The nomaal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-dep...The nomaal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-depth ratio and thus fails at large offset-to-depth ratios. We approximate the long-offset moveout using the Pade approximation. This method is superior to typical methods and flattens the seismic gathers over a wide range of offsets in multilayered media. For a four-layer model, traditional methods show traveltime errors of about 5 ms for offset-to-depth ratio of 2 and greater than 10 ms for offset-to-depth ratio of 3; in contrast, the maximum traveltime error for the [3, 3]-order Pade approximation is no more than 5 ms at offset-to-depth ratio of 3. For the Cooper Basin model, the maximum oft＇set-to-depth ratio for the [3, 3]-order Pade approximation is typically double of those in typical methods. The [7, 7]-order Pade approximation performs better than the [3.3]-order Pade armroximation.展开更多
The conventional long-offset nonhyperbolic moveout equation is derived for the transverse isotropic media with a vertical symmetric axis（VTI）.It cannot be extended to the transverse isotropic media with an arbitrary...The conventional long-offset nonhyperbolic moveout equation is derived for the transverse isotropic media with a vertical symmetric axis（VTI）.It cannot be extended to the transverse isotropic media with an arbitrary spatial orientation of symmetry axis（ATI）.In this paper,we optimize a modified long-offset nonhyperbolic moveout equation for ATI media based on the conventional nonhyperbolic moveout equation and the exact analytical solution of the quartic moveout coefficient（A_4） and NMO velocity for ATI media that were derived in our previous work.Compared with the exact traveltimes of the ray-tracing algorithm for anisotropic media,this optimized equation can be used to calculate the traveltime varying with survey line azimuth in arbitrary strong or weak ATI media.It can replace the time-consuming, multi-offset,and multi-azimuth ray tracing method for forward modeling of long-offset reflection traveltimes in ATI media,which is useful to further anisotropic parameter inversion using long-offset nonhyperbolic moveout.展开更多
The forward modeling procedure used in this article is formulated with the volume integral equation based on the tensor Green＇s function. The electromagnetic components responses are first calculated in the frequency...The forward modeling procedure used in this article is formulated with the volume integral equation based on the tensor Green＇s function. The electromagnetic components responses are first calculated in the frequency domain and then transformed to the time domain by digital filtering. The valley and hill topography with a layered earth is stimulated by a horizontal electric dipole （HED） transmitter, which is common in field surveys, and the TEM responses are calculated at the transmitter and receivers. The topography effects on the long offset electromagnetic transient （LOTEM） responses are discussed in detail. The results show that both valley and hill topography has significant effect on the LOTEM measurement. If the HED is located in the bottom of a valley, the distortion of the observed anomalous field at distance is severe. A valley at the receiver locations show a strong effect but are localized in space and time. In general, hill-shaped topography shows smaller effects no matter where its located. When the topography is located between source and receivers, the influence is negligible. We conclude that the location of the source is much more important than the receivers and it is critical to put the transmitter in an open flat area in the field survey.展开更多
基金supported by the National Natural Science Foundation of China(Nos.41130418 and 41374061)the National Major Project of China(No.2011ZX05008-006)and the Youth Innovation Promotion Association CAS(No.2012054)
文摘The nomaal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-depth ratio and thus fails at large offset-to-depth ratios. We approximate the long-offset moveout using the Pade approximation. This method is superior to typical methods and flattens the seismic gathers over a wide range of offsets in multilayered media. For a four-layer model, traditional methods show traveltime errors of about 5 ms for offset-to-depth ratio of 2 and greater than 10 ms for offset-to-depth ratio of 3; in contrast, the maximum traveltime error for the [3, 3]-order Pade approximation is no more than 5 ms at offset-to-depth ratio of 3. For the Cooper Basin model, the maximum oft＇set-to-depth ratio for the [3, 3]-order Pade approximation is typically double of those in typical methods. The [7, 7]-order Pade approximation performs better than the [3.3]-order Pade armroximation.
基金the National Natural Science Foundation of China(Grant No.40874028)the Special Fund (Grant No.2008ZX05008-006-004).
文摘The conventional long-offset nonhyperbolic moveout equation is derived for the transverse isotropic media with a vertical symmetric axis（VTI）.It cannot be extended to the transverse isotropic media with an arbitrary spatial orientation of symmetry axis（ATI）.In this paper,we optimize a modified long-offset nonhyperbolic moveout equation for ATI media based on the conventional nonhyperbolic moveout equation and the exact analytical solution of the quartic moveout coefficient（A_4） and NMO velocity for ATI media that were derived in our previous work.Compared with the exact traveltimes of the ray-tracing algorithm for anisotropic media,this optimized equation can be used to calculate the traveltime varying with survey line azimuth in arbitrary strong or weak ATI media.It can replace the time-consuming, multi-offset,and multi-azimuth ray tracing method for forward modeling of long-offset reflection traveltimes in ATI media,which is useful to further anisotropic parameter inversion using long-offset nonhyperbolic moveout.
基金supported by National Natural Science Foundation of China (Nos. 40727001, 40774073, and 40774074)the National Basic Research Programs of China (973 Program) (No. 2007CB209607)the Doctoral Program of Higher Research and Special funds (No. 20070489001)
文摘The forward modeling procedure used in this article is formulated with the volume integral equation based on the tensor Green＇s function. The electromagnetic components responses are first calculated in the frequency domain and then transformed to the time domain by digital filtering. The valley and hill topography with a layered earth is stimulated by a horizontal electric dipole （HED） transmitter, which is common in field surveys, and the TEM responses are calculated at the transmitter and receivers. The topography effects on the long offset electromagnetic transient （LOTEM） responses are discussed in detail. The results show that both valley and hill topography has significant effect on the LOTEM measurement. If the HED is located in the bottom of a valley, the distortion of the observed anomalous field at distance is severe. A valley at the receiver locations show a strong effect but are localized in space and time. In general, hill-shaped topography shows smaller effects no matter where its located. When the topography is located between source and receivers, the influence is negligible. We conclude that the location of the source is much more important than the receivers and it is critical to put the transmitter in an open flat area in the field survey.
