post stack acoustic impedance

8/13/2019 Post Stack Acoustic Impedance

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Post Stack Acoustic Impedance (AI) Inversion:"Basics and Usage

"By Ajay Badachhape"Seismic Analysis roup

Seismic Imaging !echnology enter

#$amples

1. Seismic Amplitude vs. AI Inversion section for deepwater

GOM amplitude anomaly: Grand Canyon

2. Te Comparison of Seismic Amplitude! "ecursive Trace

Inte#ration! and Sparse Spi$e Inversion sections for

Stratton %ield! Sout Te&as

3. "eservoir 'roperties from Inverted AI "esults: 'orosity

from Inverted AI for te (ellow Sand interval in te )rsa

field

Basics and Usage

1. Overview2. Te *avelet

+. %unctionality

,. 'ractical Concerns and -imitations

. /istorical Metodolo#y

0. "eservoir 'roperties from Inverted "esults
http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%201http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%201http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%202http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%202http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%202http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%203http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%203http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%203http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Overviewhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Wavelethttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Functionhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Practicalhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Historicalhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Reservoirhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%201http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%201http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%202http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%202http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%202http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%203http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%203http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Example%203http://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Overviewhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Wavelethttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Functionhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Practicalhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Historicalhttp://upstream.ho.conoco.com/sitc/SAG/Acoustic_Impedance.html#Reservoir


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%vervie&

On a basin-wide scale seismic data is the best tool currently available

to predict subsurface properties of rocks and fluids. It has the

resolution and depth of imaging to provide valuable information that

can be used to predict reservoir properties. Acoustic impedance (AI)

inversion is a term used to designate methodologies that attempt to

compute or estimate rock properties directly from measured (e.g.,

seismic) data. AI is the only rock property (or combination of rock

properties velocity multiplied by density) that can be directly

estimated from seismic data.

!"his is an estimate since modeled results do not necessarily produce a uni#ue match to the measured seismic data.

"he convolutional model for seismic reflection data assumes the

measured seismic trace is composed of the earth reflectivity

convolved with the seismic wavelet. "he earth reflectivity is generated

by interfaces which have acoustic impedance contrasts given by the

following basic e#uation$

Rc=2v2-

1v1

2v2+

1v1

where Rcis the reflection coefficient for the interface between layers

% and &, which have velocities and densities given respectively by

v%,

1and

v&,

2 .


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!he 'avelet

"he wavelet is a key part of the inversion and well log calibration

process. It is the transfer function that provides the link between well

log acoustic impedance and the seismic data. "he wavelet is scaled

and spectrally shaped so that when it is convolved with the reflectivity

series derived from the acoustic impedance log, it produces synthetic

seismic traces of the appropriate fre#uency content and amplitude to

match the seismic trace(s) closest to the well. In a given data set ('

volume, & line, or set of & lines ac#uired and processed at the

same time and in the same manner), one single wavelet typically may

be used to tie all the well logs to the seismic data and produce a good

match between the synthetic trace and nearest seismic trace for each

well. ome of the assumptions for this to be true include the

following$

imilar range of depths, times (not too steep structurally so that

one well is at %*** ms. and another is at &+** ms.), and

geologic strata so that the fre#uency content of the seismic

data will be similar

imilar range of seismic amplitudes so that the wavelet from

one well with low amplitude reflections near it would produce a

wavelet with a low peak amplitude while another one in a one

of larger amplitude reflections would result in a wavelet with ahigh peak amplitude

o large artifacts present in the seismic data at one or a few of

the wells only this includes fault shadow, salt diffractions, out

of plane energy, multiples, etc.


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If all assumptions are met, but similar wavelets are not produced from

each of the wells, typically, the log data for some or all the wells are

#uestionable and additional log processing will be necessary to edit

the acoustic logs (sonic and density) prior to use for inversion.

etermining the wavelet is e/tremely critical since most of the newer

inversion methods e/tract a wavelet from the well log and seismic

data, then assume the wavelet is known and use it to invert for the

acoustic impedances (opposite of creating a synthetic from the well).

0e are now going to assume the wavelet is constant and for each

seismic trace, solve for an impedance model that produces a

reflectivity series that when convolved with the known wavelet,

produces a synthetic that matches the seismic trace). An e/ample of

a wavelet e/traction and synthetic1seismic comparison is seen in

2igure %.

Once the wavelet amplitude, fre#uency content, and phase have

been e/tracted from the seismic data over the inversion time gate as

accurately as possible, the inversion algorithm can automatically

account for tuning and sidelobe events. 3/tra events that are due to

constructive interference from wavelet sidelobes as well as tuning

responses are purely wavelet phenomena. Once the wavelet has

been accurately e/tracted, inversion can essentially eliminate these

seismic artifacts. 2or this reason, maps of inverted AI anomalies

usually represent the true location of anomalies and are of different

sie and shape (typically) than the seismic amplitude anomalies.


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4eduction of most of the tuning and sidelobe responses places the

anomalies in their proper position.

igure : 'avelet e$traction and seismic to synthetic tie

A single wavelet is ade#uate in almost all cases. Occasionally, a very

long time gate is to be inverted (e.g., typically more than & seconds of

data), in which case two or more inversion time windows may have to

be run separately and smoothly merged later. 5aterally varying

wavelets are a tricky problem since the wavelets are estimated at the

well positions (typically, but not always), and simple linear

e/trapolation between the well1wavelet positions is not ade#uate to

properly model where the wavelet changes actually take place. "hese


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wavelet changes may be due to e/tremely anisotropic areas, gas

chimneys, salt, faults, comple/ geologic areas such as overthrusts,

etc. (typically areas where the lateral seismic fre#uency content

changes drastically). "hese situations can be modeled fairlywell using

inversion, but the approaches necessarily vary by situation and need

to be handled on an individual basis.


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unctionality

AI inversion is useful for a variety of reasons, including the following$

3nhances resolution compared to seismic data

6rovides a geologically consistent, layer-based cube or section

of acoustic impedance data from seismic data

6rovides the ability to detect small lateral changes in acoustic

impedance within layers

6rovides the ability to delineate possible reservoir ones more

accurately than seismic data (due to removal of wavelet effects

such as tuning and false events caused by sidelobe

interference)

3nhances fault detection and delineation

3nhances delineation of fluid contacts

epicts data as layer information rather than interface data

6rovides the ability to use ' visualiation techni#ues on

inverted data to view reservoir geometries

7akes interpretation1tracking of events in low amplitude (and

other difficult) ones easier

6rovides the ability to convert AI to other parameters such as

porosity, net sand, w, etc., (providing that crossplot analysis of

well log data show appropriate trends to 8ustify a conversion).

As an illustration, 2igure %.% shows a seismic section with two

potential targets indicated as trough-peak pairs with amplitude

anomalies. "he deeper target has better trough development, but the


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following peak is not as strong as in the upper target. 2igure %.&

shows the inversion results for the same section. "he upper target is

a thicker, porous sand, and the lower target is actually two thin sands

that are not as porous and have a fairly thick shale interval in

between. "he base of the second sand in the lower target is below

the interpreted base of the sand from the seismic.

"he inversion illustrates that the most anomalous part of the section

is the very hard (acoustically) shale in between the two targets. "his

(presumably dewatered) shale has an e/tent that closely corresponds

to the area in which the upper sand is seen to be lower in acoustic

impedance and most porous. It should also be noted that the

inversion has now produced information about the layers, not 8ust the

interfaces. "he tracked horions on the seismic are the centers of the

trough-peak pairs that comprise the interpreted targets. "he inversion

results show each horion tracked on a trough to be the top of the

sand units, while the horions tracked on the peaks are the bases of

the sands (the second sand in the lower target was not resolved in

the seismic). "he intervening hard shale is not identifiable as such on

the seismic it is manifested as strong peak development at the

bottom of the upper target, and as strong trough development at the

top of the lower target due to constructive interference which

increased the strength of the amplitude anomalies.


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Practical oncerns and *imitations

"he AI inversion results may be thought of as 9pseudo-logs9, which

can only be calibrated at well locations. :owever, since AI inversion

results are modeled rather than measured data, they can be prone to

some problems. 2or e/ample, the bandlimited nature of the input

(seismic) data produces results that are non-uni#ue i.e., many AI

9pseudo-logs9 produce reflectivity traces that can be convolved with

the wavelet to produce e#ually valid synthetic1seismic correlations.

"his is especially true given the bandlimited nature of seismic data

(and therefore the inverted results) and emphasies the need for a

valid low- fre#uency model and appropriate, geologically reasonable

constraints (if the inversion method incorporates the use of limits on

the results). "he AI constraints placed upon the inversion results and

the accuracy of the low-fre#uency AI model away from the wells is

crucial to producing the best possible results.

AI inversion results are therefore not a magic bullet. 4esults have to

be analyed to ensure that the data falls within ranges that are

geologically feasible and make sense when compared to the

available well data, velocity trends, or other data. "he inversion

method also has to take into account the results of other methods of

analysis, including A;A1amplitude analysis techni#ues. 0hen

inversion results do not agree with another method such as A;A

analysis, there should be a geologic reason for the discrepancy (e.g.,

presence of a hard shale above or below the target one which

complicates the reflection image but was not accounted for in the

other method).


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+istorical ,ethodology

AI inversion in a basic sense may be thought of as taking ero-phase

seismic data and applying a


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Another method that appro/imates inversion is simple bandpass

filtering and phase rotation (which can be cascaded to apply to the

entire time window), which may or may not also be merged with a

low-fre#uency AI model. 2iltering is the fastest and cheapest method,

however, neither filtering nor trace integration methods e/tend the

bandwidth or resolution beyond the seismic band. "he introduction of

low fre#uencies e/tends the bandwidth on the low-fre#uency side so

that geologic trends are introduced, but nothing more is gained.


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-eservoir Properties .rom Inverted -esults

ince the results of inversion are models of physical properties of the

earth, analysis of well data in the area can be used to produce

estimates of other properties that can be derived from acoustic

impedance. 2or e/ample, 2igure '.% shows a crossplot with a clear

trend between acoustic impedance and density (which is easily

translated to density porosity) and 2igure '.& shows a map of the

results of converting acoustic impedance to porosity for one one in

an area. 2or comparison purposes, 2igure '.' shows the minimum

seismic amplitude (ma/imum trough development) for the same

interval. 2igure '.& shows the effects of removal of tuning and

sidelobe events the anomalies are correctly positioned, they have

changed in sie and shape, and they provide better fault resolution of

what is now apparent as fault-bounded porous sand bodies.

=onversion of inverted data to other properties is only as good as the

inverted results plus the trend used for conversion. =areful analysis

of the inverted results and the information used to create the formula

or trend (crossplots or trend curves from wells in the area, etc.) used

to convert the impedances to another property must be done. It is

easy to produce dubious results from data that do not form clear

trends. =alibration to well data and comparison with results from

other methods or geologic information is critical.

0hen used in concert with all available data, AI inversion can be a

valuable tool. 4ecognition of its strengths and weaknesses is

necessary to properly utilie it and compare1supplement it with other

analysis methods.


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&ample 1Seismic Amplitude vs. AI Inversion section for deepwater

GOM amplitude anomaly: Grand Canyon

igure /: Seismic section over amplitude anomaly/!&o stacked amplitude anomalies are delineated 0y the tracked hori1ons as trough2peakpairs/

igure /3: Inversion results over amplitude anomaly/!his is a 0road 0and inversion result in &hich the #arth,odel .rom 423 +1/ is derived .romthe &ell log and the 3254 +1/ data is dra&n .rom inversion results using the 6asoneoscience 'ork0ench7s onstrained Sparse Spike inversion algorithm/!he upper seismic anomaly (0lue to green hori1ons) is sho&n to 0e due to the presence o.a thick8 porous sand/ !he lo&er seismic anomaly (yello& to cyan hori1ons) is t&o thinnersands &ith a signi.icant shale 0reak 0et&een/ !he second sand in this deeper target is


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0elo& the original ma$imum peak that &as tracked on the seismic as 0eing the 0ase o. theanomaly/ !his inversion result sho&s that the most anomalous event in the section is thehigh impedance shale 0et&een the t&o target anomalies/ !he high impedance shale ispresuma0ly a de&atered shale that has appro$imately the same lateral e$tent as theporous sand development/ !he high impedance shale caused constructive inter.erence o.0oth anomalies and 0rightened them on the seismic data/


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Example 2The Comparison of Seismic Amplitude, Recursive Trace Integration, and Sparse Spike Inversion

sections for Stratton ield, South Texas

Areas o. interest include the sections 0elo& the green / hori1on (just a0ove /5seconds) &here resistivity spikes (cyan &iggle) indicate hydrocar0on presence/ !hemagenta &iggle is the impedance log that sho&s &hich log events created the seismicevents/

Figure 2.2: Recursive Trace Integration results for cross-line 154.

The trace integration process has transforme interface ata into la!er ata. This process oes not increase

resolution an oes not incorporate lo" fre#uenc! $vertical tren% information.


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2igure &.'$ parse pike Inversion results for cross-line %+?."he inversion results closely match the well results. and morphology and lateral porositychanges are evident. A greater amount of detail is observable for a given layer compared to2igures &.%-&.&. "he background acoustic impedance has a low-fre#uency trend that is seen as agradual increase in acoustic impedance with depth.


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Example !Reservoir "roperties from Inverted AI Results#

$A%I&'()CE'TER)"orosit* rom Inverted AI for the +ellow Sand interval in the rsa field

Figure 3.1: &rossplot of 'coustic Impeance, (ensit!, an )amma Ra! $color%.

This crossplot from a eviate "ell in the eep"ater )*+ rsa fiel sho"s a clear san tren that isifferent from the shale tren. The sans $"hite to !ello" to orange, re, an green colors% are lo"er inacoustic impeance an ensit! than the shales $green to lue% in the upper right of the plot. 'n impeance

of aout 23, g/cc0ft/sec can e use as a cutoff et"een fairl! clean to clean sans versus san! shales

to shales. Impeances elo" 23, g/cc0ft/sec can e calirate on the asis of a linear tren et"een 'I

an ensit! $"hich is easil! converte to ensit! porosit!%. This tren can e use to compute porosit!

from 'I.


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Figure 3.2: +ap of orosit! compute from Inverte 'I an &rossplot ata.

This porosit! map for the ello" san reservoir in the rsa fiel sho"s clear patterns that inicate the

sans are fault oune an have t"o provenances the sans in the lo"er half of the plot proal! came

from the east-northeast, "hile the sans in the upper half proal! came from the north-north"est. The

porosit! trens closel! match the "ell ata. The 'I anomalies have een correctl! positione ue to the

removal of most of the "avelet phenomena $e.g., tuning an sieloe events%. &onversion of the 'I ata toporosit! for a given one provies aitional information aout the #ualit! of the sans.

igure 9/9: ,inimum Seismic Amplitudes over target 1one/!he seismic amplitude anomalies are not in the same position nor the same si1e andshape as the inversion results indicate/ !he .aults are not as clearly de.ined and the sandsto the south do not appear to 0e .ault 0ounded/

pecial thanks to r. 4obert =orbin for editing and to 4e/ 7c@inleyfor reviewing this article.

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