**1. Introduction**

Wave-induced fluid flow (WIFF) is considered to be the main cause of seismic wave dispersion and attenuation in fluid-saturated porous media [1,2]. Among many theories, mesoscopic heterogeneity and microscopic heterogeneity are considered to be the main mechanisms leading to WIFF. In addition, in most rocks, the coexistence of mesoscopic heterogeneity and microscopic heterogeneity can cause a significant shift in fast p-wave velocity, which means that the effects of both mechanisms on dispersion and attenuation need to be considered simultaneously. The Squirt microscopic model mainly uses the squirt mechanism of solid/fluid interaction to estimate velocity dispersion and attenuation in fully saturated rocks [3]. Pride et al. proposed the two-pore theory to explain the corresponding seismic waves in water-bearing and gas-saturated porous media, which can explain the attenuation of magnitude 10−<sup>2</sup> – 10−<sup>1</sup> within the seismic frequency band. White's model describes the complex moduli of a partially saturated spherical gas encapsulated medium and a layered medium composed of two heterogeneous porous media [4,5]. Johnson generalized gas patches of arbitrary shape [6]. In recent years, under the condition of saturated fluid and bubble phase in rock, it is believed that an obvious attenuation phenomenon will occur at the low-frequency end of an earthquake, resulting in the corresponding mechanism of gas dissolution and dissolution induced by seismic wave (pore fluid dissolution). The dissolution of wave-induced gas exsolution–dissolution is used to explain the obvious attenuation phenomenon of seismic waves [7–9], and these models reflect the meso-loss mechanism. Chapman measured the attenuation of two Berea sandstone samples, and the results show that compared with the WIFF mechanism, the pore fluid dissolution mechanism can be closer to the measured attenuation data [10]. Moreover, as a seismic wave attenuation mechanism, pore fluid dissolution can describe micron pores. It is more suitable for shale reservoirs with low porosity and low permeability.

**Citation:** Jin, Z.; Zheng, X.; Shi, Y.; Wang, W. Study on Seismic Attenuation Based on Wave-Induced Pore Fluid Dissolution and Its Application. *Appl. Sci.* **2023**, *13*, 74. https://doi.org/10.3390/ app13010074

Academic Editor: Francesco Clementi

Received: 30 November 2022 Revised: 7 December 2022 Accepted: 17 December 2022 Published: 21 December 2022

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Well logging data and seismic data are the two most basic forms of raw data in the process of oilfield exploration and development, and they play an important role in detailed reservoir description, including reservoir prediction. The reflected reservoir information is inconsistent, resulting in multiple solutions for reservoir prediction and description. Determining how to perform well-to-seismic matching has become an indispensable and important part of predicting reservoir lithology, physical parameters and oil potential in oil and gas exploration and development research. There are three main methods for velocity matching and calibration of well-to-seismic data:


In practical application, the Backus effective averaging method is simple and effective but does not consider the attenuation effect. Multiresolution analysis is highly automated but still requires accurate synthetic seismic record and stratigraphic correlation. The rock physical model calibration method can directly match data of different scales. In order to combine well logging and seismic data, it is necessary to select an appropriate rock physical model for dispersion calibration, thereby improving the accuracy of well–seismic matching.

Because the parameters of a rock physical model are large, difficult to obtain and have no actual physical significance, it is better to use a viscoelastic model instead of a rock physical model. The Zener model can fit the mesoscale White model [17], the Biot–Rayleigh model [18] and the dispersion and attenuation at two scales (meso and micro) [19]. Some researchers feel that the Cole–Cole model can more accurately simulate the acoustic properties of porous media than the rough approximation of Zener's mechanical model [20,21], but there are five parameters, which is relatively more, while the Power Law model only needs two parameters [22], which makes it easier to use. Ref. [10] studied the seismic attenuation in Berea sandstone saturated with bidirectional fluid, compared the attenuation curves of the WIFF model and the pore fluid dissolution model under different saturation and pressure, and used SLS model to fit, and they found that the fitting effect with pore fluid dissolution is very good. Some scholars also compared multiple viscoelastic models. Paul compared the attenuation and frequency relationship curves of Maxwell Model, Voight Solid, Standard Linear, Burgers Solid and Power Law. It was found that attenuation and elastic stiffness curves vary considerably with frequency, and each model has a different variation law [23]. Toverud et al. compared eight models using the zero-offset vertical seismic profile (VSP) dataset: the Kolsky–Futterman model, Power Law model, Kjartansson model, Muller model, Azimi second model, Azimi third model, Cole–Cole model and standard linear-solid-state model (SLS). It was found that in the same depth region, the SLS model has the best results in simulating attenuation [24].
