SEISMIC VELOCITIES FROM SURFACE MEASUREMENTS

C. Hewitt Dix 1955 Geophysics, 20(1), 68-86.

Seismic Imaging and modellingpresented by

Zacharia SHITAKWA HOIDI_16770632

Contents

Introduction Estimation of seismic interval velocity Basic Assumptions Field techniques Generalization Dix equation Other factors to consider Summary and conclusions

Introduction The purpose of this paper, Dix-1955, is the

discussion of field and interpretive techniques that can be used to accurately determine seismic interval velocity before the commencement of drilling.

Accurate velocity determination will lead to accurate structural interpretation and consequently gain some lithological information.

Dix formulation is closer to practical exploration scenario and though laborious it is sound.

It involves interpretation by successive determination of interval velocities from top layer to bottom.

Estimation of Seismic Interval Velocities

Seismic interval velocity is the average propagation velocity through a depth or time interval (Vint = ΔZi/ΔTi).

It is estimated from root-mean-square velocities (Vrms)

through the called Expanding Spread Technique (EST) Average velocity is the average of all the interval velocities

from the surface to the depth of a particular horizon.

Used with small angle approximations in the moveout formula Vrms closely predict travel times for any offset

For a single layer, it is apparent that Vnmo and Vavg are equal.

Variations from the model may cause severe problems, example dipping beds, and rapid lateral velocity changes within a layer can affect seismic velocity calculations.

Basic assumptions

1. Multiple horizontal layer medium of constant velocity known as root-mean-square velocity (Vrms)

2. Travel times related to nearly vertical incidence/ straight line ray paths Δti is one-way vertical travel-time through bed i

3. Source-receiver distances must be kept small relative to the distances to reflecting interface

Thus for short distances, we can state that Vrms = Vnmo, provided there is no dip on the beds.

4. Solution of the Dix equation assumes that the zero-offset ray paths to the (n-1)th and nth reflectors follow a common path.

Field technique

This is a natural extension of continous profiling technique.

Done using the shot combination alongside:1st shot regular symmetric split, the second linked to the first and the third to the second.

The result is a continuous tied range of distance x from O and the separation between S.P 3 and 4.

The tie link of each new record is through centre point B.

Generalization First layer

and

Where Tx , is the reflection time at x and V is the layer velocity. z is the depth.

A plot of X2-Tx2, will give a slope 1/V2 with T0 as

the intercept.Consider equation of a straight line y=mx +c

Second LayerIf we plot X2-Tx

2 , for layer 2 we obtain a hyperbola curving towards small values of Tx .

1

Generalization

Figure 1 Figure 2

We consider minimum distance and time paths

A true ray path will follow a minimum time path (SGDHF) which means that SG shorter GD longer

The solution of traveltime (ABCDE) in a multilayer model produces and equation of the infinite series form Tx

2=A+BX2+CX4+... where A is equal to To2

B obtained from the above series by differentiation of the eqn w.r.t X2

Generalization

Second layer_approach 1We need Using it, we can

determine 1 which we need for determining V2 . The derivative would give an uncertainity in the range of sin1.

We use the tangent LM to the Tx2-x2 at x1. The

eqn. of

Differentiating the tangent equation w.r.t x at x1 gives the derivative above which we manupilate to get

2

GeneralizationSecond layer

From 1, SG and FH can be computed together with the time to be removed from T (travel time through the 1st layer) to obtain the time from G to D to H. This gives TxR

Similarly, from β1, 2AG can be computed, and this can be subtracted from x to give xR .

Plotting (Tx)R2 –(x)R

2 we obtain a straight line whose eqn.

The gradient of the line gives V2 and the intercept gives the depth time (T0)R

The thickness is given as

3

4

Approach 2-Dix’s equation ABC and CDE we can

define tan 1 nd tan 2 as

Tan 1= and

Tan 2=

z1= and z2=

Using the right angle triangle theorem we arrive at

5

Dix equation

Divide through by x1+x2, and taking the limit x1+x2 0

then multiplying by we obtain the eqn.

The above equation is valid only for x values near zero,

For n layers, we can generalize equation 6 above as

and

If we get the difference in eqns. 7 we obtain

Note that and therefore

6

7

8

1V V

nn AA nAn V V

Multiples reflectionsEvery reflector produces multiples, we however easily pick

out those multiples that result from the ground-air interface and weathered layer- high velocity interface.

Must be identified and excluded from the data for accurate velocity determination

Dipping LayersFor a single dipping layer the slope of Tx

2 –X2 graph is given as

For layer 2 parameters determined by removing the effects of the first layer

CurvatureEffects of curvature are most difficult to correct, in practice

graphyical methods are employed.

Other factors to consider

Summary and Conclusions

Dix equation calculates interval velocities from average velocities assuming vertical incidence in horizontal layers and small source-receiver distances relative to the distances to the reflective interfaces.

Use x2-T2 plot to determine rms velocities to each layer to get interval layer velocities and thicknesses.

If the geology of an area is known, seismic velocities may be more easily interpreted.

RMS velocity >= Average velocity. Further calculations based on rms velocity for

arbitrary and nonuniform dipping lead to NMO velocity.

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