QI Adequacy and Use of Additional Data Required for Correlation, Calibration and Integration

BILL GOODWAY

QEYE LABS, SCIENTIFIC ADVISOR: QUANTITATIVE INTERPRETATION AND AVO TECHNOLOGY,

BG@QEYE-LABS.COM

 

Abstract

Quantitative Interpretation (QI) has become a popular term, but it often falls short of seismic interpreters' expectations. This is largely because QI is an ambitious and under-constrained objective. However, with proper calibration, its goals can be realized. This paper discusses the importance of incorporating under-utilized supplementary data to enhance correlation, calibration, and integration, leading to more effective AVO/QI workflows. The key elements include (1) the walkaway AVO VSP and elastic logs for combining borehole and surface seismic data through seismic inversion, especially when guided by VSP-based background offset scaling and balancing. This approach improves the correlation between elastic properties derived from AVO inversion and well log data. (2) The error-free elastic logs for AVO calibration and rock physics modeling. Errors in elastic logs can lead to incorrect interpretations and unnecessary delays. (3) The use of accurate low-frequency models for AVO inversion and the derivation of elastic properties. They may be built using well log data co-kriged with migration velocities or full-waveform inversion (FWI) velocities. (4) The use of accurate angle-dependent wavelets for AVO impedance inversion, which are usually extracted under an isotropic assumption. However, the presence of VTI anisotropy in background shales, often ignored, should also be accounted for.

 

By integrating these additional data into AVO inversion and QI processes, more reliable and encouraging results can be achieved.

 

Introduction

Over the past decade, Quantitative Interpretation (QI) has become a buzzword in our industry. While the adoption of appropriate workflows is essential, the effectiveness of QI often hinges on the inclusion of additional data for correlation, calibration, and integration. This leads many seismic interpreters to question whether QI is truly being applied effectively, or if it's just another industry trend.

 

In this context, I explore the answer to this question as applicable to AVO inversion of seismic data. The ultimate goal of applied geophysics is to remotely characterize the subsurface in all its geological complexity—accounting for factors like lithology, porosity, rock fabric, fluids, pore pressure, and in-situ stress. To achieve this ambitious objective of inverting seismic data for QI, a comprehensive and diverse range of supplementary data is required. This includes inputs from borehole logging, petrophysics, rock physics, core measurements, lithofacies descriptions, and processing velocities, among others.

Incorporating these diverse datasets is key to advancing QI beyond just being a buzzword and ensuring its effective application in subsurface interpretation.
This paper highlights the importance of incorporating under-utilized supplementary data for improved correlation, calibration, and integration in AVO/QI workflows. As illustrated in the red boxes in Figure 1, which outlines a general AVO inversion flow diagram, several critical changes could significantly enhance the effectiveness of these workflows. I propose that adopting four essential modifications would lead to more promising results:

 

1. 1. QI confirmation and calibration of walkaway AVO VSP and elastic logs: This involves combining borehole and surface seismic inversion, with a walkaway VSP guiding background offset scaling and balancing.
   2. Error-free full elastic log suite: Ensuring an error-free elastic log suite is crucial for AVO calibration and accurate rock physics modeling.
   3. Accurate low-frequency models (LFM): Correct LFM is necessary for AVO Fluid Factor and QI from both relative and absolute inversion. This can be achieved using well log co-kriged with migration velocities or Full Waveform Inversion (FWI) velocities.
   4. Wavelet estimation and VTI log tie: This includes both spectral amplitude and phase considerations, as well as ensuring spatial wavelet stability, particularly for phase accuracy.

By incorporating these key adjustments, the overall results of AVO/QI workflows could be significantly improved.

Figure 1. Typical workflow for AVO/QI.

Addressing QI adequacy

I will now elaborate on each of the points mentioned earlier, demonstrating how their careful adoption adds significant value to QI exercises. Let's begin with the first point:

1. QI confirmation/calibration of walkaway VSP AVO and elastic logs for combined borehole and surface seismic inversion: walkaway VSP-guided background offset scaling/balancing

The accuracy of inverting seismic data to derive elastic parameters, which are essential for predicting lithology and fluid type, heavily depends on the quality of prestack AVO amplitudes. These amplitudes are often compromised by noise and multiple interference, making it difficult to reliably extract elastic properties. Prestack processing aims to preserve the AVO response, but how well it does so is usually unclear.

This is where walkaway Vertical Seismic Profiling (VSP) becomes invaluable. The walkaway VSP provides a "true" AVO measurement, largely free from noise and multiple contamination, which can serve as a benchmark for calibrating surface seismic data. By using the walkaway VSP as a guide, we can correct the background offset scaling and balancing in surface seismic data. This process ensures that prestack AVO amplitudes are aligned more accurately, ultimately leading to more quantifiable and reliable inversion results.

The underutilized walkaway VSP provides a true amplitude reference for quantifying the AVO response, as supported by studies from Coulombe et al. (1996), Goodway et al. (1998), Downton et al. (1999), and Goodway (2001).

In Figure 2a, the walkaway VSP geometry is shown, designed specifically for AVO analysis and calibration. The source and receiver positions are depicted schematically by flags (for sources) and triangles (for receivers), with seven source half-offsets ranging from 50 m to 850 m. These offsets correspond to reflection offsets of 100 m to 1700 m in two-way travel time (TWT). An amplitude-preserving processing flow was applied to both the VSP and co-located 3D surface seismic data. This process was guided and calibrated using a joint log AVO synthetic model and an offset VSP method.

The result of this approach is the "true" VSP reflectivity AVO gather, as shown in Figure 2b. This AVO gather serves as a benchmark, confirming the expected AVO behavior, in this case for a Class III AVO gas sand at around 0.95 s TWT. This confirmation allows for more reliable interpretation of the AVO response in surface seismic data.

An additional benefit of the walkaway VSP AVO gathers is their ability to identify internal multiple interference. The AVO response of these multiples arises from multipathing effects generated by overlying sand and coal reflections, occurring below the lowest receiver level in the borehole, as also illustrated in Figure 2b. This insight helps in differentiating true AVO signals from interference caused by internal multiples, further improving the accuracy of the seismic interpretation.

Thus, the walkaway VSP provides critical data for calibrating surface seismic AVO, offering a clearer, more reliable AVO response while also assisting in identifying and mitigating internal multiples, and therefore, enhancing the overall value of QI workflows.

Figure 2. (a) Geometry adopted for the walkaway VSP data acquisition. (b) AVO gather from VSP PP reflections. Notice the AVO expectation for a class III gas sand in the gather at 0.95 s, as well as the later arriving internal multiple interference that also exhibits an AVO response.

When a collocated surface 3D seismic dataset is processed through a VSP-controlled, AVO-preserving workflow, it enables a direct, calibrated comparison of the reliability of various AVO simultaneous inversion outputs, such as P-impedance, S-impedance, and Lambda-Rho.

Simultaneous inversion utilizes multiple seismic sub-stacks (based on different offsets or angles) and their corresponding wavelets as inputs. The outputs of this inversion include P-impedance, S-impedance, V_P/V_S ratios, as well as elastic parameters like Lambda-Rho, Mu-Rho, and density. For each sub-stack, a unique wavelet is estimated (see section 4 for further details).

These sub-stacks and wavelets are then fed into the inversion algorithm, which compensates for offset-dependent phase, bandwidth, and tuning effects. The inversion algorithm begins by estimating angle-dependent P-wave reflectivities from the input partial stacks. These reflectivities are modeled and fitted using approximations of the full Zoeppritz equations, such as the Aki-Richards equation, to compute band-limited elastic reflectivities.

By using a VSP-controlled workflow, the calibration of the surface data is refined, improving the confidence in the AVO inversion results and ensuring that the output elastic parameters are more reliable for predicting subsurface properties like lithology and fluid content.

Figure 3 demonstrates a comparison between ground truth log data and inverted elastic parameters derived from the 3D surface seismic, P-P, and P-S converted wave VSP outputs. Qualitatively, there is a reasonable match between the inverted 3D seismic and VSP traces for both P-impedance and S-impedance. Notably, Lambda-Rho (Figure 3c) exhibits a significantly improved match to the log-derived ground truth, especially at the Viking target, underscoring the value of including this parameter in inversion analysis.

Figure 3. Comparison of VSP to surface seismic inversions and with well log information comprising (a) P-impedance, (b) S-impedance, and (c) Lambda-Rho. Notice the inverted seismic and VSP traces exhibit a reasonable match with P- and S-impedance, but an improved match is seen with Lambda-Rho.

In Figures 4a to c, the inverted 3D surface seismic and VSP data are tied directly to well logs in both depth and time, providing a quantified assessment of the correlation between inverted elastic parameters and wireline logs. Specifically, the correlation of the P-impedance traces with log data is excellent, showing a correlation of 0.85 with the log-derived P-impedance (Figure 4a). Similarly, the correlation for walkaway VSP the correlation is 0.9, and for the VSP corridor stack there is even higher correlation of 0.97.

These comparisons highlight the enhanced accuracy of VSP-guided inversion, especially when it comes to calibrating surface seismic data and improving the reliability of subsurface elastic property predictions.

Figure 4. Crossplotting of measured and inverted P-impedance for (a) surface seismic data, (b) walkaway VSP data, and (c) VSP corridor stack. Similar S-impedance crossplots are shown for (d) surface seismic data, (e) PP walkaway VSP data, and (f) PS walkaway VSP data. High correlation coefficients are seen for all the crossplots.

The comparison of S-impedance between the inverted data and log measurements also shows high correlation values, reinforcing the effectiveness of using walkaway VSP for calibration. Figure 4d shows a correlation of 0.89 for the 3D surface seismic data, indicating a strong match with the log-derived S-impedance. A slightly lower correlation of 0.87 is shown for the P-P walkaway VSP (Figure 4e) and a correlation of 0.86 was obtained for the P-S converted wave walkaway VSP.

These consistently high correlations across different datasets emphasize the value of incorporating walkaway VSP into the workflow. By using the walkaway VSP for calibration, both amplitude-preserved processing and AVO inversion can be better controlled, resulting in more reliable and accurate elastic property predictions. This highlights the necessity of integrating VSP data to optimize the seismic inversion process, ensuring that the inverted properties align more closely with true subsurface conditions.

2. Need for error-free full elastic log suite for AVO calibration and rock physics modelling

The importance of having a comprehensive set of P-wave, shear, and density logs for calibrating litho- and poroelastic facies in AVO/QI workflows is well established, and most projects manage to meet the basic requirements for elastic logs. However, a critical and often overlooked need is for edited, error-free shear sonic logs and sonic scanner anisotropic tensor solution logs. This is especially crucial for shear logs, where insufficient correlation length can result in unstable synthetic log ties. Such issues compromise the accuracy of low-frequency background reference models (LFM), depth trends, and synthetic seismic angle wavelet ties, all of which are fundamental to accurate QI.

Figure 5. Crossplot between P-impedance and S-impedance using data on P-velocity, S-velocity and density published by Castagna and Smith (1994).

A common problem arises from hidden sonic log errors, particularly in shear measurements. These errors are often missed due to a lack of understanding of how to properly analyze and identify such issues. If not corrected, they can significantly degrade the accuracy of the inversion results. Figures 5 and 6 illustrate an example of log-based error identification and analysis. In these figures, from published global log data from Castagna and Smith (1994), P-impedance versus S-impedance are compared to the equivalent Lambda-Rho versus Mu-Rho (LMR) crossplots (Goodway, 2001). These LMR crossplots offer a way to visualize and diagnose errors by highlighting inconsistencies that may otherwise go unnoticed in standard elastic log analysis using P-impedance versus S-impedance.

Ensuring that the shear logs and associated data are free from errors is essential for producing reliable synthetic ties and for constructing robust low-frequency models, ultimately enhancing the precision of the QI process.

Figure 6. Crossplot between computed Lambda-Rho and Mu-Rho using the data on P-velocity, S-velocity and density published by Castagna and Smith (1994). Notice the negative values of the elastic constants to the left of the crossplot, which appear to be erroneous.

A couple of interesting observations can be made by comparing the cross-plots:

a) The Lambda-Rho versus Mu-Rho crossplot (Figure 6) offers a more effective tool for separating gas sands from brine sands and shales within the full crossplot space. This makes it particularly valuable for lithology and fluid characterization as well as for identifying errors in the data. In contrast, the P-impedance (Ip) versus S-impedance (Is) crossplot (Figure 5) exhibits a much narrower correlation across all rock types. This narrow correlation results in relationships such as Castagna's "mudrock line", which is shown by the dark black solid lines that mark gas sand cut-offs on both crossplots.

The reason for the strong Ip-Is correlation is due to the ambiguity between V_P and V_S, which both share the shear modulus (Mu). This relationship is captured in the velocity equation: V_P² = (λ/ρ) + 2V_S², where V_P and V_S are tied to the same shear modulus. As a result, it becomes challenging to differentiate between lithologies and fluids using just the impedance crossplot.

By contrast, Lambda-Rho and Mu-Rho values are more orthogonal in their relationship. This orthogonality leads to better clustering of similar lithologies, particularly the gas sands, which appear as tight clusters in the lower-left quadrant (circled in Figure 6). Furthermore, the brine sands and shales exhibit distinct, separated linear trends (dashed orange line). This clear separation of rock types in the Lambda-Rho versus Mu-Rho space enhances the ability to not only distinguish between gas and brine sands but also to detect errors in log measurements more effectively than using the Ip-Is crossplot alone.

b) The Lambda-Rho and Mu-Rho crossplot provides not only a more intuitive interpretation of rock types but also a clearer framework for error analysis and identification. The low Mu-Rho gas sands, circled in the lower left quadrant, are most likely younger, less consolidated sands, which is evident from their low Mu-Rho values. In contrast, the three gas sand points in the upper left quadrant have mid-to-high Mu-Rho values but are clearly erroneous. These points exhibit either zero or negative Lambda and Poisson ratio values, while still showing a positive bulk modulus. This discrepancy suggests a compounding error, as these sand log values could mistakenly be used for modeling, such as Gassmann fluid substitution, without recognizing that the logs are flawed.

The situation becomes even more confusing if any of the low Mu-Rho gas sands were to fall in the negative Lambda region (highlighted by the lower-left orange triangle). In this scenario, Poisson's ratio would be positive and seemingly reasonable, while both bulk modulus, Young's modulus, and Lambda would be negative. This non-linear behavior between positive and negative values for various elastic parameters can be misleading. For example, a positive Poisson's ratio might suggest a valid rock model, while other parameters like bulk and Young's modulus would indicate an error.

The conclusion from this Lambda-Rho, Mu-Rho crossplot is that Lambda (incompressibility) is the most reliable parameter when it comes to identifying errors and inconsistencies in the elastic properties of rocks. Lambda alone clearly represents the material's true incompressibility, whereas other elastic parameters, such as bulk and Young's modulus, may obscure or confound measurement errors, complicating their use in calibrating AVO/QI. As such, the Lambda-Rho and Mu-Rho crossplot mapping helps prevent confusion by exposing these discrepancies, thus allowing for more accurate calibration of AVO workflows.

3. Need for correct low frequency models (LFM) for AVO Fluid Factor and QI from relative and absolute Inversion: well log co-kriged migration velocities or FWI velocities.

The critical need for an accurate Low-Frequency Model becomes evident when applied as a general background model workflow for absolute inversion.

a) The first step is to identify the appropriate low-frequency cutoff and apply a high-pass filter to the seismic data

b) Use the same low-pass cutoff filtered logs co-kriged with processing velocity field for LFM building.

To build the LFM, low-pass filtered well logs are co-kriged with the processing velocity field to fill in the low-frequency gaps. This approach can serve as an equivalent proxy for Full Waveform Inversion (FWI), helping to ensure that the background model is robust and well-calibrated to the available data (see Figure 7c).

c) Estimate wavelets on high-pass range frequency data.

Wavelets are estimated for the high-pass filtered seismic data, which contains the higher frequency information that will be used for relative inversion. Accurate wavelet estimation is key for preserving the amplitude and phase relationships needed for inversion.

d) Perform relative inversion on high-pass range frequency data.

A relative inversion is conducted using the high-pass filtered seismic data. This inversion captures the higher-frequency details of the subsurface, though it lacks the absolute reference provided by the low-frequency component.

e) Incorporate LFM to produce the full-frequency inversion.

The LFM is then incorporated into the workflow to produce a complete full-frequency inversion:

 

• • Use the LFM as background input to the full-frequency band absolute inversion
    The LFM serves as the background model for the absolute inversion, ensuring that the lower-frequency content, which is crucial for understanding broader geological trends, is accurately represented.

• • Use the LFM to transform the high-pass frequency relative inversion to absolute inversion
    Finally, the LFM is combined with the results from the high-pass range relative inversion, transforming it into a full-band absolute inversion. This final step integrates both low and high frequencies to produce a comprehensive model of the subsurface.

By following these steps and ensuring that the LFM is correctly constructed, the inversion results become more reliable and better suited for detailed subsurface characterization. The LFM provides the crucial low-frequency foundation upon which accurate elastic properties and lithological information can be derived.

Figure 7. Equivalent segments of a section from the (a) seismic, (b) computed relative acoustic impedance, (c) LFM with FWI input, and (d) computed absolute acoustic impedance volumes. Notice the impact of FWI on LFM building and absolute inversion. (Images courtesy of Andrew Long, PGS)

Figure 7 highlights the sequential impact and importance of integrating an accurate LFM in broadband QI workflows. The transformation from relative inversion to absolute inversion is crucial for enhancing resolution beyond what the input seismic data alone can provide. However, to achieve optimal results, the low-pass filtered elastic logs must be of sufficient length and correctly tied to the seismic data. This proper integration ensures that the LFM, when combined with relative inversion, produces an optimal broadband high-resolution absolute inversion—as demonstrated in Figure 7d for acoustic impedance (AI).

In Figure 8, the effect of this broadband uplift in absolute inversion is illustrated by comparing the inversion tied to log overlays. The left and middle panels display AI, V_P/V_S, and Rho, with the LFM track overlaid as a dashed line. These panels demonstrate how well the absolute inversion ties to the logs and how accurately the model reflects the elastic properties of the subsurface. The rightmost mini cross-section panels in Figure 8 further confirm this, showing the elastic properties tied to log tracks, revealing an optimally calibrated result.

Figure 8. Desired absolute inversion result with use of accurate LFM workflow. Note the uplift from combining the correct LFM with relative inversion for the improved detail and accuracy of the absolute inversion (shown in the inversion (blue) to log track (red) overlays in the left/middle panels for acoustic impedance, VP/VS, and density with LFM track as dashed overlay). (After Gordon et al., 2013)

The next key aspect of constructing an accurate LFM concerns the necessity of a background model reference for both QI and AVO reflectivity inversion, such as the Fluid Factor (Gidlow et al., 1992; Fatti et al., 1994).

The Fluid Factor equation, expressed as R_P/R_S = (5(V_P – A))/(5V_P – A), where R_P and R_S are P and S reflectivities derived from AVO/QI relative inversion outputs (Goodway, 2001; Hoffe et al., 2008), and A is the intercept in the Castagna mudrock relationship V_P = A + BV_S (Castagna et al., 1985). This formulation highlights the importance of having an accurate background reference model to perform reflectivity inversions correctly. The Fluid Factor helps differentiate fluids within the rock matrix by analyzing the ratio between P-wave and S-wave reflectivities and relies heavily on the background model to provide a stable reference point.

Figure 9. Variation of RS/RP slope as a function of interval VP for varying mudrock line intercept values indicated in the legend. The graph above (based on equation 2) shows the variation in the RS to RP slope relationships with increasing P velocity's dependence as a function of depth compaction on the shale or wet sand "mudrock line" intercept A (legend) fit that is used.

The advantage of the Fluid Factor formulation for the R_P/R_S ratio factor (ff) lies in its simplicity and efficiency, as it eliminates the need for explicit shear velocity or the V_P/V_S ratio. Instead, it only requires two inputs:

 

1. 1. Mudrock line intercept (A)
   2. Interval V_P (V_int), which can be derived from the V_rms PSDM velocity field.

The behavior of the R_P/R_S ratio as a function of increasing interval V_P (depth) and mudrock line intercept (A) is illustrated in the graph in Figure 9. A notable trend observed from this graph is that the R_S/R_P ratios tend to asymptotically converge and decrease with increasing interval V_P (depth), regardless of the value of the mudrock line intercept (A).

An additional intriguing observation related to the mudrock line-based background LFM for the R_P/R_S Fluid Factor slope ratio is the theoretical implication regarding V_S (shear velocity) contrasts. Both the V_S shear "fractional velocity contrasts" and R_S fractional shear impedance contrasts tend to be larger than their P-wave R_P counterparts for the same reflector. This tendency, as noted by Aki & Richards (1980) (p. 154), is consistently observed, but they do not provide a detailed theoretical explanation.

The mudrock line-based background LFM R_P/R_S factor described above is essential in establishing the AVO Fluid Factor expectation for QI. This approach leverages the time-variant function of V_P depth trends derived from NMO/PSDM interval velocities to dynamically adjust the Fluid Factor in seismic analysis.

The Fluid Factor (FF) is defined as FF = RP – (ff x RS). This equation effectively removes the background reflectivities (i.e., the "normal" or expected reflectivity values based on the mudrock line) so that the fluid hydrocarbon anomalies are isolated and highlighted within the FF section.

Figures 10 and 11 illustrate the practical application of this QI method. The correct global/background LFM-based Fluid Factor discrimination can be directly tied to the seismic R_P and R_S model reflectivities, revealing and isolating local AVO anomalies. This approach was successfully demonstrated in the model study shown in Figure 11, where it was applied to a Mackenzie Delta gas/oil discovery. The application of this method resulted in the accurate identification of hydrocarbon zones by distinguishing fluid effects from the surrounding background reflectivity patterns.

Figure 10. (a) AVO classes and fluid factor background LFM defined in the AVO reflectivity R_P vs R_S cross-plot space. (Images adapted from Hoffe et al., 2008). (b) AVO classes proposed by Rutherford and Williams (1989), Castagna et al. (1998) and Young and LoPiccolo (2003). (c) AVO classes in LMR crossplot space. (d) The adaptations in (a) and (c) can all be put together in LMR space. More QI insight can be obtained for the AVO classes in LMR space.

Figure 11. Pre-drill AVO model reflectivity prediction for R_P, R_S synthetics comprising brine (insitu) versus gas (substituted) to discriminate hydrocarbon zones for a Mackenzie Delta gas/oil discovery.

An accurate LFM reference is crucial for the successful application of Fluid Factor discrimination in identifying hydrocarbons through local reflectivity anomalies. If the background LFM is flawed or inaccurate, the method's ability to differentiate fluid effects from the background reflectivity can fail, leading to incorrect interpretations.

This potential for failure is demonstrated in Figure 12, where the comparison between Well A and Well B shows the impact of an inaccurate LFM. In Well A, the application of the Fluid Factor method was successful, with the local AVO anomalies correctly isolating hydrocarbons. However, in Well B, the same method failed because the underlying LFM reference model was inaccurate, leading to a misidentification of the reflectivity anomalies.

In the case of Well A and Well B, although the background trends converge at the crossplot origin and are identical for log points in the target zone at Well A (shown by the red circle), the choice of background becomes irrelevant in this instance. However, the issue arises due to the presence of low gas saturation (fizz-gas) in the high impedance mudrock background brine sands.

Figure 12. Fluid Factor R_P vs R_S crossplots for (a) successful, and (b) unsuccessful exploration drilling due to LFM background reference. In (a), a negative fluid factor shift (drop in VP/VS) corresponding to gas filled porosity in low impedance sand is seen (indicated by red arrow and oval). In (b), a positive fluid factor shift (increase in VP/VS) from fizz-rock mudrock trend is seen. The high impedance sand is the anomaly off the fizz-gas mudrock trend (arrow and dot). Well-A and Well-B background trends DEVIATE for log points in target zone at Well-B as shown by blue oval. Thus, the choice of background trend is critical.

This fizz-gas effect causes these sands to exhibit the same P-impedance as the surrounding background shales, which results in their placement along the Well B background trend (indicated by the blue oval in Figure 12b). In this scenario, the sands essentially blend into the background trend, making it challenging to distinguish the gas-bearing sands from the surrounding shales based on P-impedance alone.

If the Well A background trend (represented by the red line) were used as the R_P to R_S scalar for calculating the Fluid Factor in Well B, it would result in a negative Fluid Factor shift, which corresponds to a drop in V_P/V_S from the Well A trend. This shift would affect not only the low-saturation gas sands but also the rest of the Well B background shale trend (as indicated by the blue line and oval in Figure 12b).

This drop in VP/VS would lead to inaccuracies in distinguishing the gas-saturated sands in Well B from the background shale trend, as the P-impedance (RP) and S-impedance (RS) scalar from Well A does not accurately reflect the conditions in Well B, particularly where fizz-gas is present. In such cases, relying solely on the Fluid Factor method can lead to misinterpretation of the seismic data.

However, by applying a relative inversion—following the reflectivity-based Fluid Factor approach—it is possible to achieve improved quantitative discrimination between lithology, porosity, and fluid effects. This is particularly effective when using the Lambda-Rho-Mu-Rho (LMR) attributes, which provide a clearer separation of rock types and fluid content compared to the Fluid Factor method alone.

The QI of relative inversion results in the context of the Fluid Factor RP and RS analysis is shown in Figure 10c. This figure highlights the benefit of analyzing the data in LMR cross-plot space, which is overlaid with AVO classes commonly used in Fluid Factor analysis. By leveraging LMR attributes, seismic interpreters can more effectively discriminate between gas sands, brine sands, shales, and other lithologies, thus improving the overall reliability of the AVO/QI workflow.

Despite being referred to as relative inversion, there is a critical yet often overlooked requirement for a correct background reference—specifically a shale or mudrock trend—in order to accurately interpret the results. This is essential because the background trend serves as a baseline for distinguishing elastic properties that differentiate lithology, porosity, and fluid content when applying the Lambda-Rho-Mu-Rho (LMR) cross-plot template interpretation, as seen in Figure 10c.

If the background shale-mudrock trend is incorrect, the relative inversion results for properties like acoustic impedance (AI) versus V_P/V_S ratio will exhibit misleading patterns. In particular, the litho-fluid V_P/V_S trend will appear anti-correlated with what would be expected. This distortion is illustrated in Figure 13a, where the following can be observed:

 

1. 1. The correct log cross-plot V_P/V_S trend in the left panel (Figure 13a(1)) aligns with the anticipated separation of elastic properties for lithology and fluid fill.
   2. In contrast, the middle and right panels (Figures 13a(2) and 13a(3)) show the anti-correlated V_P/V_S trends when the background trend is incorrect, which confounds the interpretation of lithology and fluid effects.

A striking impact of using an incorrect shale-mudrock background as a reference in relative inversion is evident when comparing the log and inverted seismic track overlays between an incorrect and a correct model. This comparison is shown in Figure 14a (incorrect model) versus Figure 14b (correct model).

In Figure 14a, which uses an incorrect background reference model, the VP/VS inversion overlay appears anti-correlated with the log track. This misalignment between the inversion result and the actual log data is a common issue when an inappropriate reference is applied. Additionally, there is no discernible correlation for Rho, indicating that the inversion results fail to provide meaningful insights.

In contrast, Figure 14b shows the result of using the correct shale-background reference. Here, the VP/VS inversion overlay is now correlated and properly aligned with the log track, providing a more accurate depiction of subsurface properties. Furthermore, the Rho tracks exhibit an improved correlation, reinforcing the importance of selecting the appropriate background model for achieving accurate relative inversion results.

Figure 13. (1) (above) Crossplot of acoustic impedance (AI) versus VP/VS using well data colour-coded with Vshale, and (below) the same crossplot colour-coded with well name. (2) (above) Crossplot of inverted acoustic impedance (AI) versus inverted VP/VS colour-coded with Vshale, and (below) the same crossplot colour-coded with well name. (3) (above) Crossplot of inverted acoustic impedance (AI) versus well AI colour-coded with Vshale, and (below) crossplot of inverted VP/VS versus well VP/VS colour-coded with Vshale. All crossplot trends used are with (a) incorrect, (b) correct shale-mudrock background model. The relative inversion results for AI vs VP/VS are very sensitive to the background shale-mudrock trend and if this is incorrect, they will have an anti-correlated litho-fluid VP/VS trend seen in the middle and right panels compared to the correct log cross-plot VP/VS trend in the left panel in the (a) crossplots above. With the correct background shale-mudrock trend, the relative inversion results for AI vs VP/VS are correlated to the litho-fluid VP/VS trend seen in the middle and right panels compared to the correct log cross-plot VP/VS trend in the left panel in the (b) crossplots above.

Figure 14. Relative inversion AI and VP/VS calibrated to logs comparing filtered log (red track) to inversion result (blue track) for AI, VP/VS and rho with (a) incorrect, and (b) correct shale-mudrock background model. The relative inversion result for VP/VS is very sensitive to the background shale-mudrock trend and if this is incorrect, it will have an anti-correlated litho-fluid VP/VS trend seen in the middle panels' inversion (blue) to log (red) overlays. With the correct background shale-mudrock trend, the relative inversion result for VP/VS (blue overlay) is correlated to the litho-fluid VP/VS trend seen in the middle panels compared to the correct log VP/VS overlay (red).

4. Wavelet estimation including VTI- spectral (amplitude and phase) log tie and wavelet spatial estimation/stability especially for phase

The final section addresses an often overlooked yet critical issue in pre-stack inversion: ensuring optimal angle wavelet ties for background shales that exhibit vertical transverse isotropy (VTI) anisotropy.

In any pre-stack inversion, accurately estimating and compensating for the bandlimited amplitude and phase of angle-dependent wavelets is essential. These wavelets experience frequency dispersion and absorption due to wave propagation, and their precise estimation is necessary for reliable inversion results. Typically, this process involves using vertical elastic logs to generate a forward angle synthetic model, which is then tied to the seismic angle sub-stacks.

However, there is a significant limitation in this process: the absence of anisotropy measurements in the input logs. Without accounting for anisotropy, particularly VTI anisotropy in background shales, the forward synthetic model generated is inherently isotropic. This isotropic assumption leads to inaccuracies because the wave propagation characteristics, particularly in shales with VTI anisotropy, differ from those in isotropic media.

A typical result of this isotropic approach to angle-dependent wavelet estimation is illustrated in Figure 15a. Higher angle wavelets often exhibit misties and become inconsistent with wavelets at other angles, which generally show stable spectral phase and the expected amplitude decay as the angle increases. This inconsistency, particularly at higher angles, is evident in both the angle-limited mini-section ties (for angle ranges 5°-10°, 20°-25°, and 35°-40°) in the middle panels, and in the right panel, which displays the estimated wavelets for various angles. The phase of the higher angle wavelets is noticeably distorted and misaligned when compared to the near and mid-angle wavelets. As a result, in many AVO inversion projects, far-angle input data are often discarded due to the assumption that the amplitudes and AVO at the farthest angles are compromised by factors such as noise, multiple interference, wave propagation attenuation, and inadequate processing. However, what is rarely questioned is the adequacy and suitability of the log-based forward model used to generate the angle synthetics for wavelet extraction. The angle-dependent wavelet mistie, however, suggests that the issue may lie within the synthetic model itself, which does not account for an anisotropic VTI shale background. To address these VTI effects in the synthetic model's encasing shale, anisotropic VTI log or seismic NMO measurements of Thomsen's delta and epsilon parameters are required. When these parameters are incorporated into a VTI synthetic angle forward model, the extracted far-angle wavelets become consistent, and a stable match to the near- and mid-angle wavelets is achieved, as demonstrated in Figure 15b.

Figure 15. Angle stack ties and wavelet estimate QC for an (a) isotropic synthetic seismogram model, and (b) anisotropic synthetic seismogram model. A standard result of the isotropic approach to angle dependent wavelet estimates is shown in figure panels (Figure 15a). Typically, the higher angle wavelets are mis-tied and inconsistent with the other angle wavelets that have comparably stable spectral phase with the expected amplitude decay with increasing angle. Accounting for VTI effects in the synthetic models' encasing shale requires anisotropic VTI log or seismic NMO measurements of Thomsen's delta and epsilon parameters. Once these parameters are used to generate a VTI synthetic angle forward model, then the extracted far angle wavelets are now seen to be consistent and a stable match to the other near to mid angle range wavelets as shown in the Figure 15b panels and unlike the isotropic model case in Figure 15a above.

Conclusions

Regarding the question of whether QI (Quantitative Interpretation) is merely a buzzword or is being effectively implemented in our industry, I believe that in the context of AVO inversion, effective QI can be achieved by leveraging additional, often underutilized, supplementary data. This data is critical for correlation, calibration, and integration, playing a vital role in successfully applying AVO/QI workflows.

Key examples include the use of walkaway VSP AVO and elastic logs for combining borehole and surface seismic inversion, following VSP-guided background offset scaling and balancing. An error-free elastic log suite is essential for AVO calibration and rock physics modeling. Additionally, a reliable low-frequency model (LFM) is required for accurate AVO inversion and the derivation of elastic properties. Moreover, accurate angle-dependent wavelets, typically extracted under isotropic assumptions, are necessary for AVO impedance inversion, although they often fail to account for background shales with VTI anisotropy.

I strongly recommend incorporating the supplementary data mentioned above into AVO inversion and QI exercises to enhance their effectiveness. Doing so could significantly improve the overall performance and contribute meaningfully to the bottom line of oil and gas companies.

References

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About the Author

Bill Goodway obtained a B.Sc. in Geology from University College London and a M.Sc. in Geophysics from University of Calgary. After working in the United Kingdom, he joined PanCanadian Petroleum in 1985 where he became Team Lead of a Seismic Analysis Group. Following the EnCana merger he continued in Frontier-New Ventures and Canadian Gas Shales, as Advisor for Seismic Analysis. In 2010 Bill joined Apache as Manager Geophysics-Advisor Senior Staff, involved in all aspects of seismic acquisition design, processing interaction, to experimental special projects and new AVO methods. In 2019 Bill joined Qeye as Scientific Advisor Quantitative Interpretation and AVO technology.

Bill has authored numerous papers at CSEG, EAGE and SEG conventions on seismic acquisition and processing, borehole geophysics, anisotropy, multicomponent recording and QI/AVO.