Converted-Wave Processing Theory & Guidelines

Prepared by:

Jeff Grossman, Ph.D.

Senior Geoscientist, R&D Team Lead

Sensor Geophysical Ltd. 1300, 736 - 6 Avenue SW

Calgary, Alberta, Canada T2P 3T7

www.sensorgeo.com

www.globalgeophysical.com

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For internal distribution only

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Table of Contents Value of Converted-Wave Processing ......................................................................................................... 5

The Evolution of Multicomponent Seismic ............................................................................................. 5

Resolution ................................................................................................................................................. 5

Density Determination, Joint Inversion ................................................................................................... 6

Lithology Discrimination .......................................................................................................................... 7

Interpretation ........................................................................................................................................... 7

Caprock Integrity, Natural Fracture Characterization, Hydraulic Fracturing Monitoring ...................... 7

Facies Classification .................................................................................................................................. 8

Heat, Pressure, and Steam Front Mapping ............................................................................................. 8

Enhanced P-Wave Imaging....................................................................................................................... 9

CO2 Sequestration Monitoring ................................................................................................................ 9

Geomechanics .......................................................................................................................................... 9

Challenges Associated with Converted-Wave Processing ........................................................................ 10

General Processing Flow ............................................................................................................................ 11

Initial Processing......................................................................................................................................... 11

Geometry ................................................................................................................................................ 11

Receiver Tilt Corrections ........................................................................................................................ 11

RADAR (Receiver Azimuth Detection And Rotation) ............................................................................ 12

Rotation to Radial and Transverse Coordinates ................................................................................... 15

Estimating the Stacking Velocity Model and Imaging Parameters ........................................................... 17

Parameter Definitions and Important Relationships ............................................................................ 17

Stretching from PP Time to PS Time ...................................................................................................... 18

ACP Binning ............................................................................................................................................ 19

Converted-Wave Statics ......................................................................................................................... 20

Receiver Statics ...................................................................................................................................... 20

Estimating the Vertical Vp/Vs Ratio, 𝜸𝟎 ............................................................................................... 23

Estimating the Effective Vp/Vs Ratio, 𝜸𝒆𝒇𝒇.......................................................................................... 23

Prestack VTI Migration ............................................................................................................................... 24

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Shear Wave Splitting Analysis and Layer Stripping ................................................................................... 25

Indications of shear wave splitting ........................................................................................................ 26

PS Layer Stripping ................................................................................................................................... 28

SWS analysis ........................................................................................................................................... 29

References .................................................................................................................................................. 31

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Value of Converted-Wave Processing

The Evolution of Multicomponent Seismic Sensor Geophysical has been an industry pioneer of multicomponent processing for 20 years now.

Sensor’s dedicated effort has not lost steam, as we continue to make significant breakthroughs in

processing and imaging of PS data. Building on our cumulative advantage by leveraging our in-house

expertise and the sophisticated theoretical work of Li, Thomsen, Tsvankin, Cary, Harrison and many

others, we have methodically upgraded our PS processing and imaging flow, enabling state-of-the-art

treatment of layered VTI + HTI media. Key improvements stem from our recent ability to consistently

flatten gathers to much greater offset-to-depth ratios than previously offered, which was accomplished

by using highly accurate, rigorously derived anisotropic moveout and migration equations, and

developing corresponding model estimation techniques. In particular, this effort has greatly enhanced

our near surface imaging capability, which has multiple benefits: more robust estimates of statics,

vertical and effective Vp/Vs ratios, anisotropy, and shear wave splitting parameters; more precise and

accurate layer stripping; improved sensitivity to changes in the near surface, and therefore higher

processing repeatability and preservation of the 4D signal in time-lapse seismic monitoring; superior

gather conditioning for interpretation and joint PP-PS AVO inversion.

These improvements signify a milestone in the enabling potential of multicomponent seismic processing

– a shift in the value-add spectrum from ‘promising’ toward ‘indispensable’. Multicomponent processing

and inversion has matured enough to add significant value in exploration, development, and production.

We take this opportunity to review various applications of multicomponent seismic technology that

have been developed over the last few decades up to and including the present day.

Resolution Shear waves tend to attenuate, or lose high frequencies, more rapidly with travel time than P-waves.

Thus in particular, PS data tend to have less temporal resolution than PP data. On the other hand, since

S- waves propagate at about half to a quarter the speed of P-waves, it follows that for any common

temporal frequency within the two signal bands, PS data have shorter wavelength and therefore higher

spatial resolution than P data. The classic problem is, attenuation can very quickly erode this advantage

by severely narrowing the useful signal bandwidth of PS vs. PP data. Compounding this fact with

commonplace, low-budget, rushed, and therefore relatively poor near surface imaging ensures PS data

have lower resolution that PP data.

A common conclusion loosely based on these observations is that PS data tend to be noisier and lower

frequency, and thus less useful than PP data for fine structural imaging. However, one can also conclude

from this analysis that near surface PS resolution is potentially superior to that of PP. Indeed, an

example published over a decade ago by Cary and Couzens, (2000) demonstrates this superior

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resolution up to at least 500ms of P-wave time; and now that we have greatly improved near surface PS

imaging capabilities, we are observing this phenomenon frequently.

Even so, this is by far not a complete value picture and it would be rather premature to evaluate PS data

strictly on its ability or inability to image fine details. An image (migrated volume), by itself, whether it

be reconstructed from P-waves or some other mode, cannot possibly capture all of the information

content imparted by the earth’s rock/fluid fabric and stress state onto the seismic wavefield. “We would

like S-waves and their subsequent analysis to provide improved subsurface images as well as give a

measure of S-wave properties relating to rock type and saturation. If we do have P-S reflectivity, what

specifically can it be used for? Various authors (e.g., Kristiansen, 2000; Yilmaz, 2001) have suggested or

shown a number of applications of P-S data that include: enhanced imaging, lithology estimation, fluid

description, anisotropy analysis, and reservoir monitoring.” (Stewart, 2004)

In the following sections we look beyond basic imaging and explore topics relating to the information

content of multicomponent seismic data, all of which lead to added value for the interpreter.

Density Determination, Joint Inversion “There is much demand for a robust method of density estimation, and since P-wave data alone have

been shown to be generally insufficient, [Lines, 1998] we naturally look toward multicomponent data to

extract more information.” (Grossman, 2003)

“Large incidence angles for PS converted-waves are typically achieved at shorter offsets than for PP

reflections. This is because rays follow the path of least traveltime, and thus travel longer distances in

the fastest direction or mode of propagation. This means that for a given aperture, more complete AVA

[amplitude variation with angle of incidence] information is available for PS data than for PP data; thus

allowing for a more reliable parameter inversion. Moreover, at least in the absence of noise, inversion of

converted-wave data is more accurate than other sources (Ursenbach, 2003a). In the presence of noise,

Joint PP and PS inversion is better than either alone given that events can be registered (G. Margrave,

personal communication, 2003; demonstrated by Larsen, 1999).

“Although amplitude variation with offset analysis (AVO) has a potential to recover important reservoir

characteristics, quantitative AVO inversion is known to be often unstable. To improve the stability,

prestack P-wave amplitudes can be supplemented by amplitudes of converted PS-waves. The thesis

objective is to build a theoretical foundation for joint AVO inversion of PP- and PS-waves in anisotropic

media.” (Jilek, 2001)

Finally, “converted-wave data offer an extra, independent source of information. This leads to higher

resolution elastic parameter estimates, and ultimately betters knowledge of subsurface rock

properties.” (Grossman, 2003)

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Lithology Discrimination “MacLeod et al. (1999a) showed a case (now a classic!) of converted-waves successfully delineating sand

channels encased in shale at the Alba field in the North Sea. A strong contrast in S-wave velocity (from

shale to sand) is associated with the top of the reservoir. On the other hand, there is relatively little P-

wave velocity change across this lithologic boundary. Thus, the reservoir top generates strong

converted-waves, but weaker reflected P-waves.” (Stewart, 2004)

“Fortunately, not all methods of interpreting converted-wave data require the exact identification of

individual thin horizons on both the P-P and P-S final stacks. For example, the calculation of interval

Vp/Vs maps, which has been shown to be a useful diagnostic tool for discriminating between sand and

shale in the Blackfoot region of Alberta (Margrave et al., 1998), requires that corresponding horizons

above and below the zone-of-interest be picked on the P-P and P-S stacks. Since strong, high amplitude

reflectors can be used, the [potentially] lower resolution of the P-S data ends up not being a critical

factor.” (Cary, 2001)

Interpretation “There are occasional situations when the interpretation of the P-S data is so simple that anyone can see

how useful the P-S data is, such as when imaging through gas clouds in the North Sea (Granli et al.,

1999), or when imaging sand channels at the Alba field in the North Sea (MacLeod et al., 1999). However

P-S interpretation is rarely so simple.” (Cary, 2001)

“Richardson (2003) discusses shallow seismic imaging to investigate coal deposits. She notes the

importance of fault assessment in coal mine design and the benefits that multicomponent seismic

imaging can bring to coalfield understanding. An example of multicomponent surveying to provide

enhanced visibility of a coal seam over a coal mine in the Bowen Basin in Australia is shown in Figure 6

(Velseis, 2003).” (Stewart, 2004)

Caprock Integrity, Natural Fracture Characterization, Hydraulic Fracturing Monitoring “Recent observations of shear-wave splitting in the near surface have been interpreted as a

consequence of the stress state rather than the presence of fractures. The analysis of such shallow

anisotropy measurements from shear-wave splitting on converted-wave data allows us to evaluate

caprock integrity and detect areas where the stress in the caprock may deviate from the regional

faulting regime. This information is vital in discerning whether the caprock is able to withstand recovery

of shallow in-situ bitumen and heavy oil. Moreover, using time-lapse multi-component data, we can use

the changes in splitting azimuth and time delay to monitor overburden and reservoir changes occurring

during production. Here we show that converted-wave splitting changes, observed at the Conklin

Demonstration Project between 2008 and 2009, can be directly correlated to changes occurring in the

overburden. Additionally, we show that the stress state of the overburden, and in particular the

transition from one stress regime to another with depth, is considerably more complex than has

generally been assumed.” (Wikel, et al., 2012)

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“Crampin and Chastin (2003) further propose that the threshold between intact rock and fractured rock,

which varies based on factors such as rock type and burial depth, coincides with the range of 4.5 to 10%

SWVAS-S [shear wave velocity anisotropy]. The SWVAS-S parameter can thus be used to characterize

changes in stress and to distinguish intact from potentially fractured rock. Similar studies have

demonstrated the utility of analyzing SWVAS-S to monitor overburden stress state and integrity during

toe-to-heel-air-injection operations (Kendall and Wikel, 2012).” (O’Brien and Davis, 2013)

“Multicomponent seismic is one of these developing technologies that has not seen wide-spread

application throughout the oil and gas industry due to limited confidence in its ability to add value. The

azimuthal inversion performed in this thesis provides insight into the application of converted-wave

seismic for fracture characterization.” (MacFarlane, 2014)

“Numerical modeling (Li et al., 1996) suggests that gas-saturated and oriented fractures may have an

effect on anisotropic P-S reflectivity. This is in contrast to the isotropic case, where fluid saturation

appears to have less impact on S-wave velocities. In fact, Guest et al. (1998) interpreted anomalies in S-

wave splitting over a gas reservoir in Oman as evidence of an effect of gas on shear waves.” (Stewart,

2004).

Furthermore, using highly repeatably acquired and processed time-lapse PS data, Steinhoff concluded in

Grossman et al., (2012), that changes in shear wave splitting magnitude are correlated with how

successfully fractures have been propped open in the Montney Shale.

Facies Classification “Oil-sands and heavy-oil deposits are major players for the future of energy. The world’s largest deposits

are located in western Canada. The oil sands reservoir in the present study is located in the Upper

McMurray Formation, located in the Athabasca basin, one of the three major basins in Northern Alberta,

Canada.

High resolution 3C [multicomponent] 3D seismic data were processed using the most advanced

workflows in order to image several facies defined based on cores and logs available at wells in the

study area. These workflows include joint PP-PS inversion and neural network analysis and Bayesian

facies classification.

Using the above mentioned workflow in the oil-sand reservoir, we find that the method correctly locates

pay and non-pay facies allowing for prediction of oil saturation and reservoir connectivity, including

permeability and barrier baffle locations. Probability maps along with maps of the most probable facies

will be used by the team of geophysicist-geologist-engineer for in-situ operations such as planning of the

SAGD horizontal wells.” (Dumitrescu, et al., 2014)

Heat, Pressure, and Steam Front Mapping Schiltz, et al., (2014) conclude that steam chamber boundaries determined through time-lapse analysis

conform to high-density zones identified by a PNN (probabilistic neural network) density volume,

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confirming that high-density zones are shales which control steam chamber growth. They conclude that

PNN density prediction yields a way to predict success of SAGD in a given area. They also note that two

of the six attributes used to train the PNN were PS attributes, indicating (yet again!) that PS data provide

important information about density. Moreover, they found that pressure and heat effects outside the

steam chamber can be imaged with multicomponent seismic data. Areas of little to no change in Vp/Vs

indicate full steam chamber development, while areas of large Vp/Vs change surrounding the steam

chamber indicate either heated bitumen or pressurized water, depending on external data.

In previous work, the same authors model and map SAGD steam chamber evolution... “The goal of Joint

Inversion is to analyze PP and PS pre-stack CDP gathers to better invert the seismic trace for p-

impedance (Zp), s-impedance (Zs), and density (ρ) by incorporating the fact that Zs and ρ are related to

Zp. (Hampson, et al, 2005) The results from this work will be used to obtain p-wave velocity, converted-

wave velocity, and density which will then be formulated to calculate bulk and shear modulus of the

reservoir. The difference between bulk and shear modulus should be the actual steam chamber,

excluding conductive heat. Shear and bulk modulus are both a function of pressure and temperature,

however bulk modulus is also a function of fluid. The shear modulus acts as an indicator of the heat

front due to the fact that it goes to zero at a specific temperature, regardless of whether or not the

steam has reached the oil yet.” (Zeigler, Schiltz, Gray, 2013)

Enhanced P-Wave Imaging In permafrost, rock outcroppings, or other extreme conditions, one can mathematically rotate 3C

phones in line with ray arrival trajectories. Normally this is not necessary because waves tend to arrive

nearly vertically at the receiver due to relatively slow near surface velocities – this naturally separates P

and S waves onto the vertical and horizontal components, respectively. The result is to separate P and S

components in a new frame, which we can call wavefield separation (when there is P, S cross-

contamination). Such rotations are used also in 3C polarization filtering (DeMeersman, et al., 2006).

CO2 Sequestration Monitoring “Density, on the other hand shows a gradual drop with increasing concentration of CO2, indicating that

it is density not the Poisson’s ratio that will play a major role for an effective monitoring of carbon

sequestrated aquifers. Since inverting both vertical and radial components of the computed responses

in a multicomponent waveform inversion methodology can accurately extract density, we conclude that

converted-wave seismic data will be useful for monitoring of carbon sequestrated aquifers.” (Mallick, et

al., 2010)

Geomechanics “Oilfield Geomechanics has a broad range of definitions, and depending on who you ask you may get a

different answer. To this author, in its simplest form, it encompasses the study of how stresses and

strains within the earth affect what we drill into and explore for. The magnitude and direction of

stresses and how they affect the rock properties in a region, a field, and a wellbore has a massive impact

and control on what we do in unconventional resource exploration and exploitation. Unconventional in

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this case refers to tight sands and shales containing oil or gas that require stimulation to produce at

economic rates. This paper will describe how geomechanics influences wellbore stability, reservoir

properties, and hydraulic stimulations. Through this description of geomechanics I hope to convince

geophysicists that there is not so large a gap between the engineers we deal with and the seismic data

we look at every day.” (Wikel, 2011). The three principal stresses can be estimated from seismic:

overburden or vertical stress can be calculated from density, which can be estimated from joint

inversion (or well logs if available); minimum and maximum horizontal stress orientations and

magnitudes can be estimated from SWS, VVAZ, and AVAZ analyses. Multicomponent data clearly add

significant value to geomechanical modeling.

Challenges Associated with Converted-Wave Processing Converted-wave processing has certain challenges which distinguish it in complexity from conventional

P-wave processing. PS data tend to be noisier than PP data due to the greater sensitivity shear waves

have to attenuation effects. The raypaths are not symmetric about the midpoint between source and

receiver – the conversion point tends toward the receiver side of the midpoint. Converted-wave receiver

statics tend to vary by an order of magnitude greater than P-wave receiver statics. This is because shear

waves travel much more slowly than P-waves do in the typically unconsolidated earth comprising the

near surface, and P-waves are much more sensitive to variations in water table levels than S-waves are.

Thus there is typically very little correlation between P-wave and PS-wave receiver statics. Last but not

least, shear waves behave differently in the presence of azimuthal anisotropy than P-waves do. Whereas

P-waves exhibit azimuthal variations in velocity in the presence of azimuthal anisotropy, shear waves

split into two distinct polarization (particle vibration direction) modes, which are normally orthogonal to

each other and travelling at different velocities through the anisotropic layer. Regardless of whether

there is anisotropy present, it is imperative to have reliable information about the azimuthal

orientations of the two horizontal receiver components. Generally speaking, PS processing is much more

iterative and interpretive in nature than PP processing is, and as such it requires more time, effort, and

persistence to achieve quality results.

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General Processing Flow

Figure 1. Processing flow for PS data. For simplicity many steps are not included, e.g., noise attenuation, surface consistent

deconvolution and scaling. The processing flow is highly iterative and only the major iterative procedures are indicated.

Initial Processing

Geometry ******************************************************

Receiver Tilt Corrections Typically, P-S converted-wave energy is primarily recorded on the two lateral (H1 and H2) components

of the receiver. This occurs for two reasons. Firstly, velocity tends to increase with depth, which,

according to Snell’s law, causes rays to bend progressively toward the vertical as depth decreases.

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Secondly, shear waves typically propagate much more slowly than the compressional waves which

generate them upon reflection from an interface. It follows from Snell’s law that the conversion point is

not at the midpoint between source and receiver, but rather it is shifted laterally toward to the receiver.

Thus, converted-waves tend to arrive at the receiver along a more vertical trajectory than pure P-wave

reflections; hence the converted shear-wave particle motion, which oscillates within the vertical source-

receiver plane direction perpendicular to the ray trajectory, is mainly recorded on the lateral

components.

Fortunately with modern MEMS receiver technology, the DC component of acceleration – that is, the

vertical direction as indicated by the direction of the gravitational field – is measured and recorded for

each receiver. These data are then utilized to mathematically rotate the 3C receivers such that the

vertical component is aligned with the true vertical.

RADAR (Receiver Azimuth Detection And Rotation) Provided tilt corrections have been applied as required, and provided there is a relatively slow near

surface weathering layer, P-S converted-wave energy is recorded mainly on the two lateral components

of the receiver. Conventional processing of converted-wave energy includes mathematical rotation of

these laterally polarized data measurements into radial and transverse coordinates (Fig XXXX below). To

properly accomplish this, knowledge of the in-situ receiver orientation is essential. However, substantial

errors in the recorded receiver azimuth frequently arise in practice, and these errors spuriously manifest

themselves as radially polarized energy on the transverse component, thereby degrading the fidelity of

the signal recording. Further complications include potential misinterpretation of this energy seepage

onto the transverse component, for example, either as evidence of out-of-plane reflection energy, or,

perhaps worse, shear wave splitting. Indeed, Cary (2002) used forward modelling of converted-wave

data with and without minimal geometry errors (on the order of 5%) to show that such errors can

generate the same effects as shear wave splitting on limited azimuth stacks.

To address this problem, Sensor developed a high fidelity algorithm for automatically detecting the

receiver azimuths, called RADAR. This new method is based on azimuthal information extracted from

the P-wave first-break energy, which is present on all three components (see Figure XXX). For each

receiver ensemble, and for each source-receiver azimuth, a measure of the amplitude over the samples

following the first-break pick time up to the first detected zero-crossing is determined. For a given

receiver, and for each lateral component, these values are subsequently used in conjunction with an

orthogonality constraint as weights to determine the best-fit orientation for that receiver; a subsequent

analysis of the results yields a robust probability measure QC indicating the confidence level associated

with the resulting receiver-azimuth estimate. Receiver azimuth corrections are only applied if the QC

values exceed a specified threshold.

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Figure XXXX. Seismic waves interacting with a refractor, that is, a velocity interface for which the velocity increases across the

boundary. Because waves must propagate continuously through media, even when there is a discontinuity in the medium

properties, a head wave is created which connects the reflected and transmitted wavefronts (see triplicated wavefronts in

turquoise). The head wave is a plane wave propagating along the raypath (yellow), which arrives at the receiver at a non-vertical

angle of incidence. An expanded view of the receiver shows the projections (dashed orange) of the incident P-wave particle

motion (orange) onto all three measurement components (green). Given the orientation of the receiver in this particular example,

a peak is recorded as a trough on the vertical component, while peaks are measured as peaks on both lateral components.

The RADAR method relies on the ability to pick the first-break head waves on the vertical component of

the data, and makes use of the fact that these first breaks are also measured on the two lateral

components of the receiver. It also requires a sufficiently thick weathering layer (or velocity differential)

in order to distinguish the compressional from the delayed mode-converted shear head waves –

otherwise these waves can interfere and effectively corrupt the P-wave first break signature on the

horizontal components. For detailed information about RADAR, see Grossman and Couzens, (2012).

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Figure XXXX. The existence of P-wave refraction energy on all components is clearly evidenced by a real data example. Each of

the three components is displayed for a fixed receiver ensemble. The data have been tilt-corrected but no rotation has been

applied. One can also differentiate between P-wave reflections on the vertical component and PS reflections on the horizontal

components based on the differences in moveout.

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Figure XXXX. RADAR visual QC amplitude measures obtained from the first half-cycle following the first-break pick time are

displayed here for each receiver component in map view (according to the red-white-blue color scale). The receiver location is

marked as a triangle, and each amplitude measure is positioned at the relative shot location. This is a well-populated ensemble,

and it clearly demonstrates the azimuthal sensitivity which is the basis for RADAR. One can deduce that the H1 component is

oriented at approximately 110° counterclockwise from North, while the H2 component is approximately 20° counterclockwise

from North.

Rotation to Radial and Transverse Coordinates Receivers need to be mathematically rotated in the horizontal plane at various stages of the PS

processing sequence, which includes:

- applying receiver orientation corrections (e.g., RADAR, correction for magnetic declination)

- rotating to geostationary coordinates such as H1/H2 or PS1/PS2

- rotating between H1/H2 and Radial/Transverse coordinates

By definition, the Radial component, R, is directed positively outwards from source to receiver, and the

Transverse component, T, is directed 90 degrees clockwise from R (Figure XXXX). As per usual, the right-

handed system is adopted. By convention, H1 points in the inline direction, and H2 points in the

crossline direction, 90 degrees clockwise from H1. A rotation by a positive angle is a clockwise rotation

(looking down, in map view). A rotation to a positive angle is a rotation to the given angle as measured

clockwise from north.

Figure XXXX. Schematic in map view depicting azimuthal rotation of receivers from acquisition coordinates H1, H2 to the natural

processing coordinates, R, T, where R is parallel to the source-receiver azimuth.

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The R,T system is the natural coordinate system for processing converted-wave data. Indeed, for

isotropic, layered media, all converted wave energy is polarized within the vertical plane along the

source-receiver azimuth, and thus it should be isolated on the Radial component. As explained below,

any spurious coherent energy on the cross components may be indicative of shear wave splitting or

erroneously aligned receivers. Mathematical details of these component rotations can be found, e.g., in

Alford (1986), Thomsen et al. (1999) and Hardage et al. (2011).

Figure XXXX. Raw transverse-component, moveout-corrected, and muted receiver gathers. Recall that in an isotropic,

horizontally layered medium, no coherent reflection energy is expected on these gathers. The columns display the transverse

component gathers for two distinct receivers (A and B), while the rows display two different results of coordinate rotation from

the acquisition coordinates using: 1) the automatically detected azimuth from RADAR analysis (top row); and 2) the nominal

azimuth reported in the observer’s logs (bottom row). The differences between RADAR analysis and nominal azimuths are -90°

(left column) and 57° (right column) respectively. As expected, reflection events are virtually absent in the RADAR result, while

considerable coherent energy ‘leakage’ remains on the nominal result. Energy from the shear-mode head waves is also evident

in the lower left-hand corner of both results; as expected, the energy is erroneously stronger and much more coherent in the

nominal results.

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Estimating the Stacking Velocity Model and Imaging Parameters Following Li, et al., (2007) (after Alkhalifah and Tsvankin, 1995, and Thomsen, 1999, with all equations

checked and verified by J. Grossman) we use a rigorously derived VTI PS NMO moveout equation to

perform velocity analysis on ACP gathers. This is an iterative procedure used in conjunction with statics

and shear wave splitting compensation for estimating the physically meaningful stacking velocity model

parameters, 𝑉𝐶, 𝛾0, 𝛾𝑒𝑓𝑓, and 𝜒𝑒𝑓𝑓 defined in Table 1.

Once the stacking velocity model is obtained, the corresponding parameters are passed to the PS PSTM

module to perform the migration on ACP gathers. This yields CIP (common image point) gathers, which

can then be used to update the migration velocity model. The moveout is restored on the CIP gathers

using the VTI PS NMO moveout equation, and residual parameter analysis is performed as required to

flatten the gathers.

Prior to migration, the data are binned into COV (common offset vector) gathers which honour the ACP

binning. Migration is performed on each of these (ideally single-fold) gathers independently. COV

binning regularizes the data, which typically improves noise attenuation performance and also mitigates

migration artefacts caused by irregular sampling/fold coverage.

This improved processing flow avoids the complications inherent in the conventional method of

anisotropic imaging which includes CCP (common conversion point) binning, sometimes followed by

DMO. Moreover, the stacking velocity model and the imaging parameters are mathematically linked.

The new equations use physically meaningful parameters to accurately describe the moveout; this is

preferred over the conventional method which amounts to fitting a higher order polynomial to the

moveout with essentially arbitrary processing parameters. The former method makes it difficult to

bridge the gap between NMO processing and prestack migration, mainly because of this curve fitting

methodology, and also because the alternative includes processes such as CCP binning and DMO, both

of which are strongly dependent on the converted-wave velocities (Li et al., 2007).

Parameter Definitions and Important Relationships Table 1. Stacking Velocity Model Parameters

0 Average vertical Vp/Vs ratio, based on PP-PS horizon registration or well logs

2VC Converted-wave stacking velocity (hyperbolic moveout term – controls near offsets)

eff

Effective Vp/Vs ratio (asymmetric raypath/nonhyperbolic moveout term – controls mid offsets)

eff

Effective converted-wave anisotropy term (far offsets)

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𝛾0 = Vertical Vp/Vs ratio = average gamma = 𝜏𝑆/𝜏𝑃, where 𝜏𝑆 and 𝜏𝑃 are the two-way traveltimes to a

given event for the P and S legs of a vertically propagating converted-wave

𝛾2 = RMS or stacking gamma = ratio of P- and S-wave stacking velocities

𝛾𝑒𝑓𝑓 = Effective Vp/Vs ratio = 𝛾22/𝛾0

𝑉𝐶 = Converted-wave stacking velocity = short spread moveout parameter

𝜒𝑒𝑓𝑓 = Converted-wave effective VTI anisotropy parameter = 𝜂𝑃𝛾𝑒𝑓𝑓2 𝛾0 − 𝜂𝑆, where 𝜂𝑃 and 𝜂𝑆 are the

P- and S-wave VTI parameters, respectively

𝜂𝑆 = 𝜂𝑃𝛾𝑒𝑓𝑓2 , and so

𝜒𝑒𝑓𝑓 = 𝜂𝑃𝛾𝑒𝑓𝑓2 (𝛾0 − 1)

Thus, for some typical values, say 𝛾𝑒𝑓𝑓 = 1.6 and 𝛾0 = 2, we have 𝜒𝑒𝑓𝑓 = 1.28𝜂𝑃, while 𝜂𝑆 = 2.56𝜂𝑃.

So for 𝜂𝑃 = 0.05 say, we have 𝜒𝑒𝑓𝑓 = 0.064 and 𝜂𝑆 = 0.128.

PS1, PS2 = converted-wave data rotated to geostationary coordinates corresponding to the fast and

slow shear wave polarizations

Stretching from PP Time to PS Time For quick comparisons of events on PP and PS stacks, or for estimating an initial brute ACP static from

the PP CDP statics, one can visually estimate a stretch factor required to coarsely register PP and PS

events. This is equivalent to estimating the vertical Vp/Vs value, 𝛾0, which we discuss below.

A typical starting value for 𝛾0 is 2. To convert a PP arrival time to PS time, multiply the PP time scale by

a factor of (1 + 𝛾0)/2. Thus if the average Vp/Vs ratio to a given event is 2, the stretch factor up to that

event is 1.5. In other words, the event is expected to occur in PS time at 1.5 times the arrival time as

viewed in PP time.

Explicitly, we have

𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 = 𝜏𝐶

𝜏𝑃=

1 + 𝛾0

2,

where 𝜏𝐶 and 𝜏𝑃 are the two-way C- and P-wave traveltimes to a given event. This relationship is plotted

in Figure XXXX.

19 DRAFT 02/03/2015

Figure XXXX. Relationship between the stretch factor for converting between PP and PS time and the vertical Vp/Vs ratio, 𝛾0.

ACP Binning It is well known that for a given source-receiver offset, the lateral position of the P-to-S mode

conversion varies with depth, and occurs not at the midpoint but is shifted away from the midpoint

toward the receiver. This shift becomes more pronounced with decreasing reflector depth. In order to

image events properly, it is necessary to account for this conversion point movement when gathering

and stacking these data.

The simplest method of common-conversion point (CCP) gathering uses the asymptotic conversion point

(ACP) approximation, in which the conversion offset 𝑥𝑎𝑐𝑝 is approximated as

𝑥𝑎𝑐𝑝 = 𝑥𝛾0

1 + 𝛾0,

where 𝑥 is the total source-receiver offset and 𝛾0 is a constant given by the average Vp/Vs value down

to the reflector of interest (this gamma is also known as ‘vertical gamma’, ‘vertical Vp/Vs’, ‘average

gamma’, and ‘gamma-zero’). This approximation is most accurate for small offset-to-depth ratios, and

has been shown (Eaton et al., 1990) to potentially introduce artifacts such as smearing and footprinting

into the P-SV stacked section. Notice that the ACP location, 𝑥𝑎𝑐𝑝, reduces to the midpoint for the special

case of PP reflections, that is, when 𝛾0 = 1 (see Figure XXXX).

1 2 3 4 5 6 71

1.5

2

2.5

3

3.5

4

str

etc

h f

acto

r =

c /

p

0

PP to PS stretch factor vs. 0

20 DRAFT 02/03/2015

Figure XXXX. Relationship between the lateral ACP position as a fraction of total offset and the vertical Vp/Vs ratio, 𝛾0. In the

limit as the Vp/Vs ratio reduces to 1 (PP reflections), the 𝑥𝑎𝑐𝑝/𝑥 ratio reduces to ½, meaning 𝑥𝑎𝑐𝑝 corresponds with the midpoint.

As the Vp/Vs ratio increases to infinity, the 𝑥𝑎𝑐𝑝/𝑥 ratio approaches 1, and so 𝑥𝑎𝑐𝑝 tends toward the receiver location.

While the asymptotic method of binning converted-wave data may not provide the best results, it is

nevertheless useful early in the processing sequence (when accurate gamma functions are not yet

known) for creating common ACP stack sections that approximate true CCP stacks. By correlating

common events picked on P-P CMP stacks with those on P-S ACP stacks, time-variant vertical Vp/Vs

values can thus be determined. It is worth considering that for very small offset-to-depth ratios, CCP,

ACP, and CMP surface locations are essentially the same; however, the differences can be significantly

large for shallower events even at moderate offsets.

Converted-Wave Statics While converted-wave receiver statics cannot be estimated reliably from the PP refraction statics

solution (see next section), the source statics are essentially the same. Elevation statics can be

incorporated, but a shear wave replacement velocity should be used. Residual statics (e.g., mastt, max

power) may also be incorporated in the usual way.

Receiver Statics Receiver statics for converted-wave data can easily be an order of magnitude greater than receiver

statics for P-wave data. This is due to the fact that S-waves travel much more slowly than P-waves,

especially within the unconsolidated weathering layer, where Vp/Vs ratios can easily reach magnitudes

as high as 4 to 7. S-waves are also much less sensitive to water table fluctuations than P-waves, and as a

result there tends to be very little correlation between PP and PS receiver statics. Resolution of receiver

statics can have a dramatic impact on stack quality and also on the common offset stacks (COS) used for

1 2 3 4 5 6 70.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0

AC

P p

osit

ion

rela

tive t

o t

ota

l o

ffset,

x

acp /

x

ACP position as fraction of total offset vs. 0

21 DRAFT 02/03/2015

velocity analysis. Comparisons of ACP gathers or COS with and without receiver statics applied can help

resolve uncertainty with regard to different events. For example, one can usually see P-wave first breaks

quite clearly prior to applying these statics, but they tend to break up considerably afterward. Likewise,

P-wave reflection energy often appears in the shallow prior to resolving receiver statics, and tends to

attenuate considerably afterward; and coherent PS energy starts to appear in its place. These

observations provide confirmation that the receiver statics estimation is on the right track.

A conventional approach (Cary and Eaton, 1993) to receiver statics estimation involves flattening one or

more events on common receiver stacks. The idea is that whatever time shifts are required to flatten

the receiver stack are directly related to the differential receiver statics. To avoid disturbing any

structure that may be present however, one ideally should first construct a reference horizon(s), or long

wavelength ‘structural term’, by identifying and picking the corresponding event(s) on the PP common

receiver stack, and stretching the resulting horizon(s) to PS time using the best available estimate of 𝛾0.

This is used internally in the statics program to temporarily shift the traces on the PS common receiver

stack, prior to flattening for receiver statics estimation. This particular method maximizes stack power

in a window along the picked horizon(s) based on a surface consistent model, scanning over trial statics

and optionally over phase. It is a robust method for obtaining an initial estimate of large, short-

wavelength receiver statics by optimizing the trace-to-trace coherence of the common-receiver point

(CRP) stack.

One disadvantage of this framework is the need to apply moveout correction, which may be quite

challenging at first. Two new promising methods for receiver statics estimation introduced in the papers

by Cova, et al. (2015), and Guevara and Margrave (2015) should be investigated. The second is simpler

than the first, and has the advantage that it does not require moveout parameter estimation. Rather

than stacking common receiver gathers directly, the method involves crosscorrelation of common offset

pairs of traces from neighbouring receiver gathers. This approach requires a regularization step in order

to populate the common offset bins.

In many cases distinct PPP and PPS (or PSP and PSS) refracted arrivals are both present in the data

(Figure XXXX), respectively on the vertical and radial components, and the time delay between these

events (which have the same moveout) can be used to as an alternative method for estimating the

receiver statics (DeMeersman and Roizman, 2009). The weathering layer must be thick enough (for a

given Vp/Vs ratio within that layer) to allow separation in time between the two refracted modes.

Specifically, receiver function analysis can be used to estimate the time difference between an S-wave

arrival and a P-wave arrival from the base of the weathering layer (DeMeersman and Roizman, 2009).

From the P-wave refraction statics we know the time it takes a P-wave to travel from the base of the

weathering layer to the receiver. The sum of these two times is approximately equal to the S-wave

traveltime from the base of the weathering layer to the receiver, and thus it provides an estimate of the

receiver static correction.

22 DRAFT 02/03/2015

Figure XXXX. Illustrations of post-critically refracted head waves generated whenever there is a velocity increase across a

boundary. The up-going head waves arise as a consequence of the transmitted wavefield propagating faster than the incident

wavefield, and because continuity of the wavefronts must be maintained for physical reasons (see Grant and West, 1965 for a

more detailed explanation). In accordance with Huygens’ Principle, we can think of the head wave as being generated by a point

source propagating along the interface at the speed of the lower medium. PPP and PPS head waves (top) will have the same

apparent velocity, or moveout on gathers, but since they are propagating at different velocities there will be a time delay between

the faster PPP and slower PPS. Similar remarks apply to the PSP and PSS head wave pair (bottom). When the PSP, PSS refraction

pair exists, they will display slower apparent velocity than the PPP, PPS refractions.

In principle, after source statics (inherited from the PP processing) are applied to the radial-component

data, further static analysis should be constrained by keeping the source term fixed.

Sometimes shallow shear wave splitting effects can degrade event coherence enough to complicate

receiver statics estimation. In such cases, it may be beneficial to perform shallow shear wave splitting

analysis and layer stripping for the near surface anisotropy on azimuth sectored receiver gathers (limited

azimuth stacks, or LAS), prior to receiver static determination. Normally, this analysis is performed on

ACP LAS, but for shallow events the raypath spread for the upgoing shear wave within the splitting zone

is acceptably small for the analysis to be based on common receiver gathers (Cary, et al., 1993).

23 DRAFT 02/03/2015

Estimating the Vertical Vp/Vs Ratio, 𝜸𝟎 At the beginning stages of processing, usually very little is known about the Vp/Vs ratios. Sometimes

dipole sonics are available from well logs and these can be quite valuable, particularly if they are logged

up to the surface. Otherwise one must start with a good guess for 𝛾0 and update it as the processing

progresses. At this stage of the processing, a constant value of 𝛾0 has already been selected for the

purpose of ACP binning, and so the ACP binning may need to be updated as 𝛾0 is refined.

Once a brute velocity model, statics and mute are established, 𝛾0 can be re-estimated via coarse

registration of events between the PP CMP stack and the PS near offset ACP (or CCP) stack. To begin

with, one can visually estimate a constant stretch factor simply by attempting to align events on the two

stacks by manually squeezing the entire PS section vertically – the so-called ‘PowerPoint’ method of

registration. Then once the stack quality is sufficient to enable horizon picking, e.g., through refinement

of statics, velocities, deconvolution and/or noise attenuation, an improved registration can then be

carried out. From the formula above for the stretch factor between corresponding PP and PS events, we

have

𝛾0 = 2 ∗ 𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 − 1.

This relationship is illustrated in Figure XXXX above.

Estimating the Effective Vp/Vs Ratio, 𝜸𝒆𝒇𝒇

In the absence of VTI anisotropy, 𝛾𝑒𝑓𝑓 and 𝛾0 are identical quantities. Normally there is an observable

VTI effect however. This will already have been established from the PP processing results, in particular,

from the value of the P-wave VTI parameter, 𝜂𝑃. This effect manifests as a sharp upward curl of events

on NMO corrected gathers at larger offset-to-depth ratios, 𝑥 𝑧⁄ ≥ 1.5. This curl is most obvious on

shallower events at moderate offsets. The dominant imaging parameter which controls this portion of

the moveout is 𝜒𝑒𝑓𝑓, which is related to the P-wave VTI anisotropy and the effective and average

gamma parameters through

𝜒𝑒𝑓𝑓 = 𝜂𝑃𝛾𝑒𝑓𝑓2 (𝛾0 − 1).

As a starting point, one may either assume that 𝛾𝑒𝑓𝑓 is a scaled version of 𝛾0, or an estimate can be

computed based on the results obtained thus far. For the latter, the relationship is

𝛾𝑒𝑓𝑓 =𝑉𝑃2

2

𝑉𝐶22 (1 + 𝛾0) − 𝑉𝑃2

2 .

This calculation is quite sensitive to errors in 𝑉𝐶2 however, so should be used with caution.

The first method involves scanning for 𝛾𝑒𝑓𝑓 as a range of percentages of 𝛾0 by making a series of CCP

stacks based on these trial percentages, and then attempting to pick optimal estimates of 𝛾𝑒𝑓𝑓 across

the set of CCP stacks. When there is structure present in the stacks, this method can be helpful.

Otherwise it may be difficult or impossible to select the ‘best’ stack objectively (Cary and Lu, 1999).

24 DRAFT 02/03/2015

A recommended approach to parameter scanning within this framework first involves estimation of 𝑉𝐶2

and the VTI parameter 𝜒𝑒𝑓𝑓 through moveout/semblance analysis, followed by 𝛾𝑒𝑓𝑓 estimation through

an appropriate combination of the above methods, including moveout/semblance analysis. Recall that

the converted-wave stacking velocity is a hyperbolic moveout term which controls the near offset

moveout, while the effective Vp/Vs ratio is an asymmetric raypath/nonhyperbolic moveout term which

controls mid offsets, and the effective converted-wave anisotropy term controls the far offsets.

As we will see, 𝛾𝑒𝑓𝑓 is an important parameter for describing the relationship between the migration

velocity, 𝑉𝐶𝑚𝑖𝑔 and the stacking velocity, 𝑉𝐶2. It controls the lateral positioning of the conversion point,

and thus is essential in forming accurately positioned common image gathers. Nonetheless, 𝛾𝑒𝑓𝑓 can be

the most elusive of the imaging parameters to resolve.

Prestack VTI Migration At this stage of the processing, fairly accurate estimates of the converted-wave stacking velocity model

should be available. However, residual moveout analysis should still be performed on migrated gathers

after PS VTI NMO removal, and the theoretically ideal velocity used for NMO removal should be the

migration velocity, 𝑉𝐶𝑚𝑖𝑔. The migration velocity is related to the stacking velocity, 𝑉𝐶2, via 𝛾𝑒𝑓𝑓

through

𝑉𝐶𝑚𝑖𝑔

𝑉𝐶2=

2√𝛾𝑒𝑓𝑓

1 + 𝛾𝑒𝑓𝑓.

This ratio is plotted as a percentage for a range of 𝛾𝑒𝑓𝑓 values in Figure XXXX.

25 DRAFT 02/03/2015

Figure XXXX. Plot of theoretical converted wave migration velocity as a percentage of the stacking velocity for a range of effective

gamma values.

Shear Wave Splitting Analysis and Layer Stripping The phenomenon of shear wave splitting (SWS) is most readily understood in terms of a familiar form of

azimuthal anisotropy: that induced by aligned vertical fractures or cracks in brittle, otherwise isotropic

rocks (Martin and Davis, 1987). This is an example of HTI anisotropy, where HTI stands for ‘transverse

isotropy with a horizontal symmetry axis’. ‘Transverse isotropy’ refers to the isotropic plane which is

perpendicular to the symmetry axis, and the symmetry axis is perpendicular to the dominant fracture

strike and dip. When the HTI symmetry is due to vertical fracturing, the fast direction (PS1) corresponds

to propagation parallel to the fracture strike, while the slow direction (PS2) is perpendicular to the

fracture strike.

More generally, any form of azimuthal (velocity) anisotropy leads to shear wave splitting, and the cause

need not be due to fractures. In fact, any small scale structure (sub seismic wavelength) exhibiting

dominant directionality will manifest as anisotropy. For example, near surface clay tills contain clay

particles which tend to be preferentially aligned, thereby inducing HTI anisotropy. Indeed, “tectonic and

geomorphological processes such as crustal movements, tilting, moving ice sheets, erosion and

solifluction may produce soils with stresses varying in different horizontal directions” (Graham and

Houlsby, 1983). We often see strong shear wave splitting in the overburden, and specifically in so-called

non-compliant rocks (Cary et al., 2010) which tend not to support fracturing.

26 DRAFT 02/03/2015

Influences on anisotropy strength may include elevated pore pressure due to injection, temperature

increase over time, induced fracturing in brittle rocks, propping of fractures (Grossman et al., 2013), and

the degree to which fractures are aligned.

Indications of shear wave splitting In the special case where the radial and transverse coordinates of converted-wave data happen to be

aligned with the PS1 or PS2 directions in an azimuthally anisotropic, horizontally layered earth, no

splitting occurs. Thus, for these special source-receiver azimuths, no coherent energy should be present

on the transverse component. For all other source-receiver azimuths, splitting occurs and coherent

energy ‘leaks’ onto the transverse component.

The converse is not necessarily true however, that is, the presence of coherent energy on the transverse

component is not always indicative of anisotropy. It can occur when receiver orientations are not

correctly known, or when there is significant structure such as out-of-plane dip.

Limited azimuth stacks (LAS), are azimuthally sectored stacks, sorted by source-receiver azimuth (Figures

XXXX and XXXX). For moderate shear wave splitting magnitudes, these stacks reveal apparent sinusoidal

traveltime variations on the radial component and polarity reversals along the fast and slow directions

on the transverse component. When the magnitude of the time delay between fast and slow arrivals is

sufficiently large, the radial component can also display polarity reversals. From our observations above,

it follows that the polarity reversals occur on the transverse component precisely along the PS1 and PS2

azimuths. The peaks and troughs on the radial arrivals also correspond to the PS1 and PS2 azimuths,

respectively, and the time delay between fast and slow arrivals on the radial component indicates the

splitting magnitude.

27 DRAFT 02/03/2015

Figure XXXX. Limited azimuth stacks of synthetic data. The partially stacked traces are sorted by source-receiver azimuth. Note

the sinusoidal variation in traveltime on the radial component and the polarity reversals on the transverse component. The

polarity reversals on the transverse data occur along the PS1 and PS2 azimuths, and similarly for the peaks and troughs on the

radial arrivals. The time delay between fast and slow arrivals on the radial component indicates the splitting magnitude.

Figure XXXX. (After Grossman and Popov, 2014) Limited azimuth stacks for PS data at two locations A (left panel) and B (right

panel). Each of the two locations shows LAS’s for R and T components. There is clear indication of SWS at location A and very

little at location B. At location A, R events show sinusoidal variation in traveltime with azimuth, and energy has leaked onto T,

with clear polarity reversals every 90 degrees. Visual inspection of the magnified R events suggests traveltime delays of 12ms at

location A, and less than 2ms at location B.

28 DRAFT 02/03/2015

PP common-offset, common-azimuth (COCA) volumes. PP COCA volumes are created by binning P-wave

traces into common source-receiver offset and azimuth ranges and then stacking within each of the

resulting bins to assign a single trace per offset-azimuth bin (Gray, 2007). Traces from the COCA volume

may then be sorted by offset, with azimuth as secondary sort key to enable visualization of azimuthal

velocity anisotropy.

Azimuthal anisotropy for P waves manifests as a sinusoidal variation in traveltime with source-receiver

azimuth. This variation is negligible at zero offset and increases with offset as the raypaths become

more horizontal and therefore more sensitive to the azimuthal velocity variation. The COCA volume

displayed in Figure XXXX clearly displays these traveltime characteristics of azimuthal anisotropy. One

should expect SWS when the PP processing reveals azimuthal anisotropy.

Figure XXXX. Two COCA volumes, sorted by offset with source-receiver azimuth as the secondary sort key, from same locations

A and B as per Figure XXXX. Events within the yellow window are expanded for clarity. At location A (left COCA display) azimuthal

anisotropy reveals itself as a sinusoidal variation in traveltime with azimuth, and this variation increases in magnitude with offset.

Visual inspection shows a total variation of approximately 4ms. Location B (right COCA display) shows little to no azimuthal

anisotropy.

PS Layer Stripping Using rotation operators, we can mathematically simulate an experiment in which H1 and H2 are aligned

with the PS1 and PS2 directions. This process decomposes the PS wavefield into fast and slow shear

modes. Therefore, to layer strip, we rotate the data to PS1, PS2 coordinates, shift events up on PS2 to

29 DRAFT 02/03/2015

align with the corresponding events on PS1, and then rotate back to the R, T system (Figure XXXX). This

removes the effect of splitting, transfers coherent energy from T to R, and effectively replaces that layer

with an isotropic one. When layer stripping is performed correctly, events within the current layer will

be flattened on the LAS of the radial component, whereas the corresponding zones on the LAS of the

transverse component should have no coherent energy. If there is coherent energy remaining on the

transverse component below the current layer, then another iteration of layer stripping is required.

SWS analysis Since the PS1 direction is not known a priori, we first perform a brute force scan on R and T LAS’s over

all azimuths and time delays and use an objective function to determine the solution – e.g. maximize

stack power on the radial component (Li and Grossman, 2012), and then perform the layer stripping

procedure as described above. This automated scanning procedure is referred to as SWS analysis. The

outputs of the analysis include maps of the estimated PS1 azimuth, the corresponding time-delays

between the PS1 and PS2 events, and a QC factor used to determine the quality of the estimates.

Normally these attributes are surface consistent, and so each receiver is rotated according to which ACP

or CCP bin it belongs to. Sometimes, especially in the shallow portion of the section, the analysis and

correction may be performed on common receiver gathered LAS’s. This can be useful in more difficult

data when the receiver statics may not yet be resolved.

Typically, time-delays on the order of 2ms or less lead to unreliable estimates of the PS1 direction and

should be set to zero for the layer stripping procedure. Some editing of the time delay estimates should

also be performed in this case. One can threshold the QC map to construct a mask to void the unreliable

estimates and then interpolate/smooth the resulting maps as required. The layer stripping procedure is

outlined below in Figure XXXX.

30 DRAFT 02/03/2015

Figure XXXX. Shear wave splitting analysis and iterative layer stripping procedures.

31 DRAFT 02/03/2015

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