Adjoint-state method for seismic AVO inversion and time-lapse monitoring

This dissertation presents seismic amplitude versus offset (AVO) inversion methods to estimate water saturation and effective pressure quantitatively in elastic and viscoelastic media. Quantitative knowledge of the saturation and pore pressure properties from pre- or post-production seismic measurements for reservoir static or dynamic modeling has been an area of interest for the geophysical community for decades. However, the focus on the existing inversion methodologies and explicit expressions to estimate saturation-pressure variables or changes in these properties due to production or fluid injection has been based on elastic AVO models. These conventional methods do not consider the seismic wave attenuation effects on the reflection amplitudes and therefore can result in biased prediction. Numerous theoretical rock physics models and laboratory experiments have demonstrated the sensitivity of various petrophysical and seismic properties of partially fluid-filled porous media to seismic attenuation. This makes seismic wave attenuation a valuable time-lapse attribute to reliably measure the saturation (Sw) and effective pressure (Pe) properties. Therefore, in this work, I have developed two AVO inversion processes i.e., the conventional AVO inversion method for elastic media and the frequency-dependent amplitude versus offset (FAVO) inversion technique for the viscoelastic media. This dissertation first presents the inversion strategies to invert the pre-stack seismic data for the seismic velocities and density by using the conventional AVO equation and for the seismic velocities, density, and Q-factors by using the frequency-dependent AVO method. These inversion methods are then extended to estimate the dynamic reservoir changes e.g., saturation and pressure variables, and can be applied to predict the saturation and pressure variables at any stage e.g., before and during production, or fluid injection, or to estimate the changes in saturation (ΔSw) and pressure (ΔPe). The first part of the dissertation describes the theory and formulation of the elastic AVO inversion method while in the second half, I have described the viscoelastic inversion workflow. FAVO technique accounts for the dependence of reflection amplitudes on incident angles as well as seismic frequencies and P and S waves attenuation in addition to seismic velocities and density. The fluid saturation and pressure in the elastic and inelastic mediums are linked to the reflection amplitude through seismic velocities, density, and quality factors (Q). The inversion process is based on the gradient-descent method in which the least-square differentiable data misfit equation is minimized by using a non-linear limitedmemory BFGS method. The gradients of the misfit function with respect to unknown model variables are derived by using the adjoint-state method and the multivariable chain rule of derivative. The adjoint-state method provides an efficient and accurate way to calculate the misfit gradients. Numerous rock physics models e.g., the Gassmann substitution equation with uniform and patchy fluid distribution patterns, modified MacBeth’s relations of dry rock moduli with effective pressure, and constant Q models for the P and S wave attenuation are applied to relate the saturation and effective pressure variables with elastic and an-elastic properties and then forward reflectivity operator. These inversion methods have been defined as constrained problems wherein the constraints are applied e.g., bound constraints, constraints in the Lagrangian solution, and Tikhonov regularization. These inversion methods are quite general and can be extended for other rock physics models through parameterizations. The applications of the elastic AVO and the FAVO methods are tested on various 1D synthetic datasets simulated under different oil production (4D) scenarios. The inversion methods are further applied to a 2D realistic reservoir model extracted from the 3D Smeaheia Field, a potential storage site for the CO2 injection. The inversion schemes successfully estimate not only the static saturation and effective pressure variables or changes in these properties due to oil production or CO2 injection but also provide a very good prediction of seismic velocities, density, and seismic attenuation (quantified as the inverse quality factor). The partially CO2-saturated reservoir exhibits higher P wave attenuation, therefore, the addition of time-lapse P wave attenuation due to viscous friction between CO2-water patches helps to reduce the errors in the inverted CO2/water saturation variables as compared to the elastic 4D AVO inversion. This research work has a wide range of applications from the oil industry to carbon capture and storage (CCS) monitoring tools aiming to provide control and safety during the injection. The uncertainty in the inversion results is quantified as a function of the variability of the prior models obtained by using Monte Carlo simulation

Nonlinear AVO Inversion Based on Zoeppritz Equations and Its Applications

Amplitude Variation with Offset (AVO) inversion is an effective method to estimate elastic parameters of target subsurface layers. However, most conventional AVO inversions are based on linear approximations of Zoeppritz equations assuming weak contrasts and seismic isotropy. For this reason, conventional AVO inversions cannot correctly estimate elastic parameters of some geologically important formations (e.g., organic-rich shale, formations beneath salt-dome or carbonate, etc.) which are highly anisotropic and often surrounded by hard layers generating strong contrasts. To overcome this challenge, I apply a non-linear AVO inversion based on exact Zoeppritz solutions for seismic reflection amplitudes. In the dissertation, I will describe how the non-linear inversion can efficiently be implemented and how it can be beneficial for both conventional and unconventional reservoir characterization. Specifically, I will show inversion results applying the inversion with models that represent strong contrasts and strong anisotropy. Direct outputs of the inversion are three contrast parameters between overlying and underlying layers and one background values. However, with an assumption that the model parameters of the overlying (or underlying) layer are known, the proposed AVO inversion can accurately determine horizontal and vertical P-wave and S-wave velocities of target layers of the models. Therefore, seismic anisotropy of the models can also be determined. In addition, this inversion provides a benefit to differentiate density from acoustic impedance. Based on the results, I will propose a workflow to define geomechanical properties (i.e., Young’s modulus and Poisson’s ratio), and total organic carbon (TOC) content of target layers. Furthermore, I develop a new inversion method to improve the Zoeppritz AVO inversion by jointly using PP- and converted PS-seismic reflections together. This joint inversion provides better estimations of S-wave velocity, shear impedance and the ratio of background P-wave and S-wave velocities. Lastly, I apply the inversion into more complicate field seismic data in order to demonstrate the superiority of the method compared to linear inversions. With the given field example, I also introduce a new seismic attribute, ∆VP, in order to more practically estimate seismic anisotropy from real seismic data. The ∆VP attribute is well correlated with values of gamma-ray (GR) log, which can assess the amount of shale contents and that should be highly correlated to seismic anisotropy. Therefore, the effectiveness of the attribute for inference of seismic anisotropy can indirectly be verified. In summary, the non-linear Zoeppritz AVO inversion provides better estimations of elastic parameters for such challenging situations: strong contrasts in properties, and strong anisotropy in seismic velocities. With the proposed workflow and attribute based on the inversion results, further estimations of seismic anisotropy, geomechanical properties, and TOC can also be possible. On the basis of the study, the inversion can consequently contribute to the well placement, stimulated reservoir volume (SRV), and the completion design for both conventional and unconventional reservoirs

Investigating the basal and englacial properties of a West Antarctic ice rise with novel active-source seismic methods

Seismic observations of glacier beds are key to understanding processes of basal slip and incorporating these processes into ice sheet models, which in turn inform predictions of global sea level rise. Observations of seismic reflection amplitude are a powerful tool for identifying glacier bed materials. Amplitude-versus-angle (AVA) analysis is a technique commonly used to identify glacier substrates whereby the amplitude of the basal reflection is measured as a function of its incidence angle at the ice base. Glaciological AVA experiments conventionally consider only the compressional (P) wave component of the wavefield, ignoring the shear wave (S) component; however, three-component seismic acquisitions are proliferating in the glaciological community. To harness the full potential of three-component recording, analysis of PS converted waves (incident P waves converted to S waves at the glacier bed) is necessary. This thesis presents an investigation into the glaciological application of joint PP and PS AVA inversion. Prior to inverting AVA data, amplitudes must be corrected for attenuation losses. The transition of snow to firn and glacial ice represents a challenge to seismic study due to the continuous transition in elastic properties with depth. I describe a method for measuring the seismic quality factor, Q, which enables more detailed characterisation of firn's attenuative structure than previous approaches allow. Q increases from 56 +/- 23 in the uppermost firn to 570 +/- 450 between 55 and 77 m depth. This method offers a strategy of constraining attenuation in seismic reflection experiments which do not record multiples, also enabling improved constraint of source amplitude when compared with conventional methods. I present an inversion scheme which jointly inverts PP and PS AVA data for the properties of the ice-bed interface. Using synthetic AVA data, I investigate the improvement joint inversion of PP and PS amplitudes makes to constraint of bed properties when compared with PP inversion. In general, joint inversion improves upon PP inversion in both precision and accuracy over the same angular range. In many cases joint inversion of data over 0-30 degrees performs favourably with single inversion of data over 0-60 degrees. Joint inversion therefore has the potential to reduce ambiguity in substrate identification and reduce the logistical requirements of glaciological AVA surveys. The inversion scheme is applied to PP and PS data from Korff ice rise (KIR), in the Weddell Sea sector of West Antarctica. Analysis of PP and PS AVA responses at KIR shows the reflection to arise from a material with a P wave velocity of 4.03 +/- 0.05 km/s, an S wave velocity of 2.16 +/- 0.06 km/s and a density of 1.44 +/- 0.06 g/cm3. The inverted properties are consistent with a reflection from a layer of basal debris overlying frozen sediments, with a poorly-defined boundary between the two. I propose that this results from a previous episode of flow as an ice rumple, followed by grounding on the lee side of the bathymetric high occupied by KIR and subsequent freezing of basal sediments. The indication of a reflection from a basal debris layer raises questions about whether conventionally-interpreted basal reflections can truly be considered as such, and whether these interpretations may mask the true nature of the underlying subglacial material