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Time-distance (T-X) curves Single horizontal layer. T 2 = T 0 2 + X 2 /V 2 . It is a hyperbola with apex at X = 0 and T 0 = 2H/V. V and H are the layer velocity and thickness. T 2 -X 2 plot is a straight line whose slope = 1/V 2 and intercept = T 0 2 .

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## Time-distance (T-X) curves Single horizontal layer

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**Time-distance (T-X) curvesSingle horizontal layer**• T2 = T02 + X2/V2. • It is a hyperbola with apex at X = 0 and T0 = 2H/V. • V and H are the layer velocity and thickness. • T2-X2 plot is a straight line whose slope = 1/V2 and intercept = T02. • T2-X2 plot can be used to find V and H. • Normal moveout (NMO) • the difference between traveltimes at offsets X and 0 • DTNMO (X) X2/(2T0V2) • used to flatten the T-X curve before stacking • We usually know T, T0, and X from the seismic section and we want to know V and H.**Time-distance (T-X) curvesSingle horizontal layer**DTNMO(X=1000) = T(X=1000)-T0 T(X=0)=T0 T(X=1000)**Time-distance (T-X) curvesSingle horizontal layer**• Calculating layer velocity and thickness V = (slope)-1/2 , H = T0 V/2**Time-distance (T-X) curvesSingle dipping layer**• T2 = T02 cos2 + (X+2H sin)2/V2 • : layer dip angle • T-X curve is a hyperbola with apex at Xa= -2H sin and Ta=T0cos, [T0=2H/V]. • We usually know T, T0, and X from the seismic section and we want to know , V, and H. • Dip moveout (DMO): the difference between traveltimes at offsets +X and -X divided by X • DTDMO (X) 2sin/V**Time-distance (T-X) curvesSingle dipping layer**(Ta,Xa) T0 T(X=1000) T(X=-1000) DTDMO= [T(X=1000)-T(X=-1000)]/1000**Time-distance (T-X) curvesSingle dipping layer**• Calculating layer velocity, dip, and thickness • We read Ta, T0, and DTDMO from the seismic record. • Then, we use them as follows: • cos = Ta/T0 • V 2sin /DTDMO • H = V T0/2**Time-distance (T-X) curvesMultiple layers**• T-X curve is NOT a hyperbola. • It resembles a hyperbola at near offsets (X/Z < 1). • We best-fit a hyperbola to the T-X curve at near offsets. • This means that we lumped the multiple layers into one single layer. • We use the single-layer approach to find the stacking velocity. • We use Dix formula to calculate the interval velocities of the layers. • We use the interval velocities and vertical traveltimes to calculate the layer thicknesses.**Time-distance (T-X) curvesMultiple layers**T01 T02 T03**Time-distance (T-X) curvesMultiple layers**• Calculating layer interval velocities and thicknesses • Compute stacking velocities from T2-X2 curves Vsi: stacking velocity to the bottom of the ith layer Vs1 = (slope 1)-1/2 , Vs2 = (slope 2)-1/2 , Vs3 = (slope 3)-1/2 • Compute layer interval velocities using Dix formula V1 = Vs1, V2 = {[Vs22 T02 - Vs12 T01]/(T02 - T01)}1/2, V3 = {[Vs32 T03 - Vs22 T02]/(T03 - T02)}1/2, • Compute layer interval thicknesses H1 = V1 T01/2 H2 = V2 (T02 - T01)/2 H3 = V3 (T03 - T02)/2

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