### Abstract

The seismoacoustic scattering due to an irregular fluid-solid interface (i.e. the ocean bottom) must be considered when modelling seismic wave propagation in oceanic regions. In this paper, we present an accurate method to treat this problem. The method is an extension of the reflection/transmission matrix approach that was developed to model scattering due to an irregular interface between two elastic solids. This approach uses the discrete wavenumber representation of the wavefield and the Rayleigh ansatz; the wavefield is decomposed into a set of plane waves, and we assume that the scattered wavefield due to an incident plane wave can be expanded in terms of only the waves moving away from the interface. The plane waves at both sides of the interface are then connected to each other based on this hypothesis and proper boundary conditions. The elements of the reflection/transmission matrices describe these connection coefficients. As the fluid-solid interface, the direct application of the above method is difficult because the tangential displacement at the interface is not necessarily continuous. To avoid this problem, we use pressure as the variable inside the fluid layer. The reflection/transmission matrices between the pressure wave (i.e. the acoustic wave) and the elastic waves are then developed by using the standard boundary conditions at the fluid-solid interface (i.e. normal stress continuity, zero tangential stress, and normal displacement continuity) and the Rayleigh ansatz. To demonstrate the validity and feasibility of our method, we compare the results of our method with those of other methods. First, we examine the reflection of plane elastic waves by a periodic sinusoidal interface for a single frequency. The interface profile is characterized by its periodicity or wavelength (D) and peak to trough height (h). The behaviour of the reflection calculated by our method shows almost complete agreement with that calculated by a boundary element method (BEM) up to a relatively steep interface whose height to wavelength ratio (h/D) is 0.5. Second, we calculate the synthetic time domain waveforms for a plane vertically incident P wave into basin-like fluid layers. We compare the waveforms calculated by the present method with those calculated by the finite difference method (FDM). In general, the waveforms calculated by the two methods match well. A quantitative study shows that the degree of agreement indicated by the RMS residuals between the waveforms of the two methods becomes better when we use a smaller grid interval in the FDM calculation. For the models treated here, the cases of 30 grid-points per wavelength results in RMS residuals less than about 10-15 per cent. This grid interval is smaller than that usually applied (more than 5-10 grid-points per wavelength). Since, in general, the accuracy of the FDM calculation becomes better as the grid interval decreases, these results indicate the validity of the present method.

Original language | English |
---|---|

Pages (from-to) | 531-546 |

Number of pages | 16 |

Journal | Geophysical Journal International |

Volume | 139 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Finite difference methods
- Layered media
- Ocean bottom seismology
- Scattering
- Seismoacoustic problems
- Synthetic waveforms

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics

### Cite this

**A reflection/transmission matrix formulation for seismoacoustic scattering by an irregular fluid-solid interface.** / Okamoto, Taro; Takenaka, Hiroshi.

Research output: Contribution to journal › Article

*Geophysical Journal International*, vol. 139, no. 2, pp. 531-546. https://doi.org/10.1046/j.1365-246X.1999.00959.x

}

TY - JOUR

T1 - A reflection/transmission matrix formulation for seismoacoustic scattering by an irregular fluid-solid interface

AU - Okamoto, Taro

AU - Takenaka, Hiroshi

PY - 1999

Y1 - 1999

N2 - The seismoacoustic scattering due to an irregular fluid-solid interface (i.e. the ocean bottom) must be considered when modelling seismic wave propagation in oceanic regions. In this paper, we present an accurate method to treat this problem. The method is an extension of the reflection/transmission matrix approach that was developed to model scattering due to an irregular interface between two elastic solids. This approach uses the discrete wavenumber representation of the wavefield and the Rayleigh ansatz; the wavefield is decomposed into a set of plane waves, and we assume that the scattered wavefield due to an incident plane wave can be expanded in terms of only the waves moving away from the interface. The plane waves at both sides of the interface are then connected to each other based on this hypothesis and proper boundary conditions. The elements of the reflection/transmission matrices describe these connection coefficients. As the fluid-solid interface, the direct application of the above method is difficult because the tangential displacement at the interface is not necessarily continuous. To avoid this problem, we use pressure as the variable inside the fluid layer. The reflection/transmission matrices between the pressure wave (i.e. the acoustic wave) and the elastic waves are then developed by using the standard boundary conditions at the fluid-solid interface (i.e. normal stress continuity, zero tangential stress, and normal displacement continuity) and the Rayleigh ansatz. To demonstrate the validity and feasibility of our method, we compare the results of our method with those of other methods. First, we examine the reflection of plane elastic waves by a periodic sinusoidal interface for a single frequency. The interface profile is characterized by its periodicity or wavelength (D) and peak to trough height (h). The behaviour of the reflection calculated by our method shows almost complete agreement with that calculated by a boundary element method (BEM) up to a relatively steep interface whose height to wavelength ratio (h/D) is 0.5. Second, we calculate the synthetic time domain waveforms for a plane vertically incident P wave into basin-like fluid layers. We compare the waveforms calculated by the present method with those calculated by the finite difference method (FDM). In general, the waveforms calculated by the two methods match well. A quantitative study shows that the degree of agreement indicated by the RMS residuals between the waveforms of the two methods becomes better when we use a smaller grid interval in the FDM calculation. For the models treated here, the cases of 30 grid-points per wavelength results in RMS residuals less than about 10-15 per cent. This grid interval is smaller than that usually applied (more than 5-10 grid-points per wavelength). Since, in general, the accuracy of the FDM calculation becomes better as the grid interval decreases, these results indicate the validity of the present method.

AB - The seismoacoustic scattering due to an irregular fluid-solid interface (i.e. the ocean bottom) must be considered when modelling seismic wave propagation in oceanic regions. In this paper, we present an accurate method to treat this problem. The method is an extension of the reflection/transmission matrix approach that was developed to model scattering due to an irregular interface between two elastic solids. This approach uses the discrete wavenumber representation of the wavefield and the Rayleigh ansatz; the wavefield is decomposed into a set of plane waves, and we assume that the scattered wavefield due to an incident plane wave can be expanded in terms of only the waves moving away from the interface. The plane waves at both sides of the interface are then connected to each other based on this hypothesis and proper boundary conditions. The elements of the reflection/transmission matrices describe these connection coefficients. As the fluid-solid interface, the direct application of the above method is difficult because the tangential displacement at the interface is not necessarily continuous. To avoid this problem, we use pressure as the variable inside the fluid layer. The reflection/transmission matrices between the pressure wave (i.e. the acoustic wave) and the elastic waves are then developed by using the standard boundary conditions at the fluid-solid interface (i.e. normal stress continuity, zero tangential stress, and normal displacement continuity) and the Rayleigh ansatz. To demonstrate the validity and feasibility of our method, we compare the results of our method with those of other methods. First, we examine the reflection of plane elastic waves by a periodic sinusoidal interface for a single frequency. The interface profile is characterized by its periodicity or wavelength (D) and peak to trough height (h). The behaviour of the reflection calculated by our method shows almost complete agreement with that calculated by a boundary element method (BEM) up to a relatively steep interface whose height to wavelength ratio (h/D) is 0.5. Second, we calculate the synthetic time domain waveforms for a plane vertically incident P wave into basin-like fluid layers. We compare the waveforms calculated by the present method with those calculated by the finite difference method (FDM). In general, the waveforms calculated by the two methods match well. A quantitative study shows that the degree of agreement indicated by the RMS residuals between the waveforms of the two methods becomes better when we use a smaller grid interval in the FDM calculation. For the models treated here, the cases of 30 grid-points per wavelength results in RMS residuals less than about 10-15 per cent. This grid interval is smaller than that usually applied (more than 5-10 grid-points per wavelength). Since, in general, the accuracy of the FDM calculation becomes better as the grid interval decreases, these results indicate the validity of the present method.

KW - Finite difference methods

KW - Layered media

KW - Ocean bottom seismology

KW - Scattering

KW - Seismoacoustic problems

KW - Synthetic waveforms

UR - http://www.scopus.com/inward/record.url?scp=0033385584&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033385584&partnerID=8YFLogxK

U2 - 10.1046/j.1365-246X.1999.00959.x

DO - 10.1046/j.1365-246X.1999.00959.x

M3 - Article

AN - SCOPUS:0033385584

VL - 139

SP - 531

EP - 546

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 2

ER -