Hot dry rock is generally buried deep within the subsurface and exhibits high temperatures, hardness and density, with low porosity and a lack of permeable fluids. It is thus difficult to investigate and poses a high exploration risk. This paper emphasizes the role of seismic exploration in evaluating hot dry rock exploration by exploiting technical advantages, including strong penetration, high resolution and precise depth determination. Denoising and weak deep effective signal processing, unique processing methods (e.g. high-precision static correction, pre-stack noise attenuation, wide-angle reflection in weak signal areas and fine velocity analysis) are used for high-quality imaging of formations inside the hot dry rock geothermal reservoirs to address the difficulties of data static correction. The joint inversion/data fusion of seismic and other geophysical methods allow the realization of non-linear quantitative prediction and evaluation of hot dry rock reservoirs. The geothermal reservoir parameters, including lithology, physical properties and temperature, are predicted by integrating various geophysical attributes. Further, the development potential of the geothermal reservoir is accurately evaluated, and promising results achieved.

The Nile Delta, North Africa's leading gas-producing region, was the focus of this study aimed at delineating gas-bearing sandstone reservoirs from the Pleistocene to Pliocene formations using a combination of pre-stack inversion and rock physics analysis. This research employed seismic inversion techniques, including full-angle stack seismic volumes, well logs, and 3-D with rock physics modeling to refine volumes of P-wave velocity (Vp), S-wave velocity (Vs), and density. Traditional seismic attributes, such as far amplitude, proved insufficient for confirming gas presence, highlighting partial angle stacks, integrated the need for advanced methods. Extended Elastic Impedance (EEI) analysis was used to predict fluids and identify lithology in clastic reservoir environments. The EEI approach facilitated the determination of optimal projection angles for key petrophysical properties such as porosity, shale volume, and water saturation. This method was applied to the middle Pliocene (Kafr El Sheikh Formation) and the Pleistocene (El Wastani Formation), revealing promising drilling sites. In the Kafr El Sheikh Formation, porosity ranged from 16 to 29%, shale volume from 21 to 40%, and hydrocarbon saturation from 25 to 90%. The study concludes that integrating pre-stack seismic inversion with EEI significantly enhances the likelihood of identifying gas-bearing sands while reducing exploration risks. The improved POS for the Pleistocene anomaly gas bearing sand (from 49 to 69%) and the middle Pliocene anomaly (from 46 to 66%) underscores the effectiveness of this approach in the Baltim Field, Offshore Nile Delta, and supports further drilling and development wells.

Full Waveform Inversion (FWI) is a data-fitting method that allows retrieving the Earth properties from the observed pre-stack seismic data. FWI produces nearly perfect results when the input seismic data contains low-frequency components or when the initial model is very close to the actual model. However, as the FWI objective function is highly nonlinear and has many local minima, lack of recorded low frequencies might seriously harm the final FWI inversion result. We propose here to use the Normalized Integration method (NIM) for the determination of the background velocity model, later ref

Abstract One of the paramount parameters in the drilling industry is the determination of the safe drilling mud window. Incorrect specification of this parameter can lead to significant hazards such as blowouts, loss of personnel, and substantial costs. The primary objective of this study was to establish a safe mud window using pre-stack seismic inversion and wire-line logs, check shots, and geological data in one of the Southwestern Iran oil fields. Seismic inversion is based on the principle that any physical change in formation, such as porosity or fluid content, affects seismic wave properties. It is used for accurate pore pressure prediction before drilling commences for safe and efficient drilling operations. The pre-stack seismic inversion is conducted by constructing a velocity model and utilizing angle gather aggregation, statistical wavelet extraction, and initial model creation. Seismic inversion analysis revealed that the studied sandstone reservoir layer, known as the Ghar formation, possesses lower P-wave or S-wave acoustic impedance (P-/S-AI) and density compared to adjacent layers, likely due to the presence of porosity and potentially intra-formational fluids. Through seismic inversion and acquisition of AI and density, the pore pressure cube was estimated using a modified Bowers’ relationship. In modified Bowers’ relationship, constants and coefficients are modified based on the observed AI and pore pressure in the wells. The correlation between the estimat

In petroleum exploration and production, accurate reservoir characterization and seismic modeling depend on linking macroscale seismic data with microscale reservoir properties. Prior research has predominantly concentrated on forward modeling or inversion processes in isolation. As a result, a comprehensive multiscale framework that seamlessly integrates both approaches remains absent. In this study, to address this gap, a machine learning (ML)-based petrophysical inversion method was developed. This method was integrated into a unified multiscale workflow by combining rock physics modeling, seismic modeling, and seismic inversion techniques. This study was based on synthetic data. Initially, predefined reservoir petrophysical parameters were used as inputs to rock physics equations to forward model elastic parameters. Following this, seismic forward modeling was performed to generate seismic amplitude-versus-offset (AVO) data. Subsequently, seismic AVO inversion was carried out to recover elastic parameters from the AVO data, which were then converted into reservoir petrophysical parameters using ML techniques. As a result, forward modeling revealed that porosity (𝜙) significantly affects seismic AVO responses, whereas clay volume (C) and water saturation (Sw) had minimal impact. Conversely, seismic AVO inversion, constrained by wavelet effects and input uncertainties, produced a filtered and biased representation of elastic parameters. This compromised the accuracy of subsequent ML-based petrophysical inversion, particularly for Sw in oil reservoirs and C in gas reservoirs. Consequently, 𝜙 inversions demonstrated high reliability, whereas Sw and C predictions showed greater uncertainty. Therefore, by integrating petrophysics with ML, the proposed methodology effectively bridges micro-properties with macro-seismic signals, offering a precise and unified multiscale approach for quantitative seismic modeling and reservoir characterization. Furthermore, the present study capitalizes on rock-physics-generated data, providing ground truth and enabling rigorous, multiscale uncertainty analysis beyond the capabilities of isolated methods. Additionally, it can be seamlessly applied to real-field data. Finally, a comparative discussion between ML-based and physics-based methodologies was performed, leading to the recommendation of implementing explainable artificial intelligence (XAI) for improved interpretability and prediction performance.

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here, we introduce a computational framework, regularization by denoising using diffusion models for partial differential equations (RED-DiffEq), by integrating physics-driven inversion and data-driven learning. RED-DiffEq leverages pretrained diffusion models as a regularization mechanism for PDE-governed inverse problems. We apply RED-DiffEq to solve the full waveform inversion problem in geophysics, a challenging seismic imaging technique that seeks to reconstruct high-resolution subsurface velocity models from seismic measurement data. Our method shows enhanced accuracy and robustness compared to benchmark methods. Additionally, it exhibits strong generalization and domain decomposition capacity, enabling the inversion of more complex velocity models with larger domains than those used in training the diffusion model. Our framework can also be directly applied to diverse PDE-governed inverse problems.

The aim of seismic inversion is to determine the distribution of elastic parameters from recorded seismic reflection data. If a combination of elastic parameters is known, they indicate a certain fluid or lithology. Elastic parameters can therefore be very good hydrocarbon indicators. Although it is possible to interpret the reflection data from seismic acquisitions after processing, an improved analysis can be achieved by inverting for elastic properties. This can contribute to improved vertical resolution of the image. This work applies different applications of the blocky seismic inversion

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine- or Lunar Prospector-derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explored the density/velocity relationship. These efforts typically searched for the best fitting thermodynamically calculated velocity/density model, and allowed variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles derived from the Apollo seismic data through travel time inversion vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Seismic surface waves can be measured by deploying an array of seismometers on the surface of the earth. The goal of such measurement surveys is, usually, to estimate the velocity of propagation and the direction of arrival of the seismic waves. In this paper, we address the issue of sensor placement for the analysis of seismic surface waves from ambient vibration wavefields. First, we explain in detail how the array geometry affects the mean-squared estimation error (MSEE) of parameters of interest, such as the velocity and direction of propagation, both at low and high signal-to-noise ratios

Velocity-model building is the first task of seismic inversion and the foundation of the subsequent data-processing workflow. When the earth velocity becomes multivalued with respect to the propagating direction of the waves, velocity-model building becomes severely underdetermined and nonunique. The traditional workflow separates velocity-model building from lithologic inversion, which hampers both processing steps. An integrated model-building scheme is demonstrated to simultaneously consider prestack seismic data and its structural and lithologic inversion results from a previous iteration.

Seismic velocity structure is the distribution and variation of seismic wave speeds within Earth's and other planetary bodies' subsurface. It is reflective Seismic velocity structure is the distribution and variation of seismic wave speeds within Earth's and other planetary bodies' subsurface. It is reflective of subsurface properties such as material composition, density, porosity, and temperature. Geophysicists rely on the analysis and interpretation of the velocity structure to develop refined models of the subsurface geology, which are essential Seismic velocity structure is the distribution and variation of seismic wave speeds within Earth's and other planetary bodies' subsurface. It is reflective of subsurface properties such as material composition, density, porosity, and temperature. Geophysicists rely on the analysis and interpretation of the velocity structure to develop refined models of the subsurface geology, which are essential in resource exploration, earthquake seismology, and advancing our understanding of Earth's geological development. Isotropic assumptions Seismic velocity studies often assume isotropy, treating Earth's subsurface as having uniform properties in all directions. This simplification is practical for analysis but may not be accurate. The inner core and mantle, for example, likely demonstrate anisotropic, or directionally dependent, properties, which can affect the accuracy of seismic interpretations. Dimensional considerations Seismic models are frequently one-dimensional, considering changes in Earth's properties with depth but neglecting lateral variations. Although this method eases computation, it fails to account for the planet's complex three-dimensional structure, potentially misleading our understanding of subsurface characteristics. Non-uniqueness of Inverse Modelling Seismic velocity structures are inferred through inverse modeling, fitting theoretical models to observed data. However, different models can often explain the same data, leading to non-unique solutions. This issue is compounded when inverse problems are poorly conditioned, where small data variations can suggest drastically different subsurface structures.

Seismic anisotropy is the directional dependence of the velocity of seismic waves in a medium (rock) within the Earth. A material is said to be anisotropic Seismic anisotropy is the directional dependence of the velocity of seismic waves in a medium (rock) within the Earth. Seismic anisotropy is the directional dependence of the velocity of seismic waves in a medium (rock) within the Earth.