A feasibility study on the expected seismic AVA signatures of deep fractured geothermal reservoirs in an intrusive basement

The deep geothermal reservoirs in the Larderello-Travale field (southern Tuscany) are found in intensively fractured portions of intrusive/metamorphic rocks. Therefore, the geothermal exploration has been in search of possible fracture signatures that could be retrieved from the analysis of geophysical data. In the present work we assess the feasibility of finding seismic markers in the pre-stack domain which may pinpoint fractured levels. Thanks to the availability of data from boreholes that ENEL GreenPower drilled in the deep intrusive basement of this geothermal field, we derived the expected amplitude versus angle (AVA) responses of the vapour reservoirs found in some intensely, but very localized, fractured volumes within the massive rocks. The information we have available limit us to build 1D elastic and isotropic models only and thus anisotropy effects related to the presence of fractures cannot be properly modelled. We analysed the velocities and the density logs pertaining to three wells which reached five deep fractured zones in the basement. The AVA response of the fractured intervals is modelled downscaling the log data to seismic scale and comparing the analytical AVA response (computed with the Aki and Richards approximation) and the AVA extracted from a synthetic common mid point (calculated making use of a reflectivity algorithm). The results show that the amplitude of the reflections from the fractured level is characterized by negative values at vertical incidence and by decreasing absolute amplitudes with the increase of the source to receiver offset. This contrasts with many observations from hydrocarbon exploration in clastic reservoirs where gas-sand reflections often exhibit negative amplitudes at short offsets but increasing absolute amplitudes for increasing source to receiver offsets. Thereby, some common AVA attributes considered in silicoclastic lithologies would lead to erroneous fracture localization. For this reason we propose a modified AVA indicator which may highlight fracture locations in this peculiar rock type

two grid full waveform rayleigh wave inversion via a genetic algorithm part 1 method and synthetic examples

When reliable a priori information is not available, it is difficult to correctly predict near-surface S-wave velocity models from Rayleigh waves through existing techniques, especially in the case of complex geology. To tackle this issue, we have developed a new method: two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI). Adopting a two-grid parameterization of the model, the genetic algorithm inverts for unknown velocities and densities at the nodes of a coarse grid, whereas the forward modeling is performed on a fine grid to avoid numerical dispersion. A bilinear interpolation brings the coarse-grid results into the fine-grid models. The coarse inversion grid allows for a significant reduction in the computing time required by the genetic algorithm to converge. With a coarser grid, there are fewer unknowns and less required computing time, at the expense of the model resolution. To further increase efficiency, our inversion code can perform the optimization using an offset-marching strategy and/or a frequency-marching strategy that can make use of different kinds of objective functions and allows for parallel computing. We illustrate the effect of our inversion method using three synthetic examples with rather complex near-surface models. Although no a priori information was used in all three tests, the long-wavelength structures of the reference models were fairly predicted, and satisfactory matches between "observed" and predicted data were achieved. The fair predictions of the reference models suggest that the final models estimated by our genetic-algorithm FWI, which we call macromodels, would be suitable inputs to gradient-based Rayleigh-wave FWI for further refinement. We also explored other issues related to the practical use of the method in different work and explored applications of the method to field data

1D elastic full-waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm-Gibbs sampler approach

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic-algorithm-sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis-Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one-dimensional elastic full-waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the "genetic drift" effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step

two grid full waveform rayleigh wave inversion via a genetic algorithm part 2 application to two actual data sets

We have applied our two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI) to two actual data sets acquired in Luni (Italy) and Grenoble (France), respectively. Because our technique used 2D elastic finite-difference modeling for solving the forward problem, the observed data were 3D to 2D corrected prior to the inversion. To limit the computing time, both inversions focused on predicting low-resolution, smooth models by using quite coarse inversion grids. The wavelets for FWI were estimated directly from the observed data by using the Wiener method. In the Luni case, due to the strong dispersion effects on the data, to strengthen the inversion, envelopes and waveforms were considered in the objective function and an offset-marching strategy was applied. Though no a priori information was exploited, the outcomes of the Luni and Grenoble data inversion were fair. The predicted Luni [Formula: see text] model indicates a strong velocity increase from approximately 3 to 6 m, and velocity inversions have been detected at approximately 2 and 9 m depths. Analyzing the dispersion spectra, it results that the predicted Luni data reasonably reproduced the waveforms related to the fundamental mode and, likely, a small part of those related to the first higher mode. Concerning the Grenoble example, the predicted [Formula: see text] model coincides reasonably well with the long-wavelength structures presented in the [Formula: see text] profiles obtained from nearby boreholes. The data reconstruction is generally satisfactory, and when mismatches occur between the predicted and observed traces, the phase differences are always within half-periods. The fair inversion outcomes suggest that the predicted Luni and Grenoble models would likely be adequate initial models for local FWI, which could further increase the resolution and the details of the estimated [Formula: see text] models

Probabilistic estimation of reservoir properties by means of wide-angle AVA inversion and a petrophysical reformulation of the Zoeppritz equations

We apply a target-oriented amplitude versus angle (AVA) inversion to estimate the petrophysical properties of a gas-saturated reservoir in offshore Nile Delta. A linear empirical rock-physics model derived from well log data provides the link between the petrophysical properties (porosity, shaliness and saturation) and the P-wave, S-wave velocities and density. This rock-physics model, properly calibrated for the investigated reservoir, is used to re-parameterize the exact Zoeppritz equations. The so derived equations are the forward model engine of a linearized Bayesian AVA-petrophysical inversion that, for each data gather, inverts the AVA of the target reflections to estimate the petrophysical properties of the reservoir layer, keeping fixed the cap-rock properties. We make use of the iterative Gauss-Newton method to solve the inversion problem. For each petrophysical property of interest, we discuss the benefits introduced by wide-angle reflections in constraining the inversion and we compare the posterior probability distributions (PPDs) analytically obtained via a local linearization of the inversion with the PPDs numerically computed with a Markov Chain Monte Carlo (MCMC) method. It results that the porosity is the best resolved parameter and that wide-angle reflections effectively constrain the shaliness estimates but do not guarantee reliable saturation estimates. It also results that the local linearization returns accurate PPDs in good agreement with the MCMC estimates

Characterisation of shallow marine sediments using high-resolution velocity analysis and genetic-algorithm-driven 1D elastic full-waveform inversion

We estimate the elastic properties of marine sediments beneath the seabed by means of high-resolution velocity analysis and one-dimensional elastic full-waveform inversion performed on twodimensional broad-band seismic data of a well-site survey. A high-resolution velocity function is employed to exploit the broad frequency band of the data and to derive the P-wave velocity field with a high degree of accuracy. To derive a complete elastic characterisation in terms of P-wave and S-wave velocities (Vp, Vs) and density of the subsurface, and to increase the resolution of the Vp estimates, we apply a one-dimensional elastic full-waveform inversion in which the outcomes derived from the velocity analysis are used as a priori information to define the Vp search range. The one-dimensional inversion is done using genetic algorithm as the optimisation method. It is performed by considering two misfit functions: the first uses the entire waveform to compute the misfit between modelled and observed seismograms, and the second considers the envelope of the seismograms, thus relaxing the requirement of an exact estimation of the wavelet phase. The full-waveform inversion and the high-resolution velocity analysis yield comparable Vp profiles, but the full-waveform inversion reconstruction is much more detailed. Regarding the full-waveform inversion results, the final depth models of P- and S-wave velocities and density show a fine-layered structure with a significant increase in velocities and density at shallow depth, which may indicate the presence of a consolidated layer. The very similar velocities and density-depth trends obtained by employing the two different misfit functions increase our confidence in the reliability of the predicted subsurface models

Estimation of acoustic macro models using a genetic full-waveform inversion: Applications to the Marmousi model

We present a stochastic full-waveform inversion that uses genetic algorithms (GA FWI) to estimate acoustic macro-models of the P-wave velocity field. Stochastic methods such as GA severely suffer the curse of dimensionality, meaning that they require unaffordable computer resources for inverse problems with many unknowns and expensive forward modeling. To mitigate this issue, we propose a two-grid technique, that is, a coarse grid to represent the subsurface for the GA inversion and a finer grid for the forward modeling. We applied this procedure to invert synthetic acoustic data of the Marmousi model. We show three different tests. The first two tests use as prior information a velocity model derived from standard stacking velocity analysis and differ only for the parameterization of the coarse grid. Their comparison shows that a smart parameterization of the coarse grid may significantly improve the final result. The third test uses a linearly increasing 1D velocity model as prior information, a layer-stripping procedure, and a large number of model evaluations. All the three tests return velocity models that fairly reproduce the long-wavelength structures of the Marmousi. First-break cycle skipping related to the seismograms of the final GA-FWI models is significantly reduced compared to the one computed on the models used as prior information. Descent-based FWIs starting from final GA-FWI models yield velocity models with low and comparable model misfits and with an improved reconstruction of the structural details. The quality of the models obtained by GA FWI + descent-based FWI is benchmarked against the models obtained by descent-based FWI started from a smoothed version of the Marmousi and started directly from the prior information models. The results are promising and demonstrate the ability of the two-grid GA FWI to yield velocity models suitable as input to descent-based FWI

The role of clinicopathologic and molecular prognostic factors in the post-mastectomy radiotherapy (PMRT): a retrospective analysis of 912 patients

OBJECTIVE: To assess the association of clinicopathologic and molecular features with loco-regional recurrence (LRR) in post-mastectomy breast cancer patients with or without adjuvant radiotherapy (PMRT). PATIENTS AND METHODS: We retrospectively reviewed data of patients undergone to mastectomy followed or not by PMRT between January 2004 and June 2013. The patients were divided according to clinicopathologic and molecular sub-classification features. LRR and Cancer Specific Survival (CSS) were calculated using the Kaplan-Meier method; the prognostic factors were compared using long-rank tests and Cox regression model. RESULTS: A total of 912 patients underwent to mastectomy of whom 269 (29.5%) followed by PMRT and 643 (70.5%) not; among the PMRT group, 77 underwent to the chest wall (CW) and 202 to the chest wall and lymphatic drainage (CWLD) irradiation. The median follow-up was 54 months (range, 3-118). No significant difference in terms of LRR and CSS was found between non-PMRT and PMRT group (p=0.175; and p=0.628). The multivariate analysis of LRR for patients who did not undergo PMRT showed a significant correlation with the presence of extracapsular extension (ECE) (p=0.049), Ki-67>30% (p=0.048) and triple negative status (p=0.001). In the PMRT group, triple negative status resulted as the only variable significantly correlated to LRR (p=0.006) at the multivariate analysis and T-stage also showed a trend to significance (p=0.073). Finally, no difference in LRR control was shown between CW and CWLD-PMRT (p=0.078). CONCLUSIONS: After mastectomy ECE, a cut off of Ki-67>30% and triple negative status werestrictly correlated with LRR regardless of clinicopathologic stage. PMRT has a positive impact in decreasing LRR in patients with this molecular profile. Besides, CW might represent a valid option for patients with one to three positive nodes