1. A theoretical-computational model for studying Love wave propagation comprising: a heterogeneous viscoporoelastic layer (101) with depth-dependent parameters of density, rigidity, viscosity, and porosity; a viscoporoelastic half-space (102) underlying said layer; constitutive relations (103) incorporating viscoporoelastic coupling between pore fluid and solid matrix; governing equations of motion (104) derived for horizontally polarized shear waves; and boundary and continuity conditions (105) applied at the free surface and the layer–half-space interface to obtain dispersion relations.

2. A method for analyzing Love wave propagation in a heterogeneous viscoporoelastic medium, comprising: defining depth-dependent material parameters for the heterogeneous viscoporoelastic layer (101); modeling the viscoporoelastic half-space (102) as a continuum; applying constitutive relations (103) to incorporate viscous damping and poroelastic coupling; deriving governing equations of motion (104) for Love waves; and solving dispersion relations to determine phase velocity, attenuation, and dispersion characteristics.

3. The model as claimed in Claim 1, wherein heterogeneity, viscosity, and porosity parameters are jointly analyzed in a parametric sensitivity framework.

4. The method as claimed in Claim 2, wherein attenuation properties are derived by incorporating viscous dissipation terms in the governing equations.

5. The model as claimed in Claim 1, wherein poroelastic coupling accounts for fluid–solid interactions in subsurface porous structures.

6. The method as claimed in Claim 2, wherein dispersion relations are solved numerically to predict phase velocity variations under complex subsurface conditions.

7. The model as claimed in Claim 1, wherein the framework improves precision compared to homogeneous elastic or viscoelastic models.

8. The method as claimed in Claim 2, wherein boundary conditions (105) are applied at both the free surface and the interface between the heterogeneous layer and the half-space.

9. The model as claimed in Claim 1, wherein the formulation is capable of predicting seismic wave behavior in earthquake hazard analysis.

Description:FIELD OF THE INVENTION
The present invention discloses a theoretical-computational model for studying Love wave propagation in a heterogeneous viscoporoelastic layer (101) overlying a viscoporoelastic half-space (102).
BACKGROUND OF THE INVENTION
Love waves are horizontally polarized shear surface waves which travel horizontally through stratified geological formations and which get strongly affected by changes in material properties including density, rigidity, viscosity, porosity, and heterogeneity. In practical subsurface situations, the large scale properties of the upper part of the subsurface are those of a heterogeneous viscoporoelastic medium, but the lower region is composed of a viscoporoelastic half-space. This set of complicated physical features is very important to the dispersion, attenuation and the transmission of the waves. Majority of the investigations made however, presuppose simplified homogeneous elastic or viscoelastic layers, commonly ignoring the joint effect of heterogeneity, viscous damping and pore fluid solid interaction that decreases the precision of seismic interpretation and geotechnical evaluations.
As such, a more detailed study of the Love wave propagation in a heterogeneous viscoporoelastic layer over a viscoporoelastic half-space is necessary to determine a detailed theoretical and mathematical system. The model considered should include spatial variation of material parameters, viscous dissipation and poroelastic coupling and study their impacts on dispersion relations, phase velocity, and attenuation properties. The objective of the current research is to get the governing equations and dispersion relation of this complex medium and to determine the effects of parameter heterogeneity, viscosity and porosity on the behavior of Love waves, hence relevant to better seismology, earthquake related engineering, and characterization of subsurface materials.
SUMMARY OF THE INVENTION
This summary is provided to introduce a selection of concepts, in a simplified format, that are further described in the detailed description of the invention.
This summary is neither intended to identify key or essential inventive concepts of the invention and nor is it intended for determining the scope of the invention.
The proposed invention is connected with the theoretical-computational model of studying the Love waves propagation in a heterogeneous viscoporoelastic layer on the viscoporoelastic half-space. The invention presents a single mathematical model that combines simultaneously the material heterogeneity, viscous damping, and the interaction between fluids and solids via porous structures, which usually exist in the actual geological structures but are poorly modeled in the current models. The top is represented by viscoporoelastic depth-dependent parameters and the bottom half-space is a viscoporoelastic continuum. Constitutive relations Viscoporoelastic relations governing equations of motion are developed and suitable boundary and continuity conditions are placed at the free surface and the layer-half-space interface.
To further clarify advantages and features of the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof, which is illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope. The invention will be described and explained with additional specificity and detail with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
The illustrated embodiments of the subject matter will be understood by reference to the drawings, wherein like parts are designated by like numerals throughout. The following description is intended only by way of example, and simply illustrates certain selected embodiments of devices, systems, and methods that are consistent with the subject matter as claimed herein, wherein:
FIGURE 1: SYSTEM ARCHITECTURE
The figures depict embodiments of the present subject matter for the purposes of illustration only. A person skilled in the art will easily recognize from the following description that alternative embodiments of the structures and methods illustrated herein may be employed without departing from the principles of the disclosure described herein.
DETAILED DESCRIPTION OF THE INVENTION
The detailed description of various exemplary embodiments of the disclosure is described herein with reference to the accompanying drawings. It should be noted that the embodiments are described herein in such details as to clearly communicate the disclosure. However, the amount of details provided herein is not intended to limit the anticipated variations of embodiments; on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the present disclosure as defined by the appended claims.
It is also to be understood that various arrangements may be devised that, although not explicitly described or shown herein, embody the principles of the present disclosure. Moreover, all statements herein reciting principles, aspects, and embodiments of the present disclosure, as well as specific examples, are intended to encompass equivalents thereof.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms “a",” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes” and/or “including,” when used herein, specify the presence of stated features, integers, steps, operations, elements and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and/or groups thereof.
It should also be noted that in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may, in fact, be executed concurrently or may sometimes be executed in the reverse order, depending upon the functionality/acts involved.
In addition, the descriptions of "first", "second", “third”, and the like in the present invention are used for the purpose of description only, and are not to be construed as indicating or implying their relative importance or implicitly indicating the number of technical features indicated. Thus, features defining "first" and "second" may include at least one of the features, either explicitly or implicitly.
Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which example embodiments belong. It will be further understood that terms, e.g., those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The present invention relates to a unified theoretical-computational framework for analyzing Love wave propagation in complex geological media. The system comprises a heterogeneous viscoporoelastic layer (101) characterized by depth-dependent variations in density, rigidity, viscosity, and porosity, overlying a viscoporoelastic half-space (102) modeled as a continuum. Unlike conventional homogeneous elastic or viscoelastic models, the invention integrates constitutive relations (103) that capture viscous damping and fluid–solid interactions through poroelastic coupling.
The framework derives governing equations of motion (104) for horizontally polarized shear waves, incorporating heterogeneity, viscosity, and porosity simultaneously. Appropriate boundary and continuity conditions (105) are applied at the free surface and the interface between the heterogeneous layer and the half-space. This enables the derivation of new dispersion relations that predict phase velocity, attenuation, and dispersion behavior under realistic subsurface conditions.
The invention provides a parametric analysis capability to evaluate the influence of individual physical parameters—heterogeneity, viscosity, and porosity—on Love wave behavior. Numerical solutions of the dispersion relations allow accurate prediction of seismic wave propagation, attenuation, and velocity changes. The model is applicable to seismology, earthquake-resistant engineering, geotechnical evaluations, underground exploration, and subsurface material characterization.
By combining heterogeneity, viscous dissipation, and poroelastic coupling into a single analytical framework, the invention advances the precision of seismic interpretation beyond traditional homogeneous models.
The present invention discloses a theoretical-computational model for studying Love wave propagation in a heterogeneous viscoporoelastic layer (101) overlying a viscoporoelastic half-space (102). The model integrates depth-dependent heterogeneity, viscous damping, and poroelastic fluid–solid coupling through constitutive relations (103) and governing equations of motion (104). Boundary and continuity conditions (105) are applied at the free surface and the layer–half-space interface to derive dispersion relations. The framework predicts phase velocity, attenuation, and dispersion characteristics under complex subsurface conditions. Experimental analysis demonstrates improved accuracy compared to homogeneous elastic or viscoelastic models. The invention provides a robust analytical tool for seismology, earthquake engineering, geotechnical analysis, and subsurface material characterization.
The proposed invention is connected with the theoretical-computational model of studying the Love waves propagation in a heterogeneous viscoporoelastic layer on the viscoporoelastic half-space. The invention presents a single mathematical model that combines simultaneously the material heterogeneity, viscous damping, and the interaction between fluids and solids via porous structures, which usually exist in the actual geological structures but are poorly modeled in the current models. The top is represented by viscoporoelastic depth-dependent parameters and the bottom half-space is a viscoporoelastic continuum. Constitutive relations Viscoporoelastic relations governing equations of motion are developed and suitable boundary and continuity conditions are placed at the free surface and the layer-half-space interface.
The invention also gives a new dispersion formulation that can adequately predict phase velocity, dispersion, and attenuation characteristics of Love waves based on different parameters of heterogeneity, viscosity, and porosity. Structural parametric analysis can be used to calculate the impact of individual physical parameters on the behavior of waves using the framework. It can be applied as an analytic device or a numerical algorithm to seismology, earthquake-resistant design, geotechnical engineering, underground exploration, and material characterization where it can be more accurate than the traditional elastic and homogeneous propagation models of waves.
The proposed invention introduces a unified analytical framework that significantly improves the precision of seismic wave modeling compared to conventional homogeneous elastic or viscoelastic approaches. By simultaneously incorporating material heterogeneity, viscous damping, and poroelastic fluid–solid interactions, the model captures realistic subsurface conditions that are often neglected in prior studies.
1. Enhanced Accuracy in Seismic Interpretation
o The model accounts for depth-dependent variations in density, rigidity, viscosity, and porosity, enabling more reliable predictions of phase velocity, attenuation, and dispersion.
o This leads to improved seismic hazard analysis and earthquake-resistant design.
2. Integration of Poroelastic Coupling
o Unlike traditional models, the invention explicitly incorporates fluid–solid interactions in porous geological structures, providing a more complete representation of subsurface mechanics.
o This enhances the applicability of the framework to groundwater studies and subsurface material characterization.
3. Improved Dispersion Relations
o The derived dispersion formulation offers greater analytical accuracy in predicting Love wave behavior under complex geological conditions.
o Sensitivity analysis allows researchers to isolate the effects of heterogeneity, viscosity, and porosity, supporting targeted engineering applications.
4. Broader Applicability
o The framework can be applied to seismology, geotechnical engineering, underground exploration, and earthquake hazard analysis, making it versatile across multiple domains.
o It provides a computational tool that can be used both analytically and numerically, ensuring adaptability to different research and industrial needs.
5. Practical Utility
• By combining multiple physical effects into a single model, the invention reduces reliance on oversimplified assumptions, thereby increasing the reliability of seismic evaluations in real-world scenarios.
The suggested analytical model is an in-depth study of the propagation of Love wave in a heterogeneous viscoporoelastic surface layer over a viscoporoelastic half-space where the interplay between material heterogeneity, viscous damping, and pore fluid-solid interaction are combined in a single theoretical model. As opposed to the usual homogeneous elastic or viscoelastic material studies, where other parameters are usually neglected, the current methodology takes into consideration depth-related material characteristics, poroelastic interactions, and dissipation processes, which also results in a derivation of the altered governing equations and an improved dispersion relation that can be capable of precisely determining the phase velocity change, attenuation, and dispersion behaviour under complicated subsurface environments. The research is unique in assessing the heterogeneity, viscosity, and porosity parameters jointly in a parametric and sensitivity analysis, which is not yet thoroughly presented in the literature, thus providing greater analytical accuracy and practicality in the use of these parameters in seismology, earthquake hazard analysis, geotechnical, and characterization of materials used in the subsurface.
 
, Claims:1. A theoretical-computational model for studying Love wave propagation comprising:
a heterogeneous viscoporoelastic layer (101) with depth-dependent parameters of density, rigidity, viscosity, and porosity;
a viscoporoelastic half-space (102) underlying said layer;
constitutive relations (103) incorporating viscoporoelastic coupling between pore fluid and solid matrix;
governing equations of motion (104) derived for horizontally polarized shear waves; and
boundary and continuity conditions (105) applied at the free surface and the layer–half-space interface to obtain dispersion relations.
2. A method for analyzing Love wave propagation in a heterogeneous viscoporoelastic medium, comprising: defining depth-dependent material parameters for the heterogeneous viscoporoelastic layer (101); modeling the viscoporoelastic half-space (102) as a continuum; applying constitutive relations (103) to incorporate viscous damping and poroelastic coupling; deriving governing equations of motion (104) for Love waves; and solving dispersion relations to determine phase velocity, attenuation, and dispersion characteristics.
3. The model as claimed in Claim 1, wherein heterogeneity, viscosity, and porosity parameters are jointly analyzed in a parametric sensitivity framework.
4. The method as claimed in Claim 2, wherein attenuation properties are derived by incorporating viscous dissipation terms in the governing equations.
5. The model as claimed in Claim 1, wherein poroelastic coupling accounts for fluid–solid interactions in subsurface porous structures.
6. The method as claimed in Claim 2, wherein dispersion relations are solved numerically to predict phase velocity variations under complex subsurface conditions.
7. The model as claimed in Claim 1, wherein the framework improves precision compared to homogeneous elastic or viscoelastic models.
8. The method as claimed in Claim 2, wherein boundary conditions (105) are applied at both the free surface and the interface between the heterogeneous layer and the half-space.
9. The model as claimed in Claim 1, wherein the formulation is capable of predicting seismic wave behavior in earthquake hazard analysis.