics. When wuld a 1-D apprach be valid? 1.2 Prvide a cmpsitinal and physical explanatin f the main layers we are interested in (lithsphere, asthensphere, crust, and mantle). Explain the difference between the Mh and the LAB. What electrical resistivity cntrast is expected at the Mh? At the LAB? 1.3 What perid f electrmagnetic signal is required t image 200 km belw the surface (i.e. the LAB), assuming an average resistivity f 100 Ωm? Wuld an vernight recrding (12 hrs) be sufficient t btain an accurate estimate f apparent resistivity fr this perid? 2. 1D MT Frward Mdeling Use the frward mdeling MATLAB cdes yu wrte in Lab 3 and mdify as required. Reminder: ensure yur plt shws apparent resistivity, phase, and the resistivity mdel, using subplt. Use the perids frm the data files. Plt perid in secnds alng the hrizntal axis. Include all labels, units, titles, and a legend. Scale yur plts apprpriately t shw the data. Use the stairs functin fr pltting the resistivity mdel (makes steps between layers). Use the errrbar functin t plt errr bars n the apparent resistivity and phase plts. Use the errrs fund in the data files. Include the RMS misfit in the plt. Calculate the rt mean square (RMS) misfit using the equatin belw: RMS misfit = 1:N ρ dat ρ calc ρ errr 2 + φ dat φ calc 2 2N φ errr ρ dat measured apparent resistivity ρ errr errr in apparent resistivity measurement φ calc calculated mdel phase angle N number f rh (r phase) data pints ρ calc calculated mdel apparent resistivity φ dat measured phase angle φ errr errr in phase angle measurement 2

3 Lab 4 - Gephysics 424, Octber 29, Include yur full MATLAB frward mdeling script. 2.2 Fit all fur MT sundings with an RMS misfit value less than 1.6 (these are fund in the *.txt files within the data flder). This is dne by creating mdel text files similar t thse used in Lab 3. Use yur MT1D cde t calculate the data frm yur created mdel, then cmpare t the bserved data. Ensure yu use enugh layers, but nt t many (n mre than 5 layers), and that they are bth shallw and very deep (hint: think abut depth t the WCSB and LAB). Yu can use the values in md_sample.txt t start. Include yur plts (similar t Figure 1). 2.3 Save yur fitted mdels as text files and include them with yur reprt. 2.4 Nte that there is sme nise in the data, especially at the lngest perids. Can yu think f a reasn why? Fig 1: Example f frward mdeling cde pltting results. PART 3: Displaying Mdels as Crss Sectin 1. Write a MATLAB script t plt the fur mdels yu generated as a clr image. The hrizntal axis shuld be prfile distance, and the vertical axis shuld be depth. Nte that there will be sme vertical exaggeratin, as the greatest depth is much larger than the prfile length. Here are sme guidelines: 3

4 Lab 4 - Gephysics 424, Octber 29, 2018 Use the pclr functin in Matlab [pclr (X,Y,C) fr X=distance vectr, Y=depth vectr, C=resistivity matrix]. See Figure 2 fr an example. Include a resistivity clrbar. Please use red fr cnductive and blue fr resistive (use greyscale if printing in black/white). Use lg10 resistivity values t emphasize the cntrasts. Use the apprximate distances between statins in Figure 2 fr yur crss sectin. Depth shuld be shwn in metres r kilmetres, but d nt use a lgarithmic scale. D nt interplate! Layers shuld be discrete. Hint: start with a matrix f NaN (using the functin NaN ) which will plt as white in pclr. Using zeres will give yu an incrrect slid clur (ie: red). Then insert each 1D resistivity sunding int the matrix at the crrect distance alng the prfile (see Fig 2; a31, s02, s03, a30, with 2km, 1km, 4km spacings) Yu need t put each 1D sunding nt a cmmn depth array, s that each rw in yur pltted matrix crrespnds t the crrect depth fr each sunding. Ensure that yu keep the discrete nature f the mdels! Fig 2: Example crss sectin f the fur 1-D resistivity mdels. Make sure t include a clrbar and prperly labeled axes. Map n right f the 2010 field schl data. 3.1 Include yur full MATLAB script. 3.2 Include tw crss-sectins: ne shwing nly the shallw structure (tp ~5km, which is the sedimentary basin) and ne shwing all mdel layers. 4

5 Lab 4 - Gephysics 424, Octber 29, 2018 PART 4: Crss Sectin Interpretatin Yur crss-sectins shuld shw tw main areas f interest: Small scale structure within the sedimentary basin (scale <5 km) Large scale structure defining the lithsphere beneath suthern Alberta (scale ~200km) 4.1 Lking at the large-scale crss-sectin, identify the main layers belw the sedimentary basin, and explain what the electrical sundings shw deep belw the subsurface. Reference these layers t knwn layers in the Earth, and cmment n hw these depths cmpare t glbal averages. 4.2 Des the depth t the asthensphere match glbal averages, if nt, can yu think f a reasn why? See Eatn et al. (2009) fr a discussin n the lithsphere-asthensphere bundary belw cratns. 4.3 Can yu see the Mh in yur crss-sectin? Explain in detail why r why nt? At what depth wuld yu expect t find the Mh in this area? See Jnes & Fergusn (2001) fr a discussin n the electrical Mh. 4.4 Cmpare and cntrast the advantages f varius gephysical methds t identify the lcatin f the LAB and the Mh beneath Alberta. See Buzidi et al. (2002) fr a discussin n the structure f the crust belw Alberta. 4.5 Cmment n any changes in depth and resistivity yu see alng the prfile. D the layer depths and resistivities match frm statin t statin? D yu think these changes are reasnable and real? If nt, why? Discuss data and mdeling limitatins. 4.6 Next lk at the electrical structure f the sedimentary basin. Describe hw the basin changes ver the length f the prfile in terms f depth and resistivity character. It is difficult t make a gd interpretatin withut any ther infrmatin, but try t make inferences n what brad changes in the sedimentary basin culd be causing these changes. 4.7 T help yur explanatins, illustrate yur interpretatin by drawing a crss sectin sketch including the basin and much deeper structure. This des nt need t be t scale but please be detailed and clear. Label apprximate depths and distances. Use labels t relate the resistivity measurements t the gelgy. References Buzidi, Y., Schmitt, D. R., Burwash, R. A., & Kanasewich, E. R. (2002). Depth migratin f deep seismic reflectin prfiles: crustal thickness variatins in Alberta. Canadian Jurnal f Earth Sciences, 39(3), Eatn, D. W., Darbyshire, F., Evans, R. L., Grütter, H. S., Jnes, A. G., & Yuan, X. (2009). The elusive lithsphere asthensphere bundary (LAB) beneath cratns. Liths, 109(1-2), Fischer, K., Frd, Abt, & Rychert. (2010). The Lithsphere-Asthensphere Bundary. Annu. Rev. Earth Planet. Sci. di /annurev-earth Jnes, A. G., & Fergusn, I. J. (2001). The electric Mh. Nature, 409(6818),