Discover the latest developments in seismic inversion with the LTrace Inversion Suite, including a new AVO formulation for direct inversion to P-impedance and Vp/Vs ratio. Learn how these advances improve facies classification, quality control, and computational efficiency in OpendTect.
#OpendTect #SeismicInversion #BayesianInversion #AVOAnalysis #LTraceInversionSuite #FaciesClassification #RockPhysics #GeophysicsWebinar
Duration: 22:23
--- Transcript ---
Thank you everyone for attending this webinar. I've changed the title of the presentation because previously the plugin was called BLI, Bayesian Linearized Inversion,. But since we are including several new features in the plugin, we renamed it as LTrace Inversion Suite.
So this is the summary of the presentation. I will start with an introduction to the plugin, LTrace Inversion Suite, including our development pipeline,. And then I will discuss the inversion model, which is the Bayesian Linearized Inversion, and.
Then I will show the derivation of the new formulation in terms of P-impedance and VpVs ratio, which was recently published in EAGE. And Geophysics, and I will discuss also some applications of the BLI with the new formulation,. And then I have some conclusions to show.
So about our plugin, the main objective is to provide a complete suite of tools and algorithms for seismic inversion integrated with OpendTect. Here I have two short videos showing a little bit about the interface, where you can make the quality control of the inversion, comparing to the well data,. And also the angle stack seismic data around the wells, and also our new wavelet estimation, multi-trace, multi-well wavelet estimation.
So we have the well, and then you can analyze multiple traces around the well, make a correlation map here. And apply some filters to make a sub-selection of the seismic traces that you want to analyze, to define the best phase. And also the best energy, and the energy you can filter again based on a match factor with the seismic,.
And then you have an interface where you can see the histograms of the best values and tune the wavelet parameters. So in the first versions we only had the seismic inversion module, which is the BLI, Bayesian Linearized Inversion,. So that was the old name of the plugin, but since the last year LTrace is investing in developing new modules with user-friendly interface for new algorithms for quantitative interpretation workflow,.
And because of that we would like to highlight that we are currently working on ongoing updates,. So we are open for possible customization for clients and make some interface adjustments. And so in the current version of the algorithm we have the basic workflow for seismic inversion, starting from the input,.
So the low-frequency model, the wavelet estimation, and then you can go to the inversion part, the elastic inversion. And acoustic inversion, and also use the interface for quality control to get the best value of the algorithms. And in this slide I want to show all the methodology that we are currently working to include in the OpendTect,.
So the wavelet estimation here is the first one, which was released some weeks ago,. And we are still doing some improvements, and then after that we want to implement as well the Bayesian inference with an interface where you can change the parameters of the PDF direct in the cross plot,. But we also have the algorithms for geostatistical methods, joint phase inversion and rock physics inversion, all the methodologies we've worked with Professor Dario Grana.
And we published in geophysics most of the algorithms. So my objective here of showing this slide is because possibly we can get some feedback from clients who might be interested in having one of these methodologies in OpendTect,. So we can make a better priority in our development pipeline to include in the plugin.
So I want also to highlight that we lock at the price until the multi-trace wavelet estimation update is complete. As I said, we are still making some improvements and we are keeping the price until we finish that. And the plugin, you have a free trial available when working with the F3 Demo data set,.
So anyone can download the dataset and the plugin and test. And also, again, I would like to highlight that we are open for possible customization for clients. And now I want to discuss the Bayesian linearized inversion theory, which is the inversion model of our plugin.
So the method is based on the Bayesian approach for inverse problem. So in this approach, the solution of the inverse problem is given by a Bayesian posterior distribution, which accounts for observer data. And prior knowledge.
So here we have the definition of the posterior distribution, which is the product of the likelihood. And the prior. The likelihood is related to how adequate your model is to the data, and the prior is related to how adequate your model is to the prior knowledge, the prior models.
And so here, just to highlight, which is the MAP solution that we call MAP solution, Maximal Posterior Solution, which is the same thing to say that the solution which gives us the minimum error,. So the MAP solution is the maximum value of the posterior distribution. So in the particular case, the Bayesian linearized inversion is the particular case where the prior.
And the likelihood Gaussian are Gaussian and the forward model is linear. So here we have the posterior distribution here, and we have a linear model, and here we have the likelihood. We open here, assuming multivariate Gaussian distributions, and then we have the likelihood and the prior here.
We have the observer data in this vector D, the low frequency model in this vector here,. And then the convolutional model with the wavelet is here, which is our synthetic seismic data,. And in the prior we also have the spatial correlation model, which is included in this covariance matrix.
So in this particular case, again, prior and likelihood Gaussian and linear forward model, we can obtain the solution analytically. So the posterior distribution is a multivariate Gaussian distribution with this mean here and the covariance matrix here. And the MAP.
So the maximal posterior solution of the Lesky properties can be computed with this equation here. So because it's an analytical solution, it's really fast, it's really easy, fast, with a very good computational efficiency to compute the solution. And taking the advantage of GPU, the plugin computes the solution of diverse problems with 3D spatial correlation in a very, very efficient way.
And just for curiosity, we have the interpretation as an optimization process with this objective function here, where you want to minimize the error with the seismic data. And the error with the YARP low frequency models with the spatial correlation in the covariance matrix. So I don't want to enter in all the details, but the original publication of the Bayesian linearized inversion, BLI, was proposed by Bullen.
And Noury, and it was initially proposed with the Aki-Richards equation. So here just to show how we can linearize the convolutional model using the reflectivity defined by the Aki-Richards equation. So here we have the Aki-Richards equation written in terms of the logarithms of the velocities.
And density. And then we have here our forward model, where this S here is the convolutional matrix with the wavelet. This A is the Aki-Richards coefficients.
This D is this first-order derivative. And M is the logarithm of the elastic properties, the velocities and densities, stacked altogether in the same vector. And then we have the same thing for the seismic.
We have all the angles stacked in the same vector. And then that's how we can linearize the convolutional model and apply Bayesian linearized inversion to estimate VP, VS,. And density.
So here is just a work that we've done before, where we compare the BLI with the constrained sparse spike inversion. With very similar results, but BLI is six times faster than the constrained sparse spike inversion. Just to highlight how efficient the BLI is.
So now about the AVO formulation in terms of P-impedance and VpVs ratio. So we first published the formulation in the EAGE annual meeting in this work. And then we published in Geophysics the AVO formulation applied in the Bayesian linearized inversion with the facies classification.
That was published in Geophysics this year. And then what was the motivation to derive this new equation? The motivation mainly was the facies classification, because the P-impedance versus VpVs ratio is a common domain for seismic facies classification for both carbonate.
And siliciclastic rocks. So here, for example, you have two works where we can define the facies in this space for a carbonate reservoir from Brazilian pre-south. But we can also see many applications using the same space to classify facies in the North Sea Reservoir, siliciclastic rocks.
And analyzing the rock physics templates in this domain, we can also see that it shows a high sensitivity to fluid. And minerals. And also the basic workflow for facies classification is from the seismic data you apply some inversion algorithms for your elastic properties.
You can compute the P-impedance and VpVs ratio. And considering your well logs in this domain, you apply some facies classification to get your facies model from the seismic. And it's really, really common, as I showed in the many applications, you use this domain to classify fasces.
So the question was raised, is there any AVO formulation for IP and VpVs ratio where we could use in the BLI, the Basal Linearized Inversion, which we didn't find,. So we decided to try to derive it. So basically we derived four formulations, and I won't discuss all the details of the derivations,.
But it's important to highlight here that we define VpVs ratio as this variable nu. And so the first formulation is based on Foster equation. And while using the derivations rules and replacing it in the Foster equation, we derive this equation here, which we call the formulation one.
The second formulation is based on Verm and Hilterman. And it's based on the Poisson ratio in terms of VpVs using some derivation rules. We have this equation here.
And then when we replace it in the Verm and Hilterman equation, we derive this second formulation. And the third formulation we obtain when we assume that the average of VpVs ratio is two. And it's possible to show that both formulations one and two, from Foster and Verm.
And Hilterman, are reduced to this simplified formula, which we call formulation three. And the fourth formulation is based also on some differential rules, where we replace it in Fatti equation. And rearranging the term, we obtain this formulation here, which we have this dependence on density.
And to exclude this dependence on density, we use Gardner relations here, also again some differential rules. And then we obtain our fourth formulation here, which is the best formulation according to our tests. And this formulation is the one that we selected to implement in the plugin.
So now about the applications, we first show some AVO comparisons. So here we have some results for typical transitions between carbonate facies of a Brazilian pre-salt Reservoir. So we have some facies transitions here, four facies transitions, where we plot the reflectivity versus angle for these different transitions.
So here we have salt to clay rich carbonate, salt to high porosity carbonate, low porosity carbonate to clay rich carbonate,. And then low porosity carbonate to high porosity carbonate. And then we have the different formulations here.
We can see the black one is the Aki-Richards one, which is the reference for us. And we can see that the best formulation is the blue, which is close to Aki-Richards, closer than the other ones. And then we also apply the formulations to the North Sea Reservoir.
So again, four different facies transitions, from shale to oil sand, shale to gas sand, shaly sand to oil sand, shaly sand to gas sand. And then we can again see that the blue curve, which is our formulation, is better than the other ones. And the main reason for that is because this formulation in blue was derived based on Fatti's equation, whereas the other formulations that are based on Verm.
And Hilterman and Foster, they derived their equation based on Shuey's equation of two-term, Shuey's equation, which is known that it's problematic for higher angles. So about the applications, using this formulation in the Bayesian linearized inversion and facies inference, we applied in the Norwegian Sea oilfield real data here. So we have the size of the data, near, mid and far, angle stacks.
We applied BLI to estimate the P impedance and the VpVs ratio. And after that, based on the well logs, we separate three facies in the logs, sand, shaly sand. And shale.
And then applying the Bayesian inference based on the well logs, we compute the probability of each facies,. And for each point we evaluate which face gives us the highest probability to define our most likely facies model here. And then we make an application for synthetic data as well.
It's a synthetic data based on the F3 demo. The F3 Demo only provides the full stack size per data. And based on this model, we defined the synthetic data based on F3.
So it's a synthetic, but it's a very realistic case. Here we have the synthetic size per data, near, mid and far. Again, we applied Bayesian linearized inversion to estimate the P impedance and VpVs ratio.
And then based on the well logs, we defined four different facies with their PDFs here, Gaussian PDFs. And the facies are shale, shaly sand, fine sand, sand and coarse sand. We applied Bayesian inference, we compute the probabilities of each facies, and from this probability for each point we evaluate which facies presents the highest probability.
And define our most likely model here. So as conclusions, we have the greater accuracy. So the new formulation outperforms the previous one by Foster and Verm and Hilterman.
And with this formulation, Bayesian linearized inversion allows us to make a direct inversion to key properties. So we can invert direct to P impedance and VpVs ratio, which is the domain for facies classification. So the BLI with this formulation also makes the tuning and quality control easier, because you have fewer parameters, for example fewer correlations.
And standard deviations of the prior. So it makes the tuning and quality control process more efficient. It might improve the facies classification as well, the quality control of these facies, because sometimes you have to change a little bit the PDFs in the cross plot.
And working with the two-dimensional PDFs, bivariate PDFs is more intuitive than managing three-variate PDFs when you are working with the Aki-Richards or Fatti equations. And we also have some gain in computational efficiency, because you have fewer properties, which means smaller matrix leading to fast computation of the matrix. And we also want to highlight that we have the new interface in OpendTect.
And now the formulation is available in OpendTect with the new quality control interface to get the best value of the products. So thank you very much for watching and I'm available to any questions that you guys have. Thank you very much.