An Inversion Primer

An Inversion PrimerBrian Russell, Dan Hampson, and Bradley BankheadVeritas/Hampson-Russell, Calgary, Canada and Houston, Texas, USA

96 CSEG RECORDER 2006 Special Edition

Continued on Page 97

Introduction

Seismic inversion is a technique that has been in use bygeophysicists for almost forty years. Early inversion tech-niques transformed the seismic data into P-impedance (theproduct of density and P-wave velocity), from which wewere able to make predictions about lithology and porosity.However, these predictions were somewhat ambiguous sinceP-impedance is sensitive to lithology, fluid and porosityeffects, and it is difficult to separate the influence of eacheffect. To perform a less ambiguous interpretation of ourinversion results, we must perform full elastic inversion, inwhich we estimate P-impedance, S-impedance (the productof density and S-wave velocity) and density. The reason forthis is that the P and S-wave response of the subsurface issufficiently different to allow us to see the difference betweenfluid and lithology effects. We have now progressed to thepoint where inversion for P-impedance, S-impedance anddensity is feasible. This article presents both a history ofseismic inversion and an overview of the techniques them-selves, illustrated by a case study from the Gulf of Mexico.

Seismic amplitudes

The seismic reflection method was developed in the first quarterof the twentieth century and was used initially as a tool for iden-tifying stru c t u res, such as anticlines, which could act as trappingmechanisms for hydrocarbon reservoirs. This was done bysimply identifying the continuity of the reflections seen on theseismic sections. However, by the 1970s, geophysicists hadbegun to realize that information was contained in the ampli-tudes of the seismic reflections themselves. This informationcould be correlated with porosity changes, lithology changes, oreven fluid changes within the subsurface of the earth.

With the advent of 3D seismic recording in the 1980s, wecould map the seismic amplitude change over the full extent

of a prospect. For example, Figure 1 shows an extractedseismic amplitude map from a recent 3D survey over theMarlin field from the Gulf of Mexico.

Three wells are indicated on the map in Figure 1: A1, A5, andA6. Well A1 is the initial discovery well, and encountered 150ft (40 m) of gas at the reservoir level. Well A6 is the updipdelineation well, and encountered 80 ft (25 m) of gas sandand over 60 ft (20 m) of water sand at the reservoir level. WellA5 is the downdip delineation well, and encountered no gassand and 140 ft (33 m) of porous water sand at the reservoirlevel. Notice that all three of these wells correlate with ampli-tude anomaly trends (shown by the brown colour on themap), but only two of the wells are producing gas wells.Almost due east of the A1 well are two deviated wells alsocontaining gas but this is not evident from the seismic ampli-tudes. Seismic amplitude alone is therefore a fairly good indi-cator that something in the subsurface is anomalous(porosity, hydrocarbon, etc), but is an ambiguous indicator ofhydrocarbons.

Seismic reflections and mode conversion

But what does seismic amplitude really mean? The theory ofseismic wave propagation, including the reflection and trans-mission of seismic waves at elastic boundaries within theearth, has been well known for at least a century. These earlytheoretical studies recognized that both compressional waves(P-waves) and shear waves (S-waves) are generated in anelastic earth (along with many other types of waves, such asRayleigh waves, Love waves, Stonely waves, etc). Zoeppritz(1919) showed mathematically that if a P-wave was incidenton the boundary between two elastic media at an anglegreater than zero degrees, reflected and transmitted P and S-waves were created by a process called mode conversion, asshown in Figure 2. Zoeppritz’ equations, which involve thesolution of a 4x4 set of linear equations, allow us to compute

F i g u re 1. An amplitude map over the Marlin field in the Gulf of Mexico, wherewell A1 is the original discovery, well A6 is the updip delineation well, and wellA5 is the downdip delineation well. F i g u re 2. Mode conversion of an incident P-wave on an elastic boundary.

2006 Special Edition CSEG RECORDER 97

Seismic Inversion Cont’dAn Inversion PrimerContinued from Page 96


the amplitudes of each of these waves. Although we will not givethe explicit form of the Zoeppritz equations here (see Aki andRichards, 2002, for the complete derivation) a linearized versionof the equations will be discussed later in this tutorial.

Despite the early research on different types of elastic waves, theexploration seismic reflection method has traditionally limiteditself to the generation, recording and analysis of P-waves alone.(This trend is starting to change, and we are now morecommonly recording converted waves or full S-waves usingmulti-component geophones).

In a typical seismic survey, we generate an incident P-wave usinga source such as dynamite, Vi b roseis, or a marine airgun. We thenre c o rd the reflected P-wave as a function of offset, which can berelated to the angle θ shown in Figure 2 by the seismic velocity.The result is the seismic shot re c o rd. The shot re c o rd is then trans-formed by processing into a common mid-point (CMP) gather, inwhich the reflection points are grouped around a common mid-point. As we will discuss in a later section of this tutorial, the infor-mation contained in a CMP gather contains information about allt h ree physical parameters shown in Figure 2: P-wave velocity (VP) ,S-wave velocity (VS), and density (ρ). However, before looking atthis process, called AVO, let us consider the more standard seismicp rocess flow, which involves “stacking” the seismic data.

Post-stack seismic inversion

The standard seismic data processing flow involves trans-forming the CMP gathers into a stacked section, which is anapproximation to the zero-offset reflection, in which the angle θin Figure 2 is equal to zero. (It is an approximation becausestacking involves summing over all angles, which means thatany angle-dependent processes will get “smeared” together). Ifwe assume that the angle of incidence is zero in Figure 2 and thatthe layers are flat, the Zoeppritz equations simplify to the moremanageable equation given by

1)

where rPi is the zero-offset P-wave reflection coefficient at the it h

interface of a stack of N layers, and ZP i=ρiVP i is the P-impedanceof the it h layer.

Equation (1) can be used as a simplified model for the re f l e c t i o n s(and there f o re the amplitudes) found on a stacked seismic section.Lindseth (1988) was one of the first geophysicists to show that if weassume that the re c o rded seismic signal is as given in equation (1),we can invert this equation to recover the P-impedance as follows:

2)

By applying equation (2) to a seismic trace we can eff e c t i v e l ytransform, or invert, the seismic reflection data to P-impedance.H o w e v e r, as also recognized by Lindseth, there are a number ofp roblems with this pro c e d u re. The most severe problem is that there c o rded seismic trace is not the reflectivity given in equation (1)but rather the convolution of the reflectivity with a bandlimitedseismic wavelet, plus some additive noise, which can be written

3)

where st is the seismic trace, wt is the seismic wavelet, rt is thereflectivity integrated from depth to time, * denotes convolution,and nt is the noise component. The effect of the bandlimitedwavelet is to remove the low frequency component of the reflec-tivity, meaning that it can never be recovered.

Other key issues in seismic inversion involve removing the noisecomponent and correctly scaling the seismic data. After properprocessing and scaling of the seismic data, an intuitive approachto recovering the low frequency component is to simply extractthis component from well log data and add it back to the seismic,as shown in Figure 3. In this figure, the trace on the left is theseismic trace after application of equation (2), the trace in themiddle is the low frequency component, and the trace on theright is the final result.

A more recent approach to inversion is called model-based inver-sion, in which we start with a low frequency model of theinverted P-impedance, and then perturb this model until weobtain a good fit between the seismic data and a synthetic tracecomputed by applying equations (1) and (3). This also assumesthat we have extracted a good estimate of the seismic wavelet,which in itself can be a difficult task.

F i g u re 4. The inverted P-impedance section over the Marlin field.

F i g u re 3. An intuitive approach to seismic inversion, where the trace on the left isthe seismic trace after applying the inversion equation (2), the trace in the middle isa low frequency component, and the trace on the left is the final re s u l t .



The theory behind model-based post-stack inversion (Russelland Hampson, 1991) is as follows. First, we can show that thesmall reflectivity approximation for the P-wave reflectivity isgiven by re-expressing equation (1) as

4)

where i again represents the it h layer boundary.

If we consider an N sample reflectivity, the noise-free version ofequation (3) can be written in matrix form as

5)

where LP i = ln(ZP i).

Next, if we represent the seismic trace as the convolution of theseismic wavelet with the earth’s reflectivity, we can write theresult in matrix form as

6)

where si represents the it h sample of the seismic trace and wj repre-sents the jt h term of an extracted seismic wavelet. Combiningequations (5) and (6) gives us the forward model which relatesthe seismic trace to the logarithm of P-impedance:

7)

where S is the seismic trace, W is the wavelet matrix given inequation (6) and D is the derivative matrix given in equation (5).

If equation (7) is inverted using a standard matrix inversion tech-nique to give an estimate of LP from a knowledge of T and W,there are two problems. First, the matrix inversion is both costly

and potentially unstable. More importantly, a matrix inversionwill not recover the low frequency component of the impedance,which has been removed from the seismic data by convolutionwith the wavelet. An alternate strategy, and one that is quiterobust, is to build an initial guess impedance model and theniterate towards a solution using the conjugate gradient method.

The model-based inversion result for the Marlin field is shown inF i g u re 4. In this figure, notice that there is diff e rentiation betweenthe gas and non-gas zones, but the wet well is still somewhat anom-alous. However, the wells east of the A1 location are sitting on theedge of the seismic anomaly and may become better discriminatedby utilizing the prestack information in the inversion pro c e s s .

The AVO method

In the early 1980s, the AVO method was developed, in which theamplitudes of the seismic CMP gather as a function of anglewere analyzed for hydrocarbon indicators. The equation thatforms the foundation of AVO analysis has become known as theAki-Richards equation (Aki and Richards, 2002). The originalform of the equation can be re-formulated to give

8)

where,A,=

In equation (8), ΔVP, ΔVS, and Δρ indicate diff e rences of the velocityor density across a layer boundary, and VP, VS, and ρ indicate aver-ages of the velocity or density across a layer boundary. The A t e r mis called the intercept and is a linearized version of the zero off s e tP-wave reflection coefficient given in equation (1). The B termed iscalled the gradient and the C term is called the curvature.

Standard AVO analysis involves using a least-squares fittingprocedure to estimate A, B, and C from pre-stack seismic anglegathers and then cross-plotting B against A to identify deviationsaway from a wet trend line. The wet trend line can be derived byassuming that ρ and VP are related by Gardner’s relationship(Gardner et al. 1974), given in linearized form by

9)

and that VS and VP are related by Castagna’sequation (Castagna et al., 1985), given by

10)

Alternately, the product of A and B willoften reveal class 3 gas sands, in which theacoustic impedance of the sand is less thatthe surrounding sediments. Applying thismethod to the Marlin field gives the resultshown in Figure 5(a). Note that the dry hole(A5) is now showing a negative AxB, or wet,signature. However, the wells east of A1 arealso exhibiting a wet response.

F i g u re 5. The (a) intercept x gradient (A x B) and (b) AVO fluid factor results for the Marlin field.

and





The Aki-Richards equation was re-formulated by Fatti et al.(1994) as a function of zero-offset P-wave reflectivity RP 0, zero-offset S-wave reflectivity RS 0 and density reflectivity RD in theform

11)

where, c1=1+tan2θ, c2=–8ϒ2+tan2θ, ϒ=VS/ VP, and c3=–0.5tan2θ+2ϒ2

s i n2θ, RP 0 is equivalent to the A term in equation (8), and the othertwo reflectivity terms are given by Rs 0=

12[ΔVS

Vs +Δρ], and RD=Δρρ . Based on equation (11), Fatti et al. (1994) showed that aleast-squares procedure could be implemented to extract thethree reflectivity terms from the pre-stack seismic data. Using theextracted reflectivities RP 0 and RP 0 f rom this approach, theauthors then modified the fluid factor approach (which hadearlier been proposed by Smith and Gidlow (1987) is a slightlysimpler form), which can be written:

12)

The result of applying the fluid factor method to the Marlin fieldis shown in Figure 5(b). Note that the non-gas well (A5) is moreanomalous than we saw in the previous figure, indicating thatthe fluid factor technique is inadequate for distinguishing fluidsin this reservoir setting.

In the next section, we will show how to combine the techniquesof model-based inversion and AVO to develop a technique thatwe will refer to as simultaneous inversion.

Pre-stack simultaneous inversion

As we have discussed, the goal of seismic inversion is to obtainreliable estimates of P-wave velocity (VP), S-wave velocity (VS),and density (ρ) from which to predict the fluid and lithologyproperties of the subsurface of the earth. This problem has beendiscussed by several authors. Simmons and Backus (1996) devel-oped a scheme to invert for P-reflectivity (RP), S-reflectivity (RS)and density reflectivity (RD) that was based on three assump-tions: that the reflectivity terms can be estimated from the angledependent reflectivity RP P(θ) by the Aki-Richards linearized

approximation, that ρ and VP are related by Gardner’s relation-ship given by equation (5) and that VS and VP are related byCastagna’s equation of equation (6).

Buland and Omre (2003) use a similar approach which theycalled Bayesian linearized AVO inversion. Unlike Simmons andBackus (1996), their method is parameterized by the three terms,ΔVP/VP, ΔV S/ VS, and Δρ/ρ., again using the Aki-Richards approx-imation. The authors also use the small reflectivity approxima-tion to relate these parameter changes to the original parameteritself, as given in equation (4). Similar terms are given forchanges in both S-wave velocity and density. This logarithmicapproximation allows Buland and Omre (2003) to invert forvelocity and density, rather than reflectivity, as in the case ofSimmons and Backus (1996).

Hampson et al. (2005) extended the work of both Simmons andBackus (2003) and Buland and Omre (1996), and developed anew approach that allows us to invert directly for P-impedance,S-impedance, and density. It was also the goal of this work toextend model-based post-stack impedance inversion method sothat this method could be seen as a generalization to pre-stackinversion. To do this, equation (4) can be combined with equa-tion (11) to give

13)

where LS = ln(Z S) and LD = ln(ρ). Note that the wavelet is nowdependent on angle.

Equation (13) could be used for inversion, except that it ignoresthe fact that there is a relationship between LP and LS andbetween LP and LD. Because we are dealing with impedancerather than velocity, and have taken logarithms, the relationshipsare given

14)

15)

That is, we are looking for deviations away from a linear fit inlogarithmic space. This is illustrated in Figure 6.

Combining equations (14) through (15), we get

16)

Equation (16) can be implemented in matrix form as

17)

If equation (17) is solved by matrix inversionmethods, we again run into the problem that the lowfrequency content cannot be resolved. A practicalapproach is to initialize the solution to, [LP ΔLS ΔL D]T

= [In(ZP 0) 0 0]T where ZP 0 is the initial impedancemodel, and then to iterate towards a solution usingthe conjugate gradient method.

(a) (b)

F i g u re 6. Crossplots of (a) ln(ZD) vs ln(ZP) and (b) ln(ZS) versus ln(ZP) where, in both cases, a beststraight line fit has been added. The deviations away from this straight line, ΔLD and ΔLS, are thed e s i red fluid anomalies.

where and

and



Model Example

We will now apply this method to a model data example. Figure7(a) shows the well log curves for a gas sand on the left (in blue),with the initial guess curves (in red) set to be extremely smoothso as not to bias the solution. On the right are the model, theinput computed gather from the full well log curves, and theerror, which is almost identical to the input. Figure 7(b) thenshows the same displays after 20 iterations through the conju-gate gradient inversion process. Note that the final estimates ofthe well log curves match the initial curves quite well for the P-impedance, ZP, S-impedance, ZS, and the Poisson’s ratio (σ). Thedensity (ρ) shows some “overshoot” above the gas sand (at 3450ms), but agrees with the correct result within the gas sand. Thisis most likely attributable to the fact that NMO-stretch has notbeen included in the model. The results on the right of Figure7(b) show that the error is now very small.

Next, we will use Biot-Gassmann substitution to create theequivalent wet model for the sand shown in Figure 8, and againperform inversion. Figure 8(a) shows the well log curves for thewet sand on the left, with the smooth initial guess curves super-imposed in red. On the right are the model from the initial guess,the input modeled gather from the full well log curves, and theerror. Figure 8(b) then shows the same displays after 20 iterationsthrough the conjugate gradient inversion process. As in the gascase, the final estimates of the well log curves match the initialcurves quite well, especially for the P-impedance, ZP, S-imped-ance, ZS, and the Poisson’s ratio (s). The density (r) shows amuch better fit for the wet sand (which is at 3450 ms) than it didfor the gas sand.

It is important to point out that, while these results are verygood, the quality of the data that went into the study was alsovery good. For example, we used an angle range from 0 to 60degrees, which is higher than found in most seismic surveys.Also, the data was synthetic and thus noise-free. In the nextsection, we will therefore apply this method to real data and seehow well it performs.

Real Data Example

Next, we will return to the Marlin field and apply the simulta-neous inversion approach to this dataset. Recall that the P-imped-ance inversion was shown in Figure 4. However, we noted earlierthat this P-impedance inversion result is ambiguous in terms ofd i ff e rentiating fluid effects from lithologic or porosity effects, andwe need S-impedance and density to get a better estimate of theseparameters. The advantage of simultaneous inversion is that S-impedance and density are produced along with the P-imped-ance. The S-impedance inversion for the Marlin field is shown inF i g u re 9. Note that, although the three wells are still located onanomalous regions, the S-impedance trends are quite diff e re n tf rom the P-impedance trends shown in Figure 4.

The density inversion for the Marlin field is shown in Figure 10.Again, note that the three wells are located on anomalous re g i o n sof density but that the trends are diff e rent from the P-impedancet rends shown in Figure 4. Although all three wells are associatedwith density anomalies, this is most likely due to sand pre s e n c ewith the larger drops in density being influenced by gas.

Finally, we will use the output of the simultaneous inversion topredict fundamental properties of the reservoir such as porosity,sand percentage, and water saturation.

For the sand shale separation and porosity transformation, thiswill be done empirically by calibration to the well data. Figure11(a) shows a cross-plot of density versus Vshale for the threewells shown on our earlier figures (A1, A5 and A6). As shown bythe picked zones in this cross-plot, we were able to separate sandfrom shale using a cutoff of 2.32 g/cc, where sands are lowerdensity and shales higher. The slightly transparent rectangularpolygons of blue and gold, respectively, represent shales withhigher quartz content and sands that have higher clay content.The result of this transformation to sand and shale is shown inFigure 12(a), where the values represent sand frequency or asimplified net-to-gross.

Figure 11(b) shows a cross-plot of porosity versus P-impedancefor the three wells A1, A5 and A6. As shown by the lines of thiscross-plot, we can derive two empirical formulas for porosityfrom the inverted P-impedance volume. We again use a cutoff toseparate pay from non-pay (18,000 ft/sec*g/cc), then an empir-ical relationship is defined for pay and non-pay. The result of thistransformation to porosity is shown in Figure 12(b). The average

F i g u re 7. The results of inverting a gas sand model, where (a) shows the initialmodel before inversion, and (b) shows the results after inversion.

F i g u re 8. The results of inverting a wet sand model, where (a) shows the initialmodel before inversion, and (b) shows the results after inversion.





porosities from the well log data is about 27%, which is closelysupported by the seismic derived porosities.

Now that we have derived the porosities over the Marlin field,we can transform to water saturation using the porosity cubeand the density cube. This involves transforming the relation-ship between saturated density, water saturation, and porosity,given by

18)

to an equation in which water saturation is on the left hand sideof the equation, given by:

19)

In equation (19) we let ρgas = 0.1 ρW = 1, and ρmatrix =2.65.

The result of this transformation is shown in Figure 13, which isthe water saturation map at the zone of interest. Notice that theA5 well is shown as 100% water saturated, and that the A1 andA6 wells are shown as gas producers, which are the correctresults, as well as the wells to the east of the A1 well.

Conclusions

In this tutorial, we have discussed the history of seismic ampli-tude inversion, from its origin as a post-stack process to the mostrecent developments which involves the simultaneous inversionof pre-stack seismic data. Although post-stack inversion is apowerful and robust method, it suffers from the fact that its finalproduct, P-impedance does not allow us to discriminate betweenlithology, porosity and fluid effects. Other limitations of post-stack inversion, such as its inability to recover the low frequencycomponents of the impedance, and the effects of seismic noiseand scaling problems, are inherent limitations of the seismic dataitself. These data limitations lead to the development of new

seismic processing algorithms and new approaches to the tech-nique of inversion, such as model-based inversion.

The inability of post-stack inversion to discriminate between thelithology and fluid content of the reservoir lead to the develop-ment of the AVO technique for the analysis of pre-stack data. Webriefly reviewed the AVO method and then showed that thetheory of AVO could be coupled with the traditional approachesof post-stack inversion to produce estimates of P-impedance, S-Impedance and density. The simultaneous inversion method thatwe discussed is based on three assumptions: that the linearizedapproximation for reflectivity holds, that reflectivity as a func-tion of angle can be given by the Aki-Richards equations, andthat there is a linear relationship between the logarithm of P-impedance and both S-impedance and density. We illustratedour inversion methods using modelled gas and wet sands andalso a real seismic example which consisted of a gas sand playfrom the Gulf of Mexico. In our real data example, we showedthat the extraction of the primary attributes of P and S-imped-ance and density from our seismic data allows us to directlypredict porosity, sand percentage and water saturation. Thesepredictions correlated extremely well with known results. R

ReferencesAki, K., and Richards, P.G., 2002, Quantitative Seismology, 2nd Edition: W.H.Freeman and Company.

Buland, A. and Omre, H, 2003, Bayesian linearized AVO inversion: Geophysics, 68,185-198.

Castagna, J.P., Batzle, M.L., and Eastwood, R.L., 1985, Relationships between compres -sional-wave and shear-wave velocities in clastic silicate rocks: Geophysics, 50, 571-581.

Fatti, J., Smith, G., Vail, P., Strauss, P., and Levitt, P., 1994, Detection of gas in sandstonereservoirs using AVO analysis: a 3D Seismic Case History Using the Geostack Technique:Geophysics, 59, 1362-1376.

Gardner, G.H.F., Gardner, L.W. and Gregory, A.R.,1974, Formation velocity anddensity - The diagnostic basics for stratigraphic traps: Geophysics, 50, 2085-2095.

Hampson, D., Russell, B., and Bankhead, B., 2005, Simultaneous inversion of pre-stackseismic data: Ann. Mtg. Abstracts, Society of Exploration Geophysicists.

Lindseth, R. O., 1988, Synthetic sonic logs - A process of stratigraphic interpretation, inLines, L. R., Ed., Inversion of geophysical data: Soc. of Expl. Geophys., 195-218. (*Reprinted from Geophysics, 44, 3-26).

F i g u re 9. The S-impedance result from simultaneous inversion for the Marlin fieldat the zone of intere s t .

F i g u re 10. The density result from simultaneous inversion for the Marlin field atthe zone of intere s t .



F i g u re 11. The cross-plots of (a) density versus Vshale used to help predict Vshale from the density volume, and (b) porosity versus P-impedanceused to predict porosity from the P-impedance volume.

F i g u re 12. The (a) sand percentage and (b) porosity maps obtained from the simultaneous inversion results for the Marlin field using a trans -form derived from the well data.

F i g u re 13. The water saturation map obtained from the simultaneous inversionresults for the Marlin field using a transform derived from the well data.




Russell, B. and Hampson, D., 1991, A comparison of post-stackseismic inversion methods: Ann. Mtg. Abstracts, Society ofExploration Geophysicists, 876-878.

Simmons, J.L. and Backus, M.M., 1996, Waveform-based AVOinversion and AVO prediction-error: Geophysics, 61, 1575-1588.

Smith, G.C., and Gidlow, P.M., 1987, Weighted stacking for rockproperty estimation and detection of gas: Geophys. Prosp., 35,993-1014.

Zoeppritz, K.,1919, Erdbebenwellen VIIIB, On the reflection andpropagation of seismic waves: Gottinger Nachrichten, I, 66-84.

Brian Russell holds a B.Sc. in Geophysics from the University of Saskatchewan, a M.Sc. in Geophysics from the Universityof Durham, England, and a Ph.D. in Geophysics from the University of Calgary. He started his career with Chevron in 1976,and subsequently worked for both Teknica and Veritas before co-founding Hampson-Russell Software Ltd. in 1987 with DanHampson. Hampson-Russell develops seismic analysis software for the petroleum industry. Since 2002, Hampson-Russell hasbeen a fully owned subsidiary of VeritasDGC Inc. Brian is currently Vice President of Hampson-Russell Software and isactively involved in both geophysical research and training.

Brian was President of the CSEG in 1991, received the Meritorious Service Award in 1995, the CSEG medal in 1999, andCSEG Honorary Membership in 2001. Brian also served as chairman of The Leading Edge editorial board in 1995, technical co-chairman of the 1996 SEG annual meeting in Denver, and as President of SEG in 1998. In 1996, Brian and Dan Hampson were

jointly awarded the SEG Enterprise Award. Brian is registered as a Professional Geophysicist in Alberta.

Dan Hampson received his B.Sc. degree in physics from Loyola College, Montreal, in 1971, and received his M.Sc. in theore t-ical physics from McMaster University, Hamilton, in 1973. In 1993, Dan received an MBA f rom the University of Calgary.

In 1976, Dan joined Veritas Seismic Processors, where he held a number of positions, including re s e a rch manager and ultimatelyVice President for Research. In 1987, Dan left Veritas and joined with Brian Russell to form Hampson-Russell Software Services,w h e re he was president from 1987 to 2002. In 2002, Hampson-Russell was acquired by VeritasDGC, and Dan continued in the ro l eof President of the Hampson-Russell division.

Dan has been actively involved in supporting the CSEG and SEG. During the years 1979 to 1999, Dan has served as JournalE d i t o r, Second Vice President, Chairman of the Annual Convention, and President of the CSEG. In 1996, Dan Hampson and BrianRussell received the SEG’s Enterprise Aw a rd for the contribution of their company to the industry. In 2004, Dan received the CSEG

M e d a l .Dan has presented numerous papers at the CSEG, SEG, and EAGE conventions, and has received CSEG Best Paper Aw a rds twice. These papers

included work on Parabolic Radon Transform, Generalized Linear Inversion for Refraction Statics, and AVO Inversion. Most recently (2004), Danreceived the CSEG award for Best Technical Luncheon Speaker.

Bradley Bankhead joined Veritas DGC in 1999 as VP of Reservoir Technologies where he directs and manages the technicaloperations of the groups AVO and reservoir characterization business. Prior to Veritas, Brad held a variety of positions withSun Company/Oryx Energy during his 15 year tenure. As part of Brad’s tenure with Oryx he managed the AVO/inversiongroup as well as managed the integrated reservoir characterization group. Brad worked on both exploration and reservoirdevelopment projects from around the world, including, Gulf of Mexico, Texas Gulf Coast, Indonesia, Kazakhstan, Algeria,Australia, North Sea, and others.

Corresponding author: Brian Russell ([email protected])

Documents

An Inversion Primer