12 Depth

7/21/2019 12 Depth

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12.1

Depth Conversion

Depth Conversion

of Time

Interpretations

~

Volume Models

Depth Conversion

Based on the different types of velocity models that can be

derived from well data produce a ranked list of approaches

to depth conversion with the simplest, least accurate at the

top and most accurate at the bottom.

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12.2

Depth Conversion

Long Period Static Anomalies

No LVL Static CorrectionBefore we begin depth conversion

it is necessary to recognise, and

correct, any long wavelength static

anomalies in the time data.

These anomalies will probably be

seen in the times sections, time

map(s) and possibly the stacking

velocity sections or maps. The

problem and solution was first

discussed by Booker et al, 1976,then by Pickard 1992, Musgrove

1994 and Armstrong et al 2001.

After Musgrove, 1994, Time Variant Statics

Corrections During Interpretation, Geophysics v. 59,

no. 3, p. 474.

Depth Conversion


The time delay due to near

surface anomalies is estimated

from the regional – residual

separation of time delays on

shallow reflectors. For deep

anomalies it may be estimated

from well depths and velocities.

The width of the time distortion

at the target horizon is derived

from the width of the velocity

anomaly, its depth and the

target horizon depth. Fresnel

zone effects are often ignored.

From Armstrong et al, 2001, Removal of overburden

velocity anomaly effects, Geophysical Prospecting v.49, no. 1, p. 79.

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12.3

Depth Conversion


The technique then simulates

the CMP stack at the target

horizon by modelling the time

delay on each of the traces in

the CMP gather with respect to

distance along the seismic line.

This step requires a knowledge

of the mute pattern at the time

of stacking velocity analysis

(just as the bias correction did).


velocity anomaly effects, Geophysical Prospecting v.

49, no. 1, p. 79.

Tx2 = To

2 + x2 / VRMS2 - x4(VRM4

4 - VRMS4) / 4 To

2 VRMS8

with

VRM44 = Σ VIi

4ti / to.

Depth Conversion

Long Period Static AnomaliesThe time delay on the

stacked traces (the

required correction) is

then found from the

time axis intercept of a

least squares best fit

trend line of the time

delay on the different

traces in the CMP

gather plotted against

the offset squared.


velocity anomaly effects, Geophysical Prospecting v.

49, no. 1, p. 79.

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12.4

Depth Conversion

Ranked Methods for FunctionsThe least accurate methods are at the top and most accurate at the bottom.

1. Constant average velocity.

2. Mapped average velocity.

3. Average velocity function.

4. Instantaneous velocity function.

5. Instantaneous velocity function with mapped parameter.

6. Constant interval velocities.

7. Mapped interval velocities.

8. Interval or instantaneous velocity functions.

9. Interval or instantaneous velocity functions with oneparameter mapped.

10. Interval or instantaneous velocity functions with all

parameters mapped.

Depth Conversion

0

2

4

T (

s e c )

5000 Vi (ft/sec) 20,000

1

Depth conversion may use a

single velocity function from

the surface down to the layer

of interest.

• Fast

• Less accurate

An average velocity functionor an instantaneous velocity

function.

One Function

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12.5

Depth Conversion

One Function

Time

Map

Velocity

Function

Depth

Map

Velocity

Map

Depth conversion process

One Function

Depth Conversion

Time Depth

Apparent closed area depends of choice of contour

interval with respect to spill points in flat areas.

Constant Average Velocity

After Marsden, Layer cake depth conversion, Leading Edge, January 1989.

One Function

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12.6

Depth Conversion

The structure in depth

map based on well control

fails to represent the true

structural picture.

The well data is used to

provide a constant average

velocity based on a time

depth plot.

Example after Laurtent Moinard, Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data : a CaseHistory, in Geostatistical Case Studies, G. Matheron and M. Armstrong (editors) 1987, D. Reidel Publishing Co.

Constant Average Velocity with External Drift

One Function

Depth Conversion


Example after Laurtent Moinard, Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data : a Case

History, in Geostatistical Case Studies, G. Matheron and M. Armstrong (editors) 1987, D. Reidel Publishing Co.

Structure in time map;

plenty of detail due to

abundant seismic control.

This map is used to derive

the semivariogram. A

plane least squares

surface was used as thedrift so that the

semivariogram is derived

from time residuals.

One Function

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12.7

Depth Conversion

The depth map produced

from the time surface

using the constant

average velocity and the

semivariogram. This depth

map follows the shape of

the time map but departs

from it in the vicinity of the

well locations where it

matches the measured

depths.

Example after Laurtent Moinard, Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data : aCase History, in Geostatistical Case Studies, G. Matheron and M. Armstrong (editors) 1987, D. Reidel Publishing Co.


One Function

Depth Conversion

Summary - Single Function

Leman field with production platforms

25 km

Depth conversion by

a single function is

well suited to areas

with dense well

control and simple

structure.

One Function

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12.8

Depth Conversion

Single FunctionIn the marine environment we may be tempted to use a single layer

for depth conversion when the water layer appears to be relatively

uniform and the depth to the first interface appears to be relatively

deep. There is one anomalous well data point.

Top Sele

5950

6000

6050

6100

6150

6200

6250

6300

6350

0.88 0.9 0.92 0.94One Way Time sec

T V D S S

f t

Depth Conversion

Multiple Functions

In the marine environment if we separate out the water layer from

the underlying Tertiary we will obtain a much better function. The

figure shows the same formation as the previous slide with the

water layer removed. The scatter is reduced to give a better result.Undifferentiated Tertiary

5450

5500

5550

5600

5650

5700

5750

5800

5850

5900

0.780 0.790 0.800 0.810 0.820 0.830 0.840 0.850

Isochron sec

i s o p a c h

f t

7/21/2019 12 Depth


12.9

Depth Conversion

0

2

4

T ( s

e c )

5000 Vi (ft/sec) 20,000

1

A multi-layer approach

should be used in areas

where the overburden

displays lateral velocity

inhomgeneities, i.e. the

velocity structure is not

simple. Each of a number of

layers are then represented

by different functions.

• Slower

• Increased accuracy ?

Multiple Functions

Multiple Functions

Depth Conversion

Multiple FunctionsTime

Maps

Isochrons Velocity

Functions

Isochores Depth

Maps

Average

Velocity

Maps

L a y e r s

Depth conversion process

Multiple Functions

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12.10

Depth Conversion

Time to upper surface

Multi-Layer Example

From a Sattlegger brochure

Multiple Functions

Depth Conversion

Depth to upper surface

Multi-Layer Example


Multiple Functions

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12.11

Depth Conversion

Map of Vo coefficient

from Faust’s equation

Vi = Voz1/n (n=3)

Multi-Layer Example


Multiple Functions

Depth Conversion

Map of Vo coefficient

after smoothing with a

16th order polynomial

Multi-Layer Example


Multiple Functions

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12.12

Depth Conversion

Time to lower surface

Multi-Layer Example


Multiple Functions

Depth Conversion

Lower surface depth

converted using

Vi = Voz1/n (n=3)

Multi-Layer Example


Multiple Functions

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12.13

Depth Conversion

Integration

Analytic

functions

Depth

conversion

Interval,

average,

instantaneous

Macro-velocity

modelDepth maps

Seismic

horizontimes

Velocity log

Sonic logCheckshot

or VSP

Z.O. or image ray

modelling

Compare

Velocity

Maps

Multiple Functions

Depth Conversion

Summary - Multiple Functions

Depth conversion by multiple

functions is well suited to

areas with moderate well

control and moderate

structural complexity.

The functions will account for

vertical gradients and rapidlychanging bed thicknesses.1 km

When we have little well control then we have to make use of

seismic velocities to interpolate the well velocities.

Multiple Functions

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7/21/2019 12 Depth


Depth Conversion

You have to recommend a well on the structure seen at about 1.7 secs., on theaccompanying seismic section. This is a wildcat area with few wells having been

drilled. Make your depth prognosis using the function VA = 5000 + 2500t where t is the

one way time in seconds.

This function comes from good scout information which you trust. Your supervisor is

not so comfortable however and wants you to give an estimate of the error in your

depth conversion.

Make an initial guess at how accurate you think your depth prognosis is.

List the potential sources of error and assign estimates to the magnitude of each.

Exercise 12.1

12.15

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Depth ConversionExercise 1

12.16

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12.17

Depth Conversion

Average Stacking Velocity

0 4 8 miles

C.I. = 100 m/s

D a t a c o ur t e s y of A m o c o ( U.K . ) E x . C o.

Depth Conversion

of Time

Interpretations

~

Grid Models

Velocity Grids

Depth Conversion

How might we use seismically derived velocities for depth

conversion?

Velocity Grids

7/21/2019 12 Depth


Depth Conversion

Now suppose that no well velocity information was available to you. The

only velocity data are stacking velocity functions every 2 km along the line

and they were derived without the benefit of DMO.

What is your depth prognosis now given the two nearest stacking velocityfunctions?

Time

msec

0

152384

601

859

1401

1756

2151

2621

VS

m/s

1472

14721717

1865

2070

2317

2441

2616

3390

VIS

m/s

14721861

2102

2483

2662

2879

3283

5725

SP 253

Time

msec

0

165439

744

968

1438

1713

2045

2572

VS

m/s

1478

14781747

1891

2011

2192

2441

2677

3511

VIS

m/s

14781891

2081

2367

2525

3463

3661

5688

SP 155

How accurate do you suppose this depth conversion is?

Exercise 12.2

Note:

Dips are relatively gentle so any dip correction will probably do more harm thangood.

The data are relatively old and were probably acquired with a cable short enough

that the bias correction would make no appreciable difference to the results.

12.18

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12.19

Depth Conversion

Sparse Well ControlWhen there is only sparse

well control we usually

generate grid velocity

models from the seismic

data. By calibrating the

grids to the well velocities

we are making use of the

grids to interpolate the well

velocities.

In unexplored basins we

don’t always have any wells

to interpolate or extrapolate

from.

Velocity Grids

Depth Conversion

Substitutes

5000 10,0000

2

4

6

8

10

12

14

16 Average

Velocity

RMS

Velocity

Velocity - ft/sec

D e p t h - x 1 0 0 0 f e e t

Stacking

Velocity

Bias Corrected Models

0

1000

2000

3000

4000

5000

6000

1000 2000 3000 4000 5000 6000

Interval Velocity m/s

D e p t h m

Original ModelRay Trace + Semblance AnalysisBias Corrected

Velocity Grids

7/21/2019 12 Depth


12.20

Depth Conversion

Ranked approaches to depth conversion with seismicvelocities.

1. Kriging with seismic velocities and well velocities

* these approaches have constraints

2. Estimate average velocity from interval RMS velocities

* can be done without well control

3. Use seismic velocities to augment well data in deriving

functions

Velocity Grids

Depth Conversion

For Kriging:

From a GX Technology brochure

• Cokriging, kriging

with external drift

etc., require a good

linear correlation

between the different

parameters.

• Enough data points

are needed to

produce a

reasonable

variogram (a

minimum of 8 or 10).

• Histogram of

velocities to be

kriged should show

a normal

distribution.

Velocity Grids

7/21/2019 12 Depth


12.21

Depth Conversion

For Kriging

Stacking,

RMS or

Average

Velocity

Simple or

Common

Kriging

Smoothed

Velocity

Kriging

with

External Drift

Cross Plot

with Well

Velocities

Final

Velocity

Velocity Grids

Depth Conversion

Regional/Residual Calibration

A conventional

horizon oriented

stacking velocity

map. This map

can be smoothed

first by Kriging.

From Francis, Geostatistical Applications in Asset Valuation Uncertainty, PETEX 94.

Velocity Grids

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12.22

Depth Conversion



The variogram from the stacking velocities. The noise

seen in the map produces the large nugget.

RangeSill

Nugget

0 5000 10000 15000 20000 25000

0

250

500

750

1000

Sample Separation (m)

V a r i a n c e ( m 2 )

Velocity Grids

Depth Conversion



Well velocities co-

kriged with the drift

supplied by the

seismic velocities.

This is an average

velocity map to the

horizon of interest

that ties the wellcontrol and

honours the trends

in the seismic

velocities.

Velocity Grids

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12.23

Depth Conversion

Case History / Example

GOM: Mississippi Canyon

Calibrate Stacking Velocities with VSP Data

Create Depth Map for the 10-5 SequenceTime Horizon

QuantitativeGeosciences, LLP

Depth Conversion

Data:

• 77,000 seismic stacking velocities

X = Y = 2000 ft CDP spacing

Z (time in ms) = variable (5 – 15 picks)

• 2 wells with VSP time-velocity-depths

• 10-5 Sequence travel times 23,837 travel time values

Grid mesh: 1000 x 1000 ft


7/21/2019 12 Depth


12.24

Depth Conversion

Stacking Velocity and VSP Locations


Depth Conversion

10-5 Sequence Time Structure


7/21/2019 12 Depth


12.25

Depth Conversion

VSP Average Velocity Stacking Velocity

V S P T w o - W a y T i m e

V S P T w o - W a y T i m e

Calibration

VSP Average velocities and Stacking velocity functions at

the well locations.


Depth Conversion

Calibration

VSP Velocity VSP Velocity

C a l i b

S t a c k i n g V e l o c i t y

U n c a l i b S t a c k i n g V e l o c i t y

Calibrated and uncalibrated stacking velocity functions

Note the linear relationship between the uncalibrated velocities.


7/21/2019 12 Depth


12.26

Depth Conversion

Variograms in three directions


Depth Conversion

Deterministic Velocity Cube from Kriging


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7/21/2019 12 Depth


12.29

Depth Conversion

Kriging 1 – many wells

Stacking,

RMS or

Average

Velocity

Simple

Kriging

Smoothed

Seismic

Velocity

Cokriging

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Variogram

Time

Map

Deterministic

Depth

Map

This approach is best if the seismic velocities are noisy.

Velocity Grids

Depth Conversion

Kriging 1 – few wells

Stacking,

RMS or

Average

Velocity

Simple

Kriging

Smoothed

Seismic

Velocity

Kriging

with

External Drift

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Time

Map

Deterministic

Depth

Map

This approach is best if the seismic velocities are noisy.

Velocity Grids

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12.30

Depth Conversion

Kriging 2 – many wells

Stacking,

RMS or

Average

Velocity

Cokriging

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Variogram

Time

Map

Deterministic

Depth

Map

Will produce unreliable results with noisy seismic velocities.

Velocity Grids

Depth Conversion

Kriging 2 – few wells

Stacking,

RMS or

Average

Velocity

Kriging

with

External Drift

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Time

Map

Deterministic

Depth

Map

Will produce unreliable results with noisy seismic velocities.

Velocity Grids

7/21/2019 12 Depth


12.31

Depth Conversion

Ranked approaches to depth conversion with seismicvelocities.





3. Use seismic velocities to augment well data in deriving

functions

Velocity Grids

Depth Conversion

For Average Velocity

Stacking,

RMS

Velocity

Robust Filter,

Smooth

Interval RMS

Velocity

Calibrate to

Well Interval

Velocities

Final

Average

Velocity

Robust Filter,

Smooth

Robust Filter,

Smooth

Calibrate to

Average

Velocity

Calibrate to

Average

Velocity

Calibrate to

Well Interval

Velocities

Robust Filter,

Smooth

Interval RMS

Velocity

Calibrate to

Well Interval

Velocities

Velocity Grids

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12.32

Depth Conversion

CalibrationBefore depth conversion it is necessary to calibrate the

seismically derived velocities to the velocities measured in

the wells.

Calibration is the process of using the abundant seismic

estimates, which probably reflect regional geological

variations, to interpolate and extrapolate the sparse well

control which aliases the geological variations.

The result of calibration is that we have velocities in our

model which honour the well measurements and display thespatial sampling of the seismic data.

Velocity Grids

Depth Conversion

Calibration

The calibration is frequently performed in two steps.

The first is a regional calibration which takes care of any shift

between the trends of the two data sets.

The second is a residual calibration which accounts for the

local variations, the residuals, after the first calibration, and

ensures the wells are tied exactly.

Velocity Grids

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12.33

Depth Conversion

Regional CalibrationWe can correlate the VSP

or checkshot data to

stacking velocity (or VRMS

or V AS) functions. Linearity

is not required. Correlated

data points must relate to

the same points in the

subsurface, i.e. we need

the VRMS value at the same

travel time as the observedV A.

This approach correlates

the whole velocity volume.

Velocity Grids

Well v. Seismic Average Velocity

y = 3.7050934E-07x3 - 6.7773959E-03x2 + 4.1711981E+01x -

8.0315444E+04

4500

5000

5500

6000

6500

7000

4500 5000 5500 6000 6500 7000 7500

seismic

w e l l s

Depth Conversion

Regional Calibration

To calibrate the stacking

velocities (or VRMS or V AS) to

a particular horizon a

percentage calibration

factor is required or used

(93.35% in the example).

A percentage calibrationfactor is equivalent to a

linear trendline being fitted

to the data, which goes

through the origin.

Velocity Grids

Level 8 Interval Velocities

IntVel = 0.9335Vdix

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2000 4000 6000 8000Seismic

W e l l

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12.34

Depth Conversion

Regional CalibrationFor interval velocity the

interval stacking (or RMS)

velocities are cross plotted

against the corresponding

well velocities.

A good correlation is

usually observed but the

trend does not always go

through the origin.

Velocity Grids

Level 9 Interval Velocities

IntVel = 0.9662Vdix - 329.57

6800

7000

7200

7400

7600

7800

8000

7400 7600 7800 8000 8200 8400 8600Seismic

W e l l

Depth Conversion

Regional Calibration

After calibration the trend

does go through the origin.

The remaining scatter in

the data means that none

of the wells will be tied

exactly.

As with checkshot functionmisties these misties are a

measure of the overall

accuracy of the method.

Velocity Grids

Calibrated Average Velocities

4500

5000

5500

6000

6500

7000

4500 5000 5500 6000 6500 7000

Well

S e i s m i c

7/21/2019 12 Depth


12.35

Depth Conversion

Misties

Data from a Paradigm Geophysical brochure

After regional calibration the misties at the wells are greatly reduced.

Velocity Grids

Depth Conversion

Ranked approaches to depth conversion with seismic

velocities.





3. Use seismic velocities to augment well data in derivingfunctions – a hybrid approach

Velocity Grids

7/21/2019 12 Depth


12.36

Depth Conversion

We now have either a calibrated volume of seismically

derived velocities or a number of calibrated interval velocity

grids associated with different horizons which are used to

derive an average velocity to the horizon of interest.

Velocity functions from the calibrated volume may be treated

as additional checkshot values and used to augment sparse

checkshot data to derive analytical functions.

Velocity Grids

Depth Conversion

Determining K and V0 From SeismicGiven an estimate of the VRMS curve, obtained by the

correction of VS, estimates of analytical function parameters

can be obtained directly from the seismic data and mapped.

From Arnaud et al, K coefficient

determination of an interval velocity

law Vo + Kz from stacking velocityanalyses, EAEG-95 Workshop

“Depth Conversion”

K

V0

Velocity Grids

7/21/2019 12 Depth


12.37

Depth ConversionVelocity Grids

Determining K and V0 From Seismic

Vrms2 = [ΣVI

2.t] / [Σt] from our definitions

Vrms2 = [∫Vi

2.dt] / [∫dt] and Vi = dz / dt

Vrms2 = [∫(dz / dt)2.dt] / [∫dt]

Vrms2

= [∫(dz / dt).dz] / [∫dt]

Substitute any expression for dz/dt and integrate.

Depth Conversion

Determining K and V0 From Seismic

For a single layer model:

For Vi = V0 + Kz, VRMS2 = V0

2(e2Kt - 1)/2Kt

For Faust VRMS2 ={ nK/(n + 1)t}{(n - 1)Kt/n}[(n + 1)/(n - 1)]

For Evjen VRMS

2 ={ V0

K/(1 + n)t}{[1 + V0

(1 - n)Kt] [(1 + n)/(1 - n)] - 1}

It is therefore possible to use the corrected VRMS data to map

directly the parameters of standard analytic functions.

Velocity Grids

7/21/2019 12 Depth


12.38

Depth Conversion

Determining K and V0 From SeismicIt is also possible to use the

calibrated interval and

average velocity values as

‘checkshots’ thus permitting a

wider range of values to be

used in determining the

analytical function

parameters.

VELOCITY

D

E P T H

After Marsden et al, Leading Edge, 1995

Velocity Grids

Depth Conversion

Summary - Grid Models

Grids of seismically derived RMS velocities can be used when

we have no well control or sparse well control.

We can use kriging to smooth the generally noisy grids and tie

them to the well control. This approach usually yields better

results than the more traditional ways of smoothing the noisy

grids.

The velocities have to be calibrated in some way to well

velocities.

The velocities may also be used to augment well checkshot

data.

Velocity Grids

7/21/2019 12 Depth


12.39

Depth Conversion

Tying

the Well

Control

PGS Reservoir (U.S.) Inc. Doe Contract #DE-AC-22-94-PC 91008

Depth Conversion

Residual Calibration - Tying Well Control

We have our preliminary depth map that does not tie the

well control exactly. We have analysed our misties and

quantified the accuracy of our depth conversion.

How might we make the map tie the well control?

What are the disadvantages of the different methods?

Residual Calibration

7/21/2019 12 Depth


12.40

Depth Conversion

Tying Well ControlHow might we make the map tie the well control? What are the

disadvantages of the method?

• For multi-layer depth conversion only tie the target horizons.

Intermediate errors tend to cancel out.

• If the errors are random, distribute over an area whose radius

is half the average well spacing. Can produce bull’s-eyes at the

wells.

• Autocontour the errors. Produces unreasonable gradients and

error values outside the limits of well control.

• Kriging. Will separate trend and random components of the

errors.


Depth Conversion

One-Step Calibration - Wells


A popular approach when using checkshot data from

multiple wells:

• Fit a simple (linear?) function

• Fix all but one of the parameters

• Vary the one parameter to effect a tie to each data point

• Map the variation of the parameter

• Use the parameter grid in depth conversion

7/21/2019 12 Depth


12.41

Depth Conversion



Keep the slope K constant and derive a Vo for each data

point..

0 100 200 300 400 500

One Way Time (msec)

1600

1700

1800

1900

2000

Fit used

Slope (K) = 0.73

I n t e r v a l V e l o c i t y ( m / s e c )

Data courtesy of Amoco

Depth Conversion



Map of Vo from

previous plot

What are the advantages and disadvantages of this

approach to macrovelocity model building?

10 Miles

1600

1700

1800

1900

CI = 50 m/secData courtesy of Amoco

7/21/2019 12 Depth


12.42

Depth Conversion

One-Step Calibration - Seismic

Average Stacking Velocity

The regionally

calibrated seismic

velocities display

variations of geological

significance even

though they do not tie

points of well control

with the desired

accuracy.

0 4 8 miles

C.I. = 100 m/s



Depth Conversion

0 4 8 miles

C.I. = 100 m/s

Average Velocity from Wells

Velocity maps based

on well control will tie

the wells, more or less

exactly depending on

the contouring

algorithm, but alias the

geological trends.

D a t a c o ur t e s y of

A m o c o ( U.K . ) E x . C o.



7/21/2019 12 Depth


12.43

Depth Conversion

0 4 8 miles

C.I. = 2 %

Calibration Factor

The calibration factor or

residual is determined at

each well control point.

These values are then

gridded to determine the

values to be applied to the

seismic grid.

Note that steep gradients

can be introduced whichmay not be geologically

reasonable.

D a t a c o ur t e s y of A m o c o

( U.K . ) E x . C o.



Depth Conversion

0 4 8 miles

C.I. = 100 m/s

Calibrated Average Velocity

The calibrated interval

velocity map ready for

use in depth conversion.

This map ties the well

control and honours the

trends seen in the

seismic data.

Kriging can be used

instead of this traditional

approach.




7/21/2019 12 Depth


12.44

Depth Conversion

Gridding the calibration

factor or residual from

each well control point can

produce undesirable

trends and steep gradients

when dissimilar values

occur in closely spaced

wells.

Data from a Paradigm Geophysical brochure


One-Step Calibration

Depth Conversion

Random Errors

When the residuals are small and

random then the errors are

dispersed over an area with a

radius of up to one half the

average inter-well spacing. This

approach is only acceptable when

there is no spatial correlationbetween the residuals.


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12.45

Depth Conversion

Random Errors


Mistie grid.

Mistie values

when flexing

surface over too

small a radius

around wells.

Depth Conversion

Random Errors


Tied map.

When the radius

of flexing is too

small then the

circular nature of

the flexing will

show in the finalmap.

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12.46

Depth Conversion

Random Errors


Mistie grid.

Mistie values

when flexing

surface over a

distance of about

half the average

well spacing.

Depth Conversion

Random Errors


Tied map.

The circular

nature of the

mistie contour

values does not

show up.

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12.47

Depth Conversion

Random Errors


Mistie grid.

Minimum

curvature gridding

with bicubic

interpolation

of mistie values.

The extrapolation

is geologicallyunreasonable.

Depth Conversion

Random Errors


Mistie grid.

Inverse distance

weighted gridding

with bicubic

interpolation

of mistie values.

Produces almostexactly the same

correction grid as

the previous

example.

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12.48

Depth Conversion

Kriging A semivariogram of the residuals

is a powerful tool that will find

any spatial correlation.

Kriging residuals results in a

calibration grid or error grid that

shows both any remaining -

possibly undetected - trend and

the true random residual error.

The effect is a series of bulls-

eyes in a regional smooth trend.


Depth Conversion

A semivariogram of the residuals

is a powerful tool that will find

any spatial correlation.

Kriging residuals results in a

calibration grid or error grid that

shows both any remaining -

possibly undetected - trend andthe true random residual error.

The effect is a series of bulls-

eyes in a regional smooth trend.


Kriging

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12.49

Depth Conversion

Structure-in-time Map


Examples

Depth Conversion


Depth conversion using five layers and seismic interval

velocities, the one step calibration method was used.

Examples

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12.50

Depth Conversion


Depth conversion by average velocity.

Examples

Depth Conversion


Depth conversion using six analytic functions based on wells.

Examples

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12.52

Depth Conversion

Forward Modelling

Data courtesy of Paradigm Geophysical (UK) Ltd.

Normal incidence ray trace

modelling on the velocity /

depth section generates

synthetic event with diffractions

to overlay on the stack section.

Depth Conversion

Summary

When well control is adequate to define the velocity

distribution in the macrovelocity model analytical functions

are used.

When well control is inadequate then seismic velocities may

be used. The seismic velocities have to be calibrated to well

velocities.

The residual misties at the well locations are used to quantifythe accuracy of the depth conversion.

The residual error adjustment of the depth maps is made

when depth maps are required that tie the well control

exactly.

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Depth Conversion

Summary Accuracy of depth conversion: -

Rank Wildcat (50 km to well control) ~5%

Exploration well (10km to well control) ~2.5%

Appraisal well (2 or 3km to well control) ~1%

Development wells <0.5%

The final depth structures should be no more complex than

the time structures. If they are there needs to be a very good

explanation for the complex velocity model used.

Depth Conversion

Contractor Depth Conversion

CGG Time Depth Mapper

GeoQuest InDepth

GX GX VM

Paradigm Earth Model

Sattlegger

Scott-Pickford Cubit/Velit

Landmark/Promax TDQ/Mimic/Raymap/SigmaView

12 Depth

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